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  • Computational Chemistry and Molecular Modeling  (6)
  • 65F10  (3)
  • Liming  (2)
  • 1
    Electronic Resource
    Electronic Resource
    The approximate Dirichlet Domain Decomposition method. Part I: An algebraic approach (1991)
    Springer
    Computing 47 (1991), S. 137-151 
    Details
    ISSN: 1436-5057
    Keywords: AMS(MOS) 65N20 ; 65F10 ; 68A20 ; CR: G.1.3 ; G.1.8 ; Elliptic problems ; finite elements ; substructuring ; domain decomposition ; preconditioners ; parallel algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In der vorliegenden Arbeit wird ein neuer Zugang zur Konstruktion von Vorkonditionierungsoperatoren auf der Basis von Gebietsdekompositionstechniken (DD Techniken) beschrieben. Anwendungen finden diese DD Vorkonditionierungen im Verfahren der konjugierten Gradienten zur iterativen Lösung von symmetrischen und positiv definiten Finiten-Elemente Gleichungen. Die DD Technik basiert auf einer Zerlegung des Gebietes Ω inp sich nicht überlappende Teilgebiete, die später denp Prozessoren eines MIMD Rechners zugeordnet sind. Die DD Vorkonditionierung enthält drei Blockmatrizen, die für ein konkretes Anwendungsproblem jeweils zu spezifizieren sind. Eine dieser Matrizen wird genutzt, um die Knotenbasis in eine näherungsweise diskret harmonische Basis zu transformieren. Die anderen beiden Matrizen können als Blockvorkonditionierungen für die in jedem Teilgebiet entstehenden Dirichlet-Probleme und für ein modifiziertes Schurkomplement auf den Knoten der Koppelränder zwischen den Teilgebieten interpretiert werden. Die relative spektrale Konditionszahl wird abgeschätzt. Eine direkte Verbindung der vorgeschlagenen DD Vorkonditionierung zu einer Additiven Schwarzschen Methode kann gezeigt werden. Im zweiten Teil dieser Artikelserie werden die Resultate dieser Arbeit auf ebene, symmetrische Randwertprobleme für partielle Differentialgleichungen zweiter Ordnung angewandt und die numerischen Resultate, die auf einem Transputer-Hypercube erzeugt wurden, diskutiert.
    Notes: Abstract We present a new approach to the construction of Domain Decomposition (DD) preconditioners for the conjugate gradient method applied to the solution of symmetric and positive definite finite element equations. The DD technique is based on a non-overlapping decomposition of the domain Ω intop subdomains connected later with thep processors of a MIMD computer. The DD preconditioner derived contains three block matrices which must be specified for the specific problem considered. One of the matrices is used for the transformation of the nodal finite element basis into the approximate discrete harmonic basis. The other two matrices are block preconditioners for the Dirichlet problems arising on the subdomains and for a modified Schur complement defined over all nodes on the coupling boundaries between the subdomains. The relative spectral condition number is estimated. Relations to the additive Schwarz method are discussed. In the second part of this paper, we will apply the results of this paper to two-dimensional, symmetric, second-order, elliptic boundary value problems and present numerical results performed on a transputer-network.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02253431
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  • 2
    Electronic Resource
    Electronic Resource
    A parallel preconditioned conjugate gradient method using domain decomposition and inexact solvers on each subdomain (1990)
    Springer
    Computing 45 (1990), S. 217-234 
    Details
    ISSN: 1436-5057
    Keywords: AMS(MOS) 65N20 ; 65F10 ; CR: G.1.3, G.1.8 ; Domain decomposition method ; iterative solvers ; finite element equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Eine Strategie zum Einsatz des Verfahrens der konjugierten Gradienten mit Vorkonditionierung für Multiprozessorsysteme der ‘message passing’-Architektur wird beschrieben. Zur Vorkonditionierung werden die Techniken Schur-Komplement-Vorkonditionierung für “Koppelränder” zwischen Teilgebieten und beliebige Wahl einer klassischen Vorkonditionierung für die inneren Freiheitsgrade der Teilgebiete diskutiert. Der gesamte Arithmetikaufwand für die einzelnen Teilgebiete ist vollständig parallelisiert durch die Verteilung aller Teilgebietsdaten über das Prozessornetzwerk vor dem Beginn des FEM-Lösungsprozesses (incl. Generieren der Elementmatrizen, Assemblieren der Teilsteifigkeitsmatrix). Die resultierende spektrale Konditionszahl der wirkenden Vorkonditionierungsmatrix wird abgeschätzt. Für ein wichtiges Beispiel (MIC(0)*-Vorkonditionierung in jedem Teilgebiet) ergibt sich die Konditionszahl im wesentlichen als Produkt der beiden Konditionszahlen der benutzten Vorkonditionierungstechniken.
    Notes: Abstract We describe a preconditioned conjugate gradient solution strategy for a multiprocessor system with message passing architecture. The preconditioner combines two techniques, a Schurcomplement preconditioning over “coupling boundaries” between the subdomains and an arbitrary choice of classic preconditioning for the inner degrees of freedom on each subdomain. All computational work on the single subdomains is carried out in parallel by distributing the subdomain data over the processor network before starting the finite element solution process (including generating the element matrices and assemblying the local subdomain stiffness matrix). The resulting spectral condition number of the entire preconditioner is estimated. For the important example of choosing MIC(0)-*-preconditioning on the subdomains, the condition number obtained is essentially the product of the two condition numbers involved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02250634
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  • 3
    Electronic Resource
    Electronic Resource
    Effect of the inhibitors nitrapyrin and sodium chlorate on nitrification and N2O formation in an acid forest soil (1996)
    Springer
    Biology and fertility of soils 22 (1996), S. 318-325 
    Details
    ISSN: 1432-0789
    Keywords: Autotrophs ; Liming ; Nitrapyrin ; N-serve ; Nitrification ; N2O ; Sodium chlorate ; Acid beech forest soil
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract An acid forest soil from beech forest gaps, which were either limed or unlimed, and the undisturbed forest was investigated for the type of nitrifying populations and the process of N2O evolution. To see whether nitrifiers were of heterotrophic or autotrophic origin, the nitrification inhibitors nitrapyrin and sodium chlorate were applied to disturbed soil samples which underwent laboratory incubations. Nitrapyrin inhibits autotrophic nitrification. In different studies, sodium chlorate has been identified as an inhibitor either of autotrophic or of heterotrophic nitrification. In the samples investigated only nitrapyrin inhibited the autotrophic nitrification occurring in the limed soil. Sodium chlorate effectively inhibited heterotrophic nitrification. In the limed forest floor samples, where most autotrophic nitrification occured, sodium chlorate showed no inhibitory effect. In another laboratory incubation experiment, N2O evolution from undisturbed soil columns, to which the above inhibitors were applied, was investigated. In those samples, in which nitrification had been reduced, neither inhibitor significantly reduced N2O evolution. Thus it was concluded that the contribution of nitrification to N2O losses is negligible, and that N2O evolution arises from the activity of denitrifying organisms. Microbial biomass and respiration measurements showed that the inhibitors did not affect microflora negatively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00334576
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  • 4
    Electronic Resource
    Electronic Resource
    The approximate Dirichlet Domain Decomposition method. Part II: Applications to 2nd-order Elliptic B.V.P.s (1991)
    Springer
    Computing 47 (1991), S. 153-167 
    Details
    ISSN: 1436-5057
    Keywords: AMS (MOS) 65N20 ; 65F10 ; 68A20 ; CR: G. 1.3 ; G.1.8 ; Elliptic Problems ; finite elements ; substructuring ; domain decomposition ; preconditioners ; parallel algorithms ; hierarchical bases ; multigrid techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung Im ersten Teil dieser Artikelserie haben wir auf Basis von Gebietsdekompositionstechniken (DD Techniken) Vorkonditionierungsoperatoren konstruiert. Diese DD Vorkonditionierungen enthalten drei Blockmatrizen, die für spezifische Anwendungsfälle zu konkretisieren sind. In der vorliegenden Arbeit betrachten wir Finite-Elemente-Gleichungen, die bei der DD Diskretisierung von ebenen, symmetrischen, elliptischen Randwertproblemen für partielle Differentialgleichungen zweiter Ordnung entstehen. Zur Definition der oben genannten Blockmatrizen werden Mehrgitter-und hierarchische Techniken herangezogen. Die entstehenden DD-PCCCG Verfahren sind bezüglich des arithmetischen Aufwands asymptotisch fast optimal und bestens zur Parallelrechnung auf MIMD-Computern mit lokalem Speicher und Botschaftenaustausch geeignet. Die auf einem Transputer-Hypercube durchgeführten numerischen Experimente belegen nachhaltig die Effektivität der vorgeschlagenen DD Vorkonditionierungen.
    Notes: Abstract In the first part of this article series, we had derived Domain Decomposition (DD) preconditioners containing three block matrices which must be specified for specific applications. In the present paper, we consider finite element equations arising from the DD discretization of plane, symmetric, 2nd-order, elliptic b.v.p.s and specify the matrices involved in the preconditioner via multigrid and hierarchical techniques. The resulting DD-PCCG methods are asymptotically almost optimal with respect to the operation count and well suited for parallel computations on MIMD computers with local memory and message passing. The numerical experiments performed on a transputer hypercube confirm the efficiency of the DD preconditioners proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02253432
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  • 5
    Electronic Resource
    Electronic Resource
    Effect of the inhibitors nitrapyrin and sodium chlorate on nitrification and N2O formation in an acid forest soil (1996)
    Springer
    Biology and fertility of soils 22 (1996), S. 318-325 
    Details
    ISSN: 1432-0789
    Keywords: Key words Autotrophs ; Liming ; Nitrapyrin ; N-serve ; Nitrification ; N2O ; Sodium chlorate ; Acid beech forest soil
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract An acid forest soil from beech forest gaps, which were either limed or unlimed, and the undisturbed forest was investigated for the type of nitrifying populations and the process of N2O evolution. To see whether nitrifiers were of heterotrophic or autotrophic origin, the nitrification inhibitors nitrapyrin and sodium chlorate were applied to disturbed soil samples which underwent laboratory incubations. Nitrapyrin inhibits autotrophic nitrification. In different studies, sodium chlorate has been identified as an inhibitor either of autotrophic or of heterotrophic nitrification. In the samples investigated only nitrapyrin inhibited the autotrophic nitrification occurring in the limed soil. Sodium chlorate effectively inhibited heterotrophic nitrification. In the limed forest floor samples, where most autotrophic nitrification occured, sodium chlorate showed no inhibitory effect. In another laboratory incubation experiment, N2O evolution from undisturbed soil columns, to which the above inhibitors were applied, was investigated. In those samples, in which nitrification had been reduced, neither inhibitor significantly reduced N2O evolution. Thus it was concluded that the contribution of nitrification to N2O losses is negligible, and that N2O evolution arises from the activity of denitrifying organisms. Microbial biomass and respiration measurements showed that the inhibitors did not affect microflora negatively.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00334576
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  • 6
    Electronic Resource
    Electronic Resource
    Molecular mechanics of organic halides. III. Fluorinated olefins (1980)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 1 (1980), S. 111-117 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A molecular mechanical force field for fluorinated ethylenes and propylenes is described. The field computes geometries, dipole moments, and energy differences between isomers and rotamers. Component analysis indicates that “classical” strains alone (skeletal, nonbonded, electrostatic) cannot account for energy relationships. The discussion is supplemented by a semiempirical quantum chemical comparison of cis- and trans-FCH=CHF and of gauche- and anti-FCH2CH2F.
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540010202
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  • 7
    Electronic Resource
    Electronic Resource
    Towards the convergence of molecular-mechanical force fieldsOriginal proofs for this paper were delayed in the mail. (1985)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 6 (1985), S. 1-4 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: It is noticed that inclusion of an electrostatic term in the molecular-mechanical treatment of hydrocarbons would compel the nonbonding parameters of different force fields to become more alike than they are at present. Apart from removing the discontinuity in passing from the calculation of an unfunctionalized parent compound to the calculation of its functionalized derivatives, it is expected that the inclusion would improve results for the hydrocarbons themselves.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540060102
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  • 8
    Electronic Resource
    Electronic Resource
    Molecular mechanics and molecular shape. V.For Part IV, see Ref. 1. on the computation of the bare surface area of molecules (1988)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 9 (1988), S. 18-24 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: This article examines the numerical estimation of molecular surface areas within the model of overlapping atomic spheres. One has the choice of either basing the estimate on all elements that contribute to the surface, or of ignoring systematically some elements in the interatomic clefts. It is argued that the second choice, even though more approximate, implicitly improves on the model and is to be preferred. Since surface areas are not measurable, the demonstration is unavoidably roundabout, relying mostly on correlation analysis. Among the regressors occur two compounded parameters. One, ratio of the surface area of the equivalent sphere to the surface area, is interpreted as a measure of molecular globularity. It reflects the molecular axis-ratio and surface convolution. The other, ratio of the surface area to the volume, is interpreted as a measure of the global congestion of a chemical residue. Together with a measure of the local congestion at the point of attachment, it affects the steric hindrance that a residue offers. The relation between the surface area and the number of valence electrons is also discussed.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540090104
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  • 9
    Electronic Resource
    Electronic Resource
    Remarks on the molecular mechanical calculations of functionalized hydrocarbonsPresented in part at the Molecular Mechanics Symposium, Indianapolis, Indiana, June 23-24, 1983. (1984)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 5 (1984), S. 299-306 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: Molecular mechanical calculations for hetero-substituted hydrocarbons present certain difficulties that are not encountered in dealing with hydrocarbons. Ways are proposed to overcome such difficulties, sometimes by two-step or iterative computation. The following topics are considered: fitting the force field by using data from studies in solution; ways to estimate atomic charges or, alternatively, bond moments; ways to account for field effects upon atomic charges and bond moments.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540050404
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  • 10
    Electronic Resource
    Electronic Resource
    Molecular mechanics of organic halides. V. Conformational equilibria in solution (1981)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 2 (1981), S. 384-391 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: With a view of using data on solutions and liquids for parameter fitting in molecular mechanical force fields, Abraham's theory of solvation is incorporated in the force field procedure. Geometries and bond moments are estimated internally, partial account being taken of bond-bond induction, and used to calculate the intramolecular electrostatic energy, dipole moment, and the dipole and quadrupole terms in the solvation energy. Three dielectric constants are used, one for the solute in the vapor, one for the solution, and one for the intramolecular space through which dipole-dipole interactions take place. Examples are given, including such where computation differs with measurement, to illustrate the performance of the scheme.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540020405
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