Parallel direct Poisson and biharmonic solvers
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Parallel direct Poisson and biharmonic solvers

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Published by Dept. of Computer Science, University of Illinois at Urbana-Champaign in Urbana .
Written in English


  • Poisson"s equation -- Numerical solutions -- Data processing.,
  • Biharmonic equations -- Numerical solutions -- Data processing.,
  • Parallel processing (Electronic computers)

Book details:

Edition Notes

Statementby A. H. Sameh, S. C. Chen, and D. J. Kuck.
SeriesReport - UIUCDCS-R-74 ; no. 684
ContributionsChen, Shyh-ching, 1944- joint author., Kuck, David J., joint author.
LC ClassificationsQA76 .I4 no. 684, QA377 .I4 no. 684
The Physical Object
Pagination18 p. ;
Number of Pages18
ID Numbers
Open LibraryOL5255894M
LC Control Number75329134

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The modified cyclic reduction parallel Poisson solver (n = 7). IP X 4 -- X 5 6 ~g 7 Applying VLSI Poisson solvers to the biharmonic problem 15 4. VLS! Poisson solvers We can proceed with a description of the VLSI implementation of both the algorithms of the preceding by: 7. () The application of VLSI poisson solvers to the biharmonic problem. Parallel Computing , () Application of domain decomposition techniques in large-scale fluid flow by: A parallel perturbed biharmonic solver 3. A PERTURBED BIHARMONIC SOLVER Let us consider the perturbed biharmonic equation. V4u+d:u=f in R, deR, (3) where R is the unit square with the boundary conditions u(x, y) = 0 and u,,(x, y) = 0 for (x, y) ~ fiR, and u,(x, y) is the outward normal derivative at the : G. Lotti. Two methods for solving the biharmonic equation are compared. One method is direct, using eigenvalue-eigenvector decomposition. The other method is iterative, solving a Poisson equation directly at each by: 1.

We present fast methods for solving Laplace’s and the biharmonic equations on irregular regions with smooth boundaries. The methods used for solving both equations make use of fast Poisson solvers on a rectangular region in which the irregular region is embedded. They also both use an integral equation formulation of the problem where the integral equations are Cited by: Stage 1: (Parallel among all processors) After each processor 1 Poisson Solver for Multiprocessors matrix of T and by:   A direct method is developed for the discrete solution of Poisson's equation on a rectangle. The algorithm proposed is of the class of marching methods. The idea is to generalize the classical Cramer's method using Chebyshev matrix polynomials formalism. This results in the solution ofN independent diagonal system of linear equations in the eigenvector coordinate Cited by: 2. Poisson Solvers William McLean Ap Return to Math/Math Common Material. 1 Introduction Many problems in applied mathematics lead to a partial di erential equation of the form 2aru+ bru+ cu= f in. (1) Here, is an open subset of Rd for d= 1, 2 or 3, the coe cients a, band ctogether with the source term fare given functions on File Size: KB.

This algorithm is more effective than Gaussian elimination with pivoting, Gram-Schmidt, or Householder's reduction, since A.H. Sameh, D.J. Kuck/Parallel direct linear system solvers - A survey 7 6 8 5 7 9 4 6 8 10 3 5 7 9 11 2 4 6 8 10 12 1 3 5 7 9 11 13 F(Givens) = (1/n) compared to = (1/n log 2n) for the by: Full text of "Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions" See other formats Computer Science Department TECHNICAL REPORT Fast Parallel Iterative Solution of Poisson's and the Biharmonic Equations on Irregular Regions A. Mayo A. Greenbaum Technical Report January NEW YORK UNIVERSITY C 03 C . Parallel direct Poisson solver for discretisations with one Fourier diagonalisable direction Article in Journal of Computational Physics (12) June with 34 Reads. A fast solver for the Stokes equations with distributed forces in complex geometries 1 George Biros, Lexing Ying, and Denis Zorin “The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions”, SIAM As parallel computation is necessary to solve realistic problems with sufficient accuracy.