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  • 1
    Publication Date: 2014-02-26
    Description: The paper's main result is a simple derivation rule for the Jacobi polynomials with respect to their parameters, i.e. for $\partial_{\alpha} P_n^{\alpha,\beta}$, and $\partial_{\beta} P_n^{\alpha,\beta}$. It is obtained via relations for the Gaussian hypergeometric function concerning parameter derivatives and integer shifts in the first two arguments. These have an interest on their own for further applications to continuous and discrete orthogonal polynomials. The study is motivated by a Galerkin method with moving weight, presents all proofs in detail, and terminates in a brief discussion of the generated polynomials.
    Keywords: ddc:000
    Language: English
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  • 2
    Publication Date: 2014-02-26
    Description: We derive a simple accuracy matching strategy for inexact Gauss Newton methods and apply it to the numerical solution of boundary value problems of ordinary differential equations by collocation. The matching strategy is based on an affine contravariant convergence theorem, i. e. , the characteristic constants are invariant under affine transformations of the domain. The inexact Gauss Newton method is applied to an integral formulation of the BVP. As discretization for the arising linear subproblems we employ adaptive collocation at Gaussian nodes with varying local orders and stepsizes. The grids are chosen via adaptive refinement and order selection.
    Keywords: ddc:000
    Language: English
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  • 3
    Publication Date: 2015-06-01
    Description: In this article we present a method to implement orthogonal polynomials and many other special functions in Computer Algebra systems enabling the user to work with those functions appropriately, and in particular to verify different types of identities for those functions. Some of these identities like differential equations, power series representations, and hypergeometric representations can even dealt with algorithmically, i.\ e.\ they can be computed by the Computer Algebra system, rather than only verified. The types of functions that can be treated by the given technique cover the generalized hypergeometric functions, and therefore most of the special functions that can be found in mathematical dictionaries. The types of identities for which we present verification algorithms cover differential equations, power series representations, identities of the Rodrigues type, hypergeometric representations, and algorithms containing symbolic sums. The current implementations of special functions in existing Computer Algebra systems do not meet these high standards as we shall show in examples. They should be modified, and we show results of our implementations.
    Keywords: ddc:000
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  • 4
    Publication Date: 2014-02-26
    Description: {\newcommand{\R} {{\rm {\mbox{\protect\makebox[.15em][l]{I}R}}}} Given a list of $n$ numbers in $\R $, one wants to decide wether every number in the list occurs at least $k$ times. I will show that $(1-\epsilon)n\log_3(n/k)$ is a lower bound for the depth of a linear decision tree determining this problem. This is done by using the Björner-Lov\'asz method, which turns the problem into one of estimating the Möbius function for a certain partition lattice. I will also calculate the exponential generating function for the Möbius function of a partition poset with restricted block sizes in general.}
    Keywords: ddc:000
    Language: English
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  • 5
    Publication Date: 2014-02-26
    Description: Die Autoren sind sich dar{ü}ber im klaren, daß zahlreiche Imponderabilien die Ergebnisse der vorgelegten Modellrechnungen beeinflussen k{ö}nnen. Immerhin repräsentiert jedoch das vorgelegte mathematische Modell die Summe unserer derzeitigen Kenntnisse zur Fragestellung AIDS--Epidemie; neu hinzukommende Erkenntnisse lassen sich rasch einarbeiten und in ihren Konsequenzen überschauen. Die Entwicklung neuer effizienter numerischer Methoden spielte eine Schlüsselrolle bei der tatsächlichen Simulation dieses umfangreichen realitätsnahen mathematischen Modells.
    Keywords: ddc:000
    Language: German
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  • 6
    Publication Date: 2014-02-26
    Description: We present an adaptive Rothe method for two--dimensional problems combining an embedded Runge--Kutta scheme in time and a multilevel finite element discretization in space. The spatial discretization error is controlled by a posteriori error estimates based on interpolation techniques. A computational example for a thermodiffusive flame propagation model illustrates the high accuracy that is possible with the proposed method.
    Keywords: ddc:000
    Language: English
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  • 7
    Publication Date: 2014-02-26
    Description: The multicommodity linear formulation of the Fixed Charge Network Flow Design problem is known to have significantly sharp linear relaxation lower bounds. However the tradeoff is the introduction of a large amount of artificial variables. We exhibit a class of special instances for which the lower bound is tight. Further we completly describe the polyhedron in the space of the natural variables.
    Keywords: ddc:000
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  • 8
    Publication Date: 2020-03-09
    Description: Die von der DMV-Fachgruppe Scientific Computing in Kooperation mit dem gleichnamigen GAMM-Fachausschuss organisierte Tagung \glqq Scientific Computing in der Theoretischen Physik\grqq~fand vom 16. - 18. März 1994 am Fachbereich Mathematik und Informatik der Freien Universität Berlin statt. Ziel des Workshops war, die Kontakte zwischen den Fachleuten der Gebiete {\em Computational Physics} und {\em Scientific Computing} zu intensivieren. Schwerpunkte des Workshops waren numerische Simulation von Transportmodellen der Astrophysik und Halbleiterphysik, Multilevel-Methoden für partielle Differentialgleichungen sowie Monte-Carlo-Methoden und molekulardynamische Verfahren für Probleme der Statistischen Physik und Quantenfeldtheorie. Der Workshop fand ein äusserst positives Echo und führte über 70 Teilnehmer der verschiedenen Teilgebiete der Theoretischen Physik und ca. 50 Teilnehmer aus dem Bereich der Numerischen Mathematik zusammen. \originalTeX
    Keywords: ddc:000
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  • 9
    Publication Date: 2015-06-01
    Description: We give an overview of an approach on special functions due to Truesdell, and show how it can be used to develop certain type of identities for special functions. Once obtained, these identities may be verified by an independent algorithmic method for which we give some examples.
    Keywords: ddc:000
    Language: English
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  • 10
    Publication Date: 2015-06-01
    Description: {\newcommand{\N} {{\rm {\mbox{\protect\makebox[.15em][l]{I}N}}}} In several publications the first author published an algorithm for the conversion of analytic functions for which derivative rules are given into their representing power series $\sum\limits_{k=0}^{\infty}a_{k}z^{k}$ at the origin and vice versa, implementations of which exist in {\sc Mathematica}, {\sc Maple} and {\sc Reduce}. One main part of this procedure is an algorithm to derive a homogeneous linear differential equation with polynomial coefficients for the given function. We call this type of ordinary differential equations {\sl simple}. Whereas the opposite question to find functions satisfying given differential equations is studied in great detail, our question to find differential equations that are satisfied by given functions seems to be rarely posed. In this paper we consider the family $F$ of functions satisfying a simple differential equation generated by the rational, the algebraic, and certain transcendental functions. It turns out that $F$ forms a linear space of transcendental functions. % with polynomial function coefficients. Further $F$ is closed under multiplication and under the composition with rational functions and rational powers. These results had been published by Stanley who had proved them by theoretical algebraic considerations. In contrast our treatment is purely algorithmically oriented. We present algorithms that generate simple differential equation for $f+g$, $f\cdot g$, $f\circ r$ ($r$ rational), and $f\circ x^{p/q}$ ($p,q\in\N_0$), given simple differential equations for $f$, and $g$, and give a priori estimates for the order of the resulting differential equations. We show that all order estimates are sharp. After finishing this article we realized that in independent work Salvy and Zimmermann published similar algorithms. Our treatment gives a detailed description of those algorithms and their validity.}
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  • 11
    Publication Date: 2020-11-17
    Description: The power of the symbolic math system {\small REDUCE} for solving large and difficult problems in science and engineering is demonstrated by a set of model problems. These include algebraic equation solving, formal variable elimination, formal power series, symbolic treatment of differential equations and applications from theoretical physics.
    Keywords: ddc:000
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  • 12
    Publication Date: 2014-02-26
    Description: Results from finite-element-calculations are usually visualized by colored surface- and contour-line-plots or polygonal patches or simply displaced lines and grids. In computer graphics however more advanced techniques like texture-mapping and NURBS are well established and there exist efficient algorithms and implementations. We show that these techniques are not only easy to use, but form a very natural and far more efficient approach for visualization of higher order finite-element's solutions like in $p$- and $h$-$p$-version. Texture-mapping is useful for displaying vector-valued data, too.
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  • 13
    Publication Date: 2014-02-27
    Description: In Quantum Chemistry the field of Laser--Assisted Molecular Control'' has received a considerable amount of attention recently. One key problem in this new field is the simulation of the dynamical reaction of a molecule subjected to external radiation. This problem is described by the Schrödinger equation, which, after eigenfunction expansion, can be written in the form of a large system of ordinary differential equations, the solutions of which show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. Standard smoothing techniques (averaging, filtering) would kill the whole process and thus, lead to wrong numerical results. To avoid this unwanted effect and nevertheless speed up computations, this paper presents a quasiresonant smoothing algorithm (QRS). In QRS, a natural splitting parameter $\delta$ controls the smoothing properties. An adaptive QRS--version (AQRS) is presented which includes an error estimation scheme for choosing this parameter $\delta$ in order to meet a given accuracy requirement. In AQRS $\delta$ is permanently adapted to the solution properties for computing the chemically necessary information'' only. The performance of AQRS is demonstrated in several test problems from the field Laser--Assisted Selective Excitation of Molecules'' in which the external radiation is a picosecond laser pulse. In comparison with standard methods speedup factors of the order of $10^2$ are observed.
    Keywords: ddc:000
    Language: English
    Type: doctoralthesis , doc-type:doctoralThesis
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  • 14
    Publication Date: 2015-06-01
    Description: This article describes the REDUCE package ZEILBERG implemented by Gregor Stölting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper (The sum package contains also a partial implementation of the Gosper algorithm.) and Zeilberger algorithms for indefinite, and definite summation of hypergeometric terms, respectively. An expression $a_k$ is called a {\sl hypergeometric term} (or {\sl closed form}), if $a_{k}/a_{k-1}$ is a rational function with respect to $k$. Typical hypergeometric terms are ratios of products of powers, factorials, $\Gamma$ function terms, binomial coefficients, and shifted factorials (Pochhammer symbols) that are integer-linear in their arguments.
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  • 15
    Publication Date: 2014-02-26
    Description: We test the performance of the multicanonical approach for biological molecules. The simulated molecules are frustrated systems with a complicated energy landscape. The resulting slowing down in simulations is alleviated by our ansatz. We perform a multicanonical simulation of nonpolar amino acids and study their $\alpha$-helix propensities. The results are shown to be in agreement with recent experimental results.
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  • 16
    Publication Date: 2014-02-26
    Description: In an array of coupled oscillators {\em synchronous chaos} may occur in the sense that all the oscillators behave identically although the corresponding motion is chaotic. When a parameter is varied this fully symmetric dynamical state can lose its stability, and the main purpose of this paper is to investigate which type of dynamical behavior is expected to be observed once the loss of stability has occurred. The essential tool is a classification of Lyapunov exponents based on the symmetry of the underlying problem. This classification is crucial in the derivation of the analytical results but it also allows an efficient computation of the dominant Lyapunov exponent associated with each symmetry type. We show how these dominant exponents determine the stability of invariant sets possessing various instantaneous symmetries and this leads to the idea of {\em symmetry breaking bifurcations of chaotic attractors}. Finally the results and ideas are illustrated for several systems of coupled oscillators.
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  • 17
    Publication Date: 2020-12-15
    Description: We present new Monte Carlo results in non-compact lattice QED with staggered fermions down to $m_0 = 0.005$. This extends our previous investigations on the nature of the continuum limit of QED.
    Keywords: ddc:000
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  • 18
    Publication Date: 2015-06-01
    Description: The celebrated Zeilberger algorithm which finds holonomic recurrence equations for definite sums of hypergeometric terms $F(n,k)$ is extended to certain nonhypergeometric terms. An expression $F(n,k)$ is called hypergeometric term if both $F(n+1,k)/F(n,k)$ and $F(n,k+1)/F(n,k)$ are rational functions. Typical examples are ratios of products of exponentials, factorials, $\Gamma$ function terms, binomial coefficients, and Pochhammer symbols that are integer-linear with respect to $n$ and $k$ in their arguments. We consider the more general case of ratios of products of exponentials, factorials, $\Gamma$ function terms, binomial coefficients, and Pochhammer symbols that are rational-linear with respect to $n$ and $k$ in their arguments, and present an extended version of Zeilberger's algorithm for this case, using an extended version of Gosper's algorithm for indefinite summation. In a similar way the Wilf-Zeilberger method of rational function certification of integer-linear hypergeometric identities is extended to rational-linear hypergeometric identities. The given algorithms on definite summation apply to many cases in the literature to which neither the Zeilberger approach nor the Wilf-Zeilberger method is applicable. Examples of this type are given by theorems of Watson and Whipple, and a large list of identities (``Strange evaluations of hypergeometric series'') that were studied by Gessel and Stanton. It turns out that with our extended algorithms practically all hypergeometric identities in the literature can be verified. Finally we show how the algorithms can be used to generate new identities. REDUCE and MAPLE implementations of the given algorithms can be obtained from the author, many results of which are presented in the paper.
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  • 19
    Publication Date: 2014-02-26
    Description: We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of different types of solutions within the same framework. \\{\bf Abstract: }We present a set of C++ classes that realize an abstract inexact Gauss Newton method in combination with a continuation process for the solution of parameter dependent nonlinear problems. The object oriented approach allows the continuation of different types of solutions within the same framework.
    Keywords: ddc:000
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  • 20
    Publication Date: 2014-02-26
    Description: We investigate the behavior of randomized simplex algorithms on special linear programs. For this, we develop combinatorial models for the Klee-Minty cubes and similar linear programs with exponential decreasing paths. The analysis of two randomized pivot rules on the Klee-Minty cubes leads to (nearly) quadratic lower bounds for the complexity of linear programming with random pivots. Thus we disprove two bounds conjectured in the literature. At the same time, we establish quadratic upper bounds for random pivots on the linear programs under investigation. This motivates the question whether some randomized pivot rules possibly have quadratic worst-case behavior on general linear programs.
    Keywords: ddc:000
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  • 21
    Publication Date: 2014-02-26
    Description: We consider nested iterations, in which the multigrid method is replaced by some simple basic iteration procedure, and call them {\em cascadic iterations}. They were introduced by Deuflhard, who used the conjugate gradient method as basic iteration (CCG method). He demonstrated by numerical experiments that the CCG method works within a few iterations if the linear systems on coarser triangulations are solved accurately enough. Shaidurov subsequently proved multigrid complexity for the CCG method in the case of $H^2$-regular two-dimensional problems with quasi-uniform triangulations. We show that his result still holds true for a large class of smoothing iterations as basic iteration procedure in the case of two- and three-dimensional $H^{1+\alpha}$-regular problems. Moreover we show how to use cascadic iterations in adaptive codes and give in particular a new termination criterion for the CCG method.
    Keywords: ddc:000
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  • 22
    Publication Date: 2014-02-26
    Description: The results from invariant theory and the results for semi-invariants and equivariants are summarized in a way suitable for the combination with Gröbner basis computation. An algorithm for the determination of fundamental equivariants using projections and a Poincar\'{e} series is described. Secondly, an algorithm is given for the representation of an equivariant in terms of the fundamental equivariants. Several ways for the exact determination of zeros of equivariant systems are discussed
    Keywords: ddc:000
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  • 23
    Publication Date: 2021-03-16
    Description: We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.
    Keywords: ddc:000
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  • 24
    Publication Date: 2021-03-16
    Description: In this paper we consider the problem of $k$-partitioning the nodes of a graph with capacity restrictions on the sum of the node weights in each subset of the partition, and the objective of minimizing the sum of the costs of the edges between the subsets of the partition. Based on a study of valid inequalities, we present a variety of separation heuristics for so-called cycle, cycle with ears, knapsack tree and path-block-cycle inequalities. The separation heuristics, plus primal heuristics, have been implemented in a branch-and-cut routine using a formulation including the edges with nonzero costs and node variables. Results are presented for three classes of problems: equipartitioning problems arising in finite element methods and partitioning problems associated with electronic circuit layout and compiler design.
    Keywords: ddc:000
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  • 25
    Publication Date: 2014-02-26
    Description: {\def\N{{\mbox{{\rm I\kern-0.22emN}}}} Let a set $N$ of items, a capacity $F \in \N$ and weights $a_i \in \N$, $i \in N$ be given. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality $$\sum_{i \in N} a_i x_i \leq F.$$ In this paper we present a linear description of the 0/1 knapsack polytope for the special case where $a_i \in \{\mu,\lambda\}$ for all items $i \in N$ and $1 \leq \mu 〈 \lambda \leq b$ are two natural numbers. The inequalities needed for this description involve elements of the Hilbert basis of a certain cone. The principle of generating inequalities based on elements of a Hilbert basis suggests further extensions.}
    Keywords: ddc:000
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  • 26
    Publication Date: 2014-02-26
    Description: We compare a few variants of the recently proposed multicanonical method with the well known simulated annealing for the effectiveness in search of the energy global minimum of a biomolecular system. For this we study in detail Met-enkephalin, one of the simplest peptides. We show that the new method not only outperforms simulated annealing in the search of the energy groundstate but also provides more statistical-mechanical information about the system.
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  • 27
    Publication Date: 2014-02-26
    Description: We demonstrate the effectiveness of the multicanonical algorithm for the tertiary structure prediction of peptides and proteins. Unlike to simulated annealing the relationship to the canonical ensemble remains exactly controlled. Hence, the new method allows not only the prediction of the lowest-energy conformation, but also the calculation of thermodynamic quantities at various temperature from one run.
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  • 28
    Publication Date: 2014-02-26
    Description: Die enorme algorithmische Beschleunigung durch diskrete Galerkin-Methoden f{ü}r abz{ä}hlbare Differentialgleichungssysteme hat der Simulation von Polymerisationsprozessen neue, industriell relevante Problembereiche er{ö}ffnet, die mit den bis dahin verf{ü}gbaren Methoden nicht zug{ä}nglich waren.
    Keywords: ddc:000
    Language: German
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  • 29
    Publication Date: 2014-02-26
    Description: Large chemical computations show the need for full adaptivity supporting the development of robust and highly efficient programs. For solutions possessing sharp moving spatial transitions, as travelling wavefronts or emerging boundary and internal layers, an automatic adjustment of both the space and the time stepsize is generally accepted to be more successful in efficient resolving critical regions of high spatial and temporal activity. In contrast to the widespread discretization sequence first space then time the reversed sequence first time then space is employed. Full adaptivity of the proposed algorithm is realized by combining embedded time discretization and multilevel finite element space discretization. In this paper the algorithm is described for one--dimensional problems. The numerical results show the significantly new perspectives opened by this approach.
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  • 30
    Publication Date: 2019-05-10
    Description: An error controlled finite elemente method (FEM) for solving stationary Schrödinger equations in three space dimensions is proposed. The method is based on an adaptive space discretization into tetrahedra and local polynomial basis functions of order $p=1$--$5$ defined on these tetrahedra. According to a local error estimator the triangulation is automatically adapted to the solution. Numerical results for standard problems appearing in vibrational motion and molecular structure calculations are presented and discussed. Relative precisions better than 1e-8 are obtained. For equilateral H$_3^{++}$ the adaptive FEM turns out to be superior to global basis set expansions in the literature. Our precise FEM results exclude in a definite manner the stability or metastability of equilateral H$_3^{++}$ in its groundstate.
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  • 31
    Publication Date: 2020-03-09
    Description: {\def\NP{\hbox{$\cal N\kern-.1667em\cal P$}} The {\sl storage assignment problem} asks for the cost minimal assignment of containers with different sizes to storage locations with different capacities. Such problems arise, for instance, in the optimal control of automatic storage devices in flexible manufacturing systems. This problem is known to be $\NP$-hard in the strong sense. We show that the storage assignment problem is $\NP$-hard for {\sl bounded sizes and capacities}, even if the sizes have values $1$ and~$2$ and the capacities value~$2$ only, a case we encountered in practice. Moreover, we prove that no polynomial time $\epsilon$-approximation algorithm exists. This means that almost all storage assignment problems arising in practice are indeed hard.}
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  • 32
    Publication Date: 2014-02-26
    Description: We consider the numerical treatment of Hamiltonian systems that contain a potential which grows large when the system deviates from the equilibrium value of the potential. Such systems arise, e.g., in molecular dynamics simulations and the spatial discretization of Hamiltonian partial differential equations. Since the presence of highly oscillatory terms in the solutions forces any explicit integrator to use very small step-size, the numerical integration of such systems provides a challenging task. It has been suggested before to replace the strong potential by a holonomic constraint that forces the solutions to stay at the equilibrium value of the potential. This approach has, e.g., been successfully applied to the bond stretching in molecular dynamics simulations. In other cases, such as the bond-angle bending, this methods fails due to the introduced rigidity. Here we give a careful analysis of the analytical problem by means of a smoothing operator. This will lead us to the notion of the smoothed dynamics of a highly oscillatory Hamiltonian system. Based on our analysis, we suggest a new constrained formulation that maintains the flexibility of the system while at the same time suppressing the high-frequency components in the solutions and thus allowing for larger time steps. The new constrained formulation is Hamiltonian and can be discretized by the well-known SHAKE method.
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  • 33
    Publication Date: 2014-02-26
    Description: We investigate the generating sets (``Gröbner bases'') of integer lattices which correspond to the Gröbner bases of the associated binomial ideals. Extending results in Sturmfels and Thomas, preprint 1994, we obtain a geometric characterization of the universal Gröbner basis in terms of the vertices and edges of the associated corner polyhedra. We emphasize the special case where the lattice has finite index. In this case the corner polyhedra were studied by Gomory, and there is a close connection to the ``group problem in integer programming'' Schrijver, p.~363. We present exponential lower and upper bounds for the size of a reduced Gröbner basis. The initial complex of (the ideal of) a lattice is shown to be dual to the boundary of a certain simple polyhedron.
    Keywords: ddc:000
    Language: English
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  • 34
    Publication Date: 2014-02-26
    Description: We consider periodic orbits of autonomous parameter dependent ODE's. Starting from a shooting algorithm for the numerical computation of periodic orbits via an adaptive Poincar\'e-section we develop a pathfollowing algorithm for periodic solutions based on a tangential continuation method with implicit reparametrization. For ODE's equivariant w.r.t. a finite group we show that spatial as well as spatio-temporal symmetries of periodic orbits can be exploited within the (multiple) shooting context. We describe how turning points, period doubling bifurcations and Hopf points along the branch of periodic solutions can be handled. Furthermore equivariant Hopf points and generic secondary bifurcations of periodic orbits with $ Z_m$-symmetry are treated. We tested the code with standard examples, e.g., the period doubling cascade in the Lorenz equations. To show the efficiency of the described methods we also used the program for an application from electronics, a ring oscillator with $n $ inverters. In this example the exploitation of symmetry reduces the amount of work for the continuation of periodic orbits from ${\cal O}(n^2)$ to ${\cal O}(n)$
    Keywords: ddc:000
    Language: English
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  • 35
    Publication Date: 2015-06-01
    Description: In this article algorithmic methods are presented that have been incorporated in computer algebra systems in the last five years. The methods can be used to identify transcendental functions. The essential idea due to Zeilberger is to represent the functions by systems of holonomic differential and recurrence equations, and the identification procedure utilizes algorithms of Stanley and Zeilberger. Also a noncommutative version of the Buchberger algorithm can be applied.
    Keywords: ddc:000
    Language: German
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  • 36
    Publication Date: 2014-02-26
    Description: In this paper we modify Buchberger's $S$-pair reduction algorithm for computing a Gröbner basis of a toric ideal so as to apply to an integer program in inequality form with fixed right hand sides and fixed upper bounds on the variables. We formulate the algorithm in the original space and interpret the reduction steps geometrically. In fact, three variants of this algorithm are presented and we give elementary proofs for their correctness. A relationship between these (exact) algorithms, iterative improvement heuristics and the Kernighan-Lin procedure is established.
    Keywords: ddc:000
    Language: English
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  • 37
    Publication Date: 2014-02-26
    Description: Adopting a statistical approach for the computation of turbulent combustion flows an approximation for the probability density function (PDF) of the composition variables is often required to treat the highly non-linear reaction term in a satisfactory way. One class of methods currently being used are the moment methods which employ transport equations for low order statistical moments and use a parametrized shape of the PDF. A second class solves a transport equation for the joint PDF by a Monte Carlo method. In the present paper we develop an intermediate algorithm based on a Galerkin method for the PDF transport equation. The solution is developed in terms of an orthogonal or bi-orthogonal basis of a suitable Hilbert space. The unconventional use of the related weight function as a prefactor (moving weight approach) permits adaptivity and results in a generalization of the $\beta-$closure for bounded scalar quantities. We present the approximation procedure in detail and apply it to the evolution of the composition in a homogeneous well-stirred reactor. The extension to non-homogeneous flow simulations is straightforward.
    Keywords: ddc:000
    Language: English
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  • 38
    Publication Date: 2014-02-26
    Description: Combinatorial optimization problems pervade many areas of human problem solving especially in the fields of business, economics and engineering. Intensive mathematical research and vast increases in raw computing power have advanced the state of the art in exact and heuristic problem solving at a pace that is unprecedented in human history. We survey here in layman's terms some of the fundamental concepts and principles that have led this progress. (This article will appear -- possibly in modified form -- in a popular science magazine.)
    Keywords: ddc:000
    Language: English
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  • 39
    facet.materialart.
    Unknown
    Publication Date: 2014-02-26
    Description: {\def\N{{\mbox{{\rm I\kern-0.22emN}}}} Given a set $N$ of items and a capacity $b \in \N$, and let $N_j$ be the set of items with weight $j$, $1 \leq j \leq b$. The 0/1 knapsack polytope is the convex hull of all 0/1 vectors that satisfy the inequality $$\sum_{j=1}^b \sum_{i \in N_j} jx_i \leq b.$$ In this paper we first present a complete linear description of the 0/1 knapsack polytope for two special cases: (a) $N_j = \emptyset$ for all $1 〈 j \leq \lfloor {b \over 2} \rfloor$ and (b) $N_j = \emptyset$ for all $1 〈 j \leq \lfloor {b \over 3} \rfloor$ and $N_j = \emptyset$ for all $j \geq \lfloor {b \over 2} \rfloor + 1$. It turns out that the inequalities that are needed for the complete description of these special polytopes are derived by means of some ``reduction principle''. This principle is then generalized to yield valid and in many cases facet defining inequalities for the general 0/1 knapsack polytope. The separation problem for this class of inequalities can be solved in pseudo polynomial time via dynamic programming techniques.}
    Keywords: ddc:000
    Language: English
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  • 40
    Publication Date: 2014-02-26
    Description: In the field of deep regional hyperthermia, one of the most widely used devices is the BSD--2000 Hyperthermia System which employs the Sigma 60 applicator. The Sigma 60 consists of four independent sources, giving it the potential to control the energy pattern within the patient. The independent amplitudes and phases, as well as frequency selection and applicator position, present a large number of parameters for the operator to determine. Computer simulation has long been recognized as an attractive approach to optimizing these parameters. A treatment planning program was used in clinical practice at Stanford University Medical Center for two years. It demonstrated the feasibility of computer simulation for deep regional hyperthermia in a clinical situation. However, several parts of this system were written in a language specific to one workstation, which severely restricted the wider distribution of the program to other users of the Sigma 60. A new treatment planning system for the BSD 2000 has been developed and put into clinical practice at the Rudolf Virchow Clinic of the Free University of Berlin. The new method, which we will refer to as the Berlin system, has a simpler model construction program and a considerably better graphics capability. However, the most important feature is that all programs are written in FORTRAN, C, or the X Window graphics system. Therefore, the entire treatment planning system is completely portable to other workstations.
    Keywords: ddc:000
    Language: English
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  • 41
    Publication Date: 2014-02-26
    Description: In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.
    Keywords: ddc:000
    Language: English
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  • 42
    Publication Date: 2014-02-26
    Description: The aim of this paper is to compute all isolated solutions to symmetric polynomial systems. Recently, it has been proved that modelling the sparse structure of the system by its Newton polytopes leads to a computational breakthrough in solving the system. In this paper, it will be shown how the Lifting Algorithm, proposed by Huber and Sturmfels, can be applied to symmetric Newton polytopes. This symmetric version of the Lifting Algorithm enables the efficient construction of the symmetric subdivision, giving rise to a symmetric homotopy, so that only the generating solutions have to be computed. Efficiency is obtained by combination with the product homotopy. Applications illustrate the practical significance of the presented approach.
    Keywords: ddc:000
    Language: English
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  • 43
    Publication Date: 2014-02-26
    Description: In this paper we describe the convex hull of all solutions of the integer bounded knapsack problem in the special case when the weights of the items are divisible. The corresponding inequalities are defined via an inductive scheme that can also be used in a more general setting.
    Keywords: ddc:000
    Language: English
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  • 44
    Publication Date: 2022-04-11
    Description: Die Kombination von elektronischer Fachinformation mit den neuen Mitteln der Kommunikation eröffnet neue Perspektiven für die Mathematik in Deutschland. Aufbauend auf das laufende, BMFT-geförderte Projekt ``Fachinformation'' der Deutschen Mathematiker-Vereinigung (DMV) plant die DMV eine Querschnittsaktivität für die Mathematik. Diese soll nicht nur die mathematischen Fachbereiche und Forschungsinstitute einbeziehen, sondern auch mathematische Forschungslabors aus der Industrie und die Informationsversorger der Mathematik, insbesondere die wissenschaftlichen Verlage, die TIB Hannover, die Bibliotheken der Universitäten und \mbox{-- nicht zuletzt --} das FIZ Karlsruhe mit dem Zentralblatt für Mathematik. \noindent Auf der technischen Grundlage des Internet und seiner weltweit verbreiteten Informationsdienste (Gopher, WAIS, WorldWideWeb, Hyper-G, ftp und E-mail) soll ein verteiltes, mathematisches Informationssystem geschaffen werden, bei dem die Partner des gemeinsamen Vorhabens ihre örtlichen Ressourcen untereinander und zugleich weltweit verfügbar machen. Diese Ziele sind durch konsequenten Einsatz von Software erreichbar, die nach dem Client-Server-Modell strukturiert und die im Internet verbreitet bzw.~anerkannt ist. \noindent Die Bereitstellung von Technik reicht keineswegs aus. Ohne die Schaffung einer personellen, organisatorischen und technischen Infrastruktur ist die Durchführung eines solchen Projekts nicht möglich. Als Massnahmen sind - für alle Partner - geplant: \hspace*{2mm} * Schaffung der Funktion des Informationsbeauftragten \hspace*{2mm} * Einrichtung eines gemeinsamen ``Forums für mathematische Information'' \hspace*{2mm} * Errichtung und Betreuung von mathematischen Informationsstationen \hspace*{2mm} * Teilnahme an nationalen und internationalen Standardisierungsmassnahmen \hspace*{2mm} * Workshops und regelmässige Schulungen, Öffentlichkeitsarbeit \noindent Als Aktivitäten - mit Focus auf mathematische Fachinformation - sind folgende Teilaufgaben und Pilotvorhaben bei allen Partnern geplant: \hspace*{2mm} * Einrichtung von elektronischen Informationssystemen \hspace*{2mm} * Verteiltes elektronisches Angebot von Preprints und Skripten (Volltexte) \hspace*{2mm} * Verteiltes elektronisches Angebot von Software- und Datensammlungen \hspace*{2mm} * Zugriff auf globale Informationssysteme in der Mathematik \hspace*{2mm} * Organisation eines Lebenden Mathematischen Museums \hspace*{2mm} * Zugriff auf elektronische Kataloge von Bibliotheken, insbesondere Fachbereichsbibliotheken \hspace*{2mm} * Schaffung eines organisatorischen Rahmens für elektronische mathematische Journale \hspace*{2mm} * Elektronisches Angebot von eingescannten historischen Dokumenten und Büchern \hspace*{2mm} * Schaffung einer Organisationsform für elektronisches Reviewing \hspace*{2mm} * Erprobung von Verfahren zur elektronischen Lieferung von Dokumenten \hspace*{2mm} * Elektronische Projektorganisation \noindent Das Vorhaben zielt ab auf die Schaffung einer informationstechnischen Infrastruktur für Datenbank-Retrieval, E-mail, ``Electronic Conferencing'' und fachspezifische Informationsnetze in exemplarischer Form für Wissenschaft und Industrie - auch für andere Fachgebiete.
    Keywords: ddc:000
    Language: German
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  • 45
    Publication Date: 2022-04-11
    Description: \begin{footnotesize} \noindent Combining electronic specialized information, such as electronic information retrieval from central databases, with the new means of communication opens up new perspectives for mathematics in Germany. Based on the current Fachinformationsprojekt (Specialized Information Project) run by the Deutsche Mathematiker-Vereinigung (DMV) and supported by the Federal Minister for Research and Technology (BMFT), the DMV is planning a new infrastructure activity for mathematics. This activity will not only include mathematical university departments and research institutes, but also partners from mathematical research laboratories in industry as well as suppliers of mathematical information, in particular, scientific publishing houses, the Technical Information Library (TIB) Hannover, university libraries and -- last but not least -- the Fachinformationszentrum (FIZ) Karlsruhe with the Zentralblatt für Mathematik. \noindent On the technical basis of the Internet and its worldwide information services (Gopher, WAIS, World Wide Web, Hyper-G, ftp and e-mail), a distributed mathematical information system is to be created, whose partners make their local resources available both to other partners and to the worldwide Internet community. These aims can be achieved by means of the consequent use of software that is structured according to the client-server model and distributed and accepted within the Internet. \noindent Providing the technical equipment, however, is by far not enough. Without the creation of a personal, technical and organizational infrastructure, realization of such a project will not be possible. For every partner the realization of the following measures is envisaged:\\[-7mm] \noindent \end{footnotesize} \begin{small} \begin{itemize} \item[*] Establishing an Information Coordinator\/ at every participating institution\\[-8mm] \item[*] Creation of a Forum for Mathematical Information\/\\[-8mm] \item[*] Installation and maintenance of Mathematical Information Stations\/\\[-8mm] \item[*] Participation in national and international Standardization Activities\/\\[-8mm] \item[*] Regular workshops and training courses, public relations\\[-7mm] \end{itemize} \noindent The following activities (carried out by all partners or within pilot projects by special groups) focusing on mathematical and mathematics-related information are planned:\\[-7mm] \noindent \begin{itemize} \item[*] Set up of Electronic Information Systems\/ by all partners \\[-8mm] \item[*] Distributed\/ electronic offer of Preprints\/ and scripts (full texts) by all partners\\[-8mm] \item[*] Distributed\/ electronic offer of Software and Data Collections\/ by all partners\\[-8mm] \item[*] Access to Global Information Systems in Mathematics\/\\[-8mm] \item[*] Organization of a Living Museum of Mathematics\/\\[-8mm] \item[*] Access to {\it Electronic Library Catalogs,}\/ esp.~to libraries of university departments\\[-8mm] \item[*] Electronic offer of Scanned Historical Books and Documents\/\\[-8mm] \item[*] Creation and management of Electronic Mathematical Journals\/\\[-8mm] \item[*] Creation of a framework for various kinds of Electronic Reviewing\/\\[-8mm] \item[*] Testing of new methods for Electronic Document Delivery\/\\[-8mm] \item[*] Electronic Project Organization\/\\[-7mm] \end{itemize} \noindent \end{small} \begin{footnotesize} The project aims, at its beginning, at the creation of an information infrastructure for database retrieval, e-mail, electronic conferencing and subject-specific information networks. Its focus is on mathematics in Germany. The general scope, however, is broader. The project is open for discussion, coordination, and cooperation with partners in other areas of science, industry or in other countries. It is also hoped that this project may form an example along which other models of electronic information and communication can be developed. Moreover, the project is also meant to enhance the offer from German mathematics to the worldwide "give and take" within the Internet community. \end{footnotesize}
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  • 46
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 47
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 1-9 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method is introduced for computing second-order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
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  • 48
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 11-19 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of the semi-Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
    Additional Material: 4 Ill.
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  • 49
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 21-32 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution to boundary-value problems may be based on the application of a suitably truncated T-complete set of Trefftz functions over individual subdomains and on linking the fields by a least-squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non-conventional boundary-element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p-method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so-called hybrid-Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T-element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
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  • 50
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 167-178 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A sixth-order polynomial shape function is developed for BIE analysis. The function is applied over only three-noded elements, but with the support for the function extending over adjacent elements. This avoids the oscillations near the ends of the range which otherwise are characteristic of high-order polynomial interpolation. Various test problems are explored, and it is shown that results as accurate as those from conventional quadratic elements are obtained with larger nodal spacings, and thus giving the potential for significant reductions in matrix storage requirements and solution times.
    Additional Material: 9 Ill.
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  • 51
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 155-166 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element formulation based on superposition is proposed for a lifting aerofoil in incompressible potential flow. An accuracy improvement technique for the singularity at the aerofoil trailing edge is discussed. It is shown that the quarter-node quadrilateral element can be readily employed to simulate this singularity. It is also demonstrated that the circulation in the flow field can be easily represented by a single constraint equation rather than introducing an artificial cut line in the mesh. The influence of finite-element mesh size on solution accuracy and the correct form of the boundary condition have been investigated as well. Numerical examples are given for both steady and quasisteady Joukowski aerofoils of various thicknesses and at a range of incidences. In all test cases, good agreement is observed between the analytical solution and the numerical result.
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  • 52
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 53
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 183-194 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An 8-node element (HMITC) for 3D non-linear analysis of solids is presented. The new element is based on an element developed by Wilson and Ibrahimbegovic, that incorporates incompatible modes, and on the method of mixed interpolation of tonsorial components. The HMITC element does not contain spurious zero energy modes and satisfies Irons' Patch Test. The numerical experimentation indicates that the HMITC has good performance even with distorted meshes.
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  • 54
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 203-215 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we consider an explicit finite-element method, with elements adaptively oriented in space-time, for the solution of one-dimensional conservation laws, extending previous work dealing with linear convection-diffusion and incompressible flow. In particular we consider Burgers' equation and the compressible Euler equations.
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  • 55
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 195-201 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method, based on neural-network-based functions, for solving partial differential equations is reported in the paper. Using a ‘universal approximator’ based on a neural network and point collocation, the numerical problem of solving the partial differential equation is transformed to an unconstrained minimization problem. The method is extremely easy to implement and is suitable for obtaining an approximate solution in a short period of time. The technique is illustrated with the aid of two numerical examples.
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  • 56
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 217-225 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient algorithm for consideration of axial and cyclic symmetry in the boundary-element method is presented. The appropriate transformation relationships was derived. The algorithm is then implemented in a boundary element program for the analysis of 2D elastostatic problems. Through analysis of typical problems the validity of the algorithm and its implementation is verified. A high level of accuracy and substantial reduction in computer time and storage was achieved.
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  • 57
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 227-235 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The diffusion of oxygen into an absorbing medium as an example of an implicit moving boundary problem has been dealt with by a number of authors using various numerical techniques, and, where appropriate, approximate analytical expressions. To evaluate the time for complete absorption, extrapolation is usually employed. An unconditionally stable explicit numerical scheme that avoids the limitations of such methods is presented and tested herein. Unlike existing schemes this method is fully numerical; it avoids the large array size, generally required for existing methods, by using a variable-length time step. The time for complete absorption emerges from the final step in the normal computing procedure with no recourse to extrapolation. Furthermore, owing to the implicit condition prevailing at the moving boundary, no iterations are needed to evaluate the time step required for the moving boundary to move a single space increment. The numerical results obtained compare very favourably with those due to earlier authors.
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  • 58
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 237-248 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we have developed a new formulation for solution of structural-acoustic coupling problems by boundary elements using the multiple reciprocity method. It is assumed that the structure is composed of plate components and is excited by the external or the internal noise source. The efficiency of the proposed formulation becomes especially remarkable if the boundary-value problem is to be solved repeatedly for different values of frequency. The accuracy of the numerical computations has been compared with the analytical solution in a test example.
    Additional Material: 2 Ill.
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  • 59
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 257-265 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Techniques for stress- and strain-controlled in situ homogenization of inelastic periodic composites are presented. The results of homogenization computations on a specific elastoplastic composite solid are then employed to validate the form of an orthotropic elastoplasticity model with a tensorial kinematic hardening law.
    Additional Material: 3 Ill.
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  • 60
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 10 (1994), S. 249-255 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An algorithm for evaluation of friction in general contact-impact interfaces is described. The algorithm is based on an explicit finite-element method. Coulomb's friction law is assumed. The defence node algorithm is used such that the sticking condition can be imposed with the Lagrange multiplier method even in explicit dynamic analysis. The algorithm is supposed to be applicable in general situations, including large deformations of the contact-impact bodies and large relative sliding between the contact-impact boundaries. Numerical results are presented to demonstrate the performance of the algorithm.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 275-277 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Communications in Numerical Methods in Engineering 10 (1994) 
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  • 63
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    Communications in Numerical Methods in Engineering 10 (1994), S. 267-273 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalization of the r(1-m)/m strain singularity of higher-order isoparametric elements is presented. It is shown that, by variable placement of the side nodes between their original and singular positions, the point of singularity sensed by the element can be controlled. The transition elements have a strain singularity outside their domain. The singular and non-singular elements are elements are special cases of the general mapping. The transition elements, together with the singular isoparametric elements, can be used for solving crack problems.
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  • 64
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    Communications in Numerical Methods in Engineering 10 (1994), S. 279-290 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the design of members with flaws, it is necessary to keep the stress intensity factor K of any sharp crack below the fracture toughness Kcr of the materials. Stress-intensity factor equations for the more common basic specimen geometries and various loading conditions are available in the literature. The application of these equations to complex structures involves geometric problems such as the identification of the outline of each member and the sizing of the equivalent specimen for each flaw. The paper gives a response to such difficulties.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 303-312 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple, yet storage-effective ‘linear’ programming code is given. The assumption of non-negative variables is bypassed without increasing the size of the problem. Furthermore, the objective is allowed to be summed over not just linear, but also concave, functions. A specific truss topology optimization example is shown.
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  • 66
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    Communications in Numerical Methods in Engineering 10 (1994), S. 291-296 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We propose in this paper a nine-point, fourth-order difference method for the numerical solution of the quasilinear Poisson equation \documentclass{article}\pagestyle{empty}\begin{document}$$ Au_{zz} + \frac{1}{r}u_r + Bu_{rr} = f\left({r,z,u,u_r,u_z} \right) $$\end{document} with appropriate boundary conditions. The method is based on five evaluations of f. The numerical results of four problems obtained using this method are listed. The results demonstrate the fourth-order accuracy of the method.
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  • 67
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    Communications in Numerical Methods in Engineering 10 (1994), S. 297-302 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Singularly perturbed second-order elliptic equations with boundary layers are considered. These may be considered as model problems for the advection of some quantity such as heat or a pollutant in a flow field or as linear approximations to the Navier-Stokes equations for fluid flow. Numerical methods composed of central-difference operators on special piece-wise-uniform meshes are constructed for the above problems. Numerical results are obtained which show that these methods give approximate solutions with error estimates that are independent of the singular perturbation parameter. An open theoretical problem is posed.
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  • 68
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    Communications in Numerical Methods in Engineering 10 (1994), S. 313-320 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the paper we present a superconvergent patch recovery technique for obtaining higher-order-accurate finite-element solutions and thus a postprocessed type of L2 norm error estimate. Two modifications make our procedure different from the one proposed by Zienkiewicz and Zhu (1992), in which higher-order-accurate derivatives of the finite-element solution at nodes are determined. Firstly, the recovery process is made for element, not for nodes. An ‘element patch’, which represents the union of an element under consideration and the surrounding elements, is introduced. Secondly, the local error estimate is calculated directly from the improved solution for this element. Numerical tests on both 1D and 2D model problems show that this method can provide an asymptotically exact a posteriori L2 norm error estimate if the used element possesses superconvergent points for the solutions.
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  • 69
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    Communications in Numerical Methods in Engineering 10 (1994), S. 321-331 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to developing serendipity quadrilateral infinite elements is presented. Using these elements universal matrices for quasiharmonic equation are developed. For a particular member of the family these matrices are independent of the size and shape of the element. Using these matrices the element stiffness matrix can be generated in a simpler manner by taking into account the size and shape of the element.
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  • 70
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    Communications in Numerical Methods in Engineering 10 (1994), S. 333-338 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new global secant relaxation (GSR)-method-based improvement procedure is used to improve the overall convergency performance of the modified Newton-Raphson iteration in carrying out the solution of discrete systems resulting from the finite-element discretization of a certain class of structural problems involving non-linear deformation behaviour.
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  • 71
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    Communications in Numerical Methods in Engineering 10 (1994), S. 339-353 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Theoretical and experimental analysis of free-surface electrohydrodynamic flow is fragmented and incomplete. Simulation studies of this phenomenon are further limited by the inherent complexities in the modelling process. In this note a mathematical model is developed to analyse free-surface electrohydrodynamic flow in two dimensions, and preliminary results of the simulation are described. The configurations examined include electrified conducting surfaces, the dielectrophoretic forces, and a conducting jet. The simulation is compared with analytical results in the first two investigations and is shown to be quite accurate. In the last simulation it is demonstrated that in the initial formation of a conducting jet, a 10 per cent increase in applied voltage results in about a 10 per cent increase in fluid velocity.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 355-357 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 359-360 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 361-371 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dual reciprocity boundary element method, first proposed by Nardini and Brebbia (1982, 1985), is a powerful technique for solving elliptic partial differential equations. Adopting this approach, a singular volume integral, which needs to be evaluated with a traditional boundary element method, can be converted into a boundary integral. However, when the governing equation is of a certain type, this conversion fails due to the singularities being introduced inside the physical domain and on the boundary arising by differentiating distance functions. We avoid these artificially created singularities by constructing a transformation which leads to improved numerical results.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 743-749 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This is a study about one of the core questions in the GMRES(k) method regarding the obtaining of vector yk for the least-squares problem, argminy |Hky - β(n)e1|2 (see Saad and Schultz1). We propose a simple but efficient approach to the resolution of this problem and a low cost computation of the residual and the residual norm, including both in a complete and detailed FGMRES(k) algorithm. The whole algorithm of minimization only involves two backward substitutions with triangular matrices and a dot product. The residual and the residual norm are computed, making use of results in the least-squares problem.
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    Communications in Numerical Methods in Engineering 10 (1994), S. 759-760 
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    Communications in Numerical Methods in Engineering 10 (1994), S. 761-762 
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  • 80
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. i 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 75-75 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
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  • 82
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 127-139 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: In this paper the traditional square mesh 2D-TLM algorithm is generalized for rectangular meshes of arbitrary aspect ratio. It is shown that the anisotropic rectangular TLM network can be conceived in such a way that the propagation vector remains independent of the direction of propagation in the infinitesimal approximation. A full dispersion analysis of the rectangular mesh in then performed for the general case, and results are compared to that of the traditional square mesh.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 155-166 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The radiation field patterns of rectangular waveguides and horns of finite dimensions are obtained numerically. The electric field integral equation is formulated to relate their radiation patterns to the surface current distribution. These currents are determined numerically by reducing the integral equation to a matrix equation, using the moment method. The computed currents are then used to calculate the radiation patterns and cross-polar fields of the finite wavegiudes and horns. The method is numerically efficient and can be applied to the computation and optimization of the antenna feed configurations.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 167-177 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Ray-besed methods have been previously developed for accurately predicting the electromagnetic scattering from cavity interiors that allowed for realistic modelling of complex cavities such as jet engine inlets. An analytic geometric model is developed for bifurcated cavities based on connecting sections of generalized super-ellipse functions. The electromagnetic scattering from such cavities using the ‘shooting and bouncing rays’ (SBR) method is discussed.
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  • 85
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 209-221 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A theoretical analysis has been developed to study the crosstalk in crossed bundles of parallel lines. The model is based on the theory of the coupled transmission lines and the resulting system of differential equations has been solved by means of the finite difference, time-domain (FDTD) method. The frequency response of the network has been achieved by the discrete fourier transform (DFT) algorithm; measurements, performed with a vectorial network analyser, show a good agreement with numerical simulation.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 35-41 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: The eigenmodes in electromagnetic cavities, loaded with arbitrarily shaped dielectric materials, are computed by the edge element method. The computation shows that the well known ‘spurious modes’ no longer appear. Formulae are given and verified so that the number of zero eigenvalues, which come from ∇ × H = 0, may be accurately predicted. Formulae for the order and density of the global matrices are given for a rectangular cavity regularly divided into bricks and tetrahedra, allowing an associated comparison between the contrasting edge and nodal element formulations. Comparison of the computed results with available theoretical and previously published data show the edge element approach to be a robust, accurate and effective method.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 253-265 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A numerical frequence-domain modelling of two-terminal, non-linear microwave circuits is presented. It basically relies on a process allowing the solution of the frequency-domain curcuit harmonic balance equations while accounting for the semiconductor device by means of an accurate numerical macroscopic physical model. In its present state of development, the model allows the study of a single two-terminal device circuit operating in harmonic mode. Its capabilites are illustrated by means of the results of a study devoted to the optimization of the load curcuit configuration of a millimetre-wave avalanche diode frequency multiplier. The influence of the output load impedance level on the circuit output RF performance has been investigated for different input power levels in direct frequency multiplication mode and in the presence of additional circuit tunings at low harmonic rank idler frequencies.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994) 
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    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 309-319 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper describes a rigorous and systematic procedure to derive a non-linear distributed FET model that an easily be implemented in CAD routines of simulators based on harmonic balance techniques. The new model is derived from a knowldge of the conventional linear lumped equivalent circuit, from non-linear current sources extracted with pulsed measurements, and from the physical dimensions of the FET.For fundamental and haromonic requencies, the FET is modelled by N identical cells. Each cell is made up of a non-linear two-port section inserted between two linear four-port sections that simulate the coupling and the distributed effects along the electrodes of the FET in the width direction only. This non-linear distributed scaling approach to FET modelling has been applied to the analysis of a submicrometre-gate GaAs FET at Millimetre-wave frequencies, and the results were compared to the non-linear lumped element approach. This approach can be applied to other transistors used in non-linear regions at microwave and millimetre-wave frequencies.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 375-375 
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    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 91
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. ii 
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    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
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  • 92
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 399-405 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Symbolic computational systems introduce some unique features in computational engineering. There have been several papers published on the solution of differential equations under given boundary conditions by symbolic systems. The finite element formalism has received prime attention in the course of development of symbolic computation in engineering. The main idea has been to develop a symbolic FEM package to reduce the burden of manual algebra, eliminate errors introduced by numerical quadrature, and improve the efficiency of element generation.This work discusses a symbolic solution to electromagnetic linear antenna problems. The solution is a method of moments that transforms Pocklington's integral equation to a matrix equation. The symbolic system is used to produce (1) analytical integration, (2) the parametric expression for the input impedance and (3) computational code for forward and reverse problem of the input impedance.
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 419-432 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: This paper presents a new finite element formulation in the Laplace domain for both diffusion and wave equations with applications in the field of electrical engineering. With the aid of congruence transformation of matrices, the finite element equations in the Laplace domain are solved and time-domain results can be obtained through the inverse Laplace transform. In a test problem, good agreement between the numerical results derived with the present method and the analytical solutions has been found. For applications in which only Dirichlet and Neumann boundary conditions are involved, this new finite element approach can be applied and provide both frequency-domain and time-domain results in one run without any timestepping scheme. The limitations of using the congruence transformation in solving propagation problems are also addressed in this paper.
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  • 94
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    International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 7 (1994), S. 433-452 
    ISSN: 0894-3370
    Keywords: Engineering ; Electrical and Electronics Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: A hybrid method obtained as a combination of the coupled-mode method (CMM) and the mode-matching method (MMM) is developed and applied in the analysis of multiple dielectric and magnetic discontinuities in rectangular waveguides. As both are moment methods, some kind of truncation has to be carried out in the computer implementation. It is shown that selection of a different number of modes in the two methods is not necessary, unless low-permittivity meida inside the waveguide are considered. As a consequence, the procedure for slecting the number of basis functions is only done in one of the methods. Numerical examples are presented showing the behaviour of the method and the proofs of convergence. Examples are included illustrating the power of this hybrid technique, especially in relation to non-reciprocal structures containing magnetized ferrites.
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  • 95
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1481-1497 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure for the optimization of stretched triangular grids is described. The method is based on the construction and minimization of a function that represents a generalized version for stretched grids of a non-linear spring system. The function is minimized using a gradient method based on the steepest descent. Examples are provided to show the applicability of the method to computational fluid dynamics problems.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1465-1480 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Multigrid method is used to accelerate the convergence of the numerical solution of the set of partial differential equations for generating the Body-Fitted Co-ordinate system (BFC) for both simply and doubly connected domain problems. The multigrid method is based on the full approximation scheme with bilinear interpolation as prolongation operator. The other components of the multigrid method such as the relaxation method, restriction operator, number of relaxation sweeps per cycle and direction of relaxation sweeps are varied with a view to obtaining the general principle in implementing an efficient multigrid algorithm for the generation of the BFCs.
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    International Journal for Numerical Methods in Engineering 37 (1994), S. 1531-1555 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this work, Paulino et al.1 have presented an algorithm for profile and wavefront reduction of large sparse matrices of symmetric configuration. This algorithm is based on spectral properties of a Finite Element Graph (FEG), An FEG has been defined as a nodal graph G, a dual graph G* or a communication graph G· associated with a generic finite element mesh. The novel algorithm has been called Spectral FEG Resequencing (SFR). This algorithm has specific features that distinguish it from previous algorithms. These features include (1) use of global information in the graph, (2) no need of a pseudoperipheral vertex or the endpoints of a pseudodiameter, and (3) no need of any type of level structure of the FEG. To validate this algorithm in a numerical sense, extensive computational testing on a variety of problems is presented here. This includes algorithmic performance evaluation using a library of benchmark test problems which contains both connected and non-connected graphs, study of the algebraic connectivity (λ2) of an FEG, eigensolver convergence verification, running time performance evaluation and assessment of the algorithm on a set of practical finite element examples. It is shown that the SFR algorithm is effective in reordering nodes and/or elements of generic finite element meshes. Moreover, it computes orderings which compare favourably with the ones obtained by some previous algorithms that have been published in the technical literature.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
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  • 98
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 1557-1572 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: To exploit the benefits of parallel computer architectures for multibody system simulation, an interdisciplinary approach has been pursued, combining knowledge of the three disciplines of dynamics, numerical mathematics and computer science. An analysis of the options available for the formulation and numerical solution of the dynamical system equations yielded a surprising result. A method initially proposed to solve the inverse problem of dynamics is the best choice to generate the system equations required for solving the simulation problem, when relying on implicit integration routines. Such routines have the particular advantage of handling stiff systems, too. The new O(N)-residual formalism, generating the system equations in a form required for implicit numerical integration, has a high potential to benefit from parallel computer architectures. Two strategies of medium and coarse grain parallelization have been implemented on a Transputer network to obtain a package for parallel multibody simulation. An analysis of the performance of this package demonstrates for typical multibody simulation problems that the new code is five times faster than existing codes when implemented on a serial computer. An additional speed-up by the same order of magnitude is obtained when the code is implemented on a Transputer network.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
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  • 99
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 181-201 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general Finite Volume Method (FVM) for the analysis of structural problems is presented. It is shown that the FVM can be considered to be a particular case of finite elements with a non-Galerkin weighting. For structural analysis this can readily be interpreted as equivalent to the unit displacement method which involves mainly surface integrals. Both displacement and mixed FV formulations are presented for static and dynamic problems.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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  • 100
    Electronic Resource
    Electronic Resource
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 37 (1994), S. 229-256 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. In contrast to an earlier formulation by Nayroles and coworkers, certain key differences are introduced in the implementation to increase its accuracy. The numerical examples in this paper show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed in this paper.
    Additional Material: 26 Ill.
    Type of Medium: Electronic Resource
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