Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Domain-imbedding alternating direction method for linear elliptic equations on irregular regions using collocation (1993)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 9 (1993), S. 93-106 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new method is presented for solving elliptic partial differential equations over two-dimensional irregular regions. The scheme imbeds the irregular region in a rectangle, and then uses an alternating direction iteration to solve the resulting system of linear equations. Collocation with cubic Hermite splines is used for discretization. The method is shown to be equivalent to a multiboundary alternating direction method. A theory of convergence for a simplified case is given, details of implementation are discussed, and two numerical illustrations are presented. © 1993 John Wiley & Sons, Inc.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690090109
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    An iterative solver for a coupled system of Helmholtz equations (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 207-219 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: An iterative solver for a pair of coupled partial differential equations that are related to the Maxwell equations is discussed. The convergence of the scheme depends on the choice of two parameters. When the first parameter is fixed, the scheme is seen to be a successive under-relaxation scheme in the other parameter. A theory for convergence of the scheme is discussed for a special case of the equations, and several numerical examples are presented. © 1996 John Wiley & Sons, Inc.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    A coupled double splitting ADI scheme for the first biharmonic using collocation (1990)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 6 (1990), S. 321-333 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new method for solving the first biharmonic equation via a double splitting into coupled systems of ordinary differential equations is presented. The first splitting reduces this fourth order partial differential equation into the coupled system uxx + uyy = v and vxx + vyy = f, where u carries both Dirichlet and Neumann boundary data and v carries no boundary data. The pair is then iteratively solved using coupled alternating direction collocation on the resulting systems of ordinary differential equations. This can also be viewed as an alternating direction method of lines for a system of partial differential equations. Although there is no separation of variables underlying the splitting, the method yields a convergent sequence of iterates for a variety of examples under a restricted range of acceleration parameters, and possesses O(h4) accuracy. Desirable features of the algorithm are discussed together with the reduction of bandwidth of the associated collocation matrices under intersticing of u and v variables. Interesting open questions are also discussed.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690060404
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    Alternating direction collocation for irregular regions (1996)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 147-159 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Several methods are presented for solving separable elliptic partial differential equations over an irregular region B using alternating direction collocation on a rectangular grid over an embedding rectangle R. The methods are geometric predictor-corrector schemes. At each iterative step, the numerical solution is predicted on R via a full ADI sweep. The forcing term is then updated (corrected) on collocation points interior to B. By this means, the geometry of B and boundary conditions on ∂B are approximated implicitly using rectangular grids on R. The methods are O(h4) in the L2(R) norm and are boundary exact, in that the computed solution converges exactly to the given boundary conditions on ∂B for appropriate choices of a pair of acceleration parameters. A number of examples are presented. Proof of convergence is established elsewhere. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...