High order fast laplace solvers for the dirichlet problem on general regions

Victor Pereyra, Wtodzimierz Proskurowski, Olof Widlund

Research output: Contribution to journalArticle

Abstract

Highly accurate finite difference schemes are developed for Laplace's equation with the Dirichlet boundary condition on general bounded regions in Rn. A second order accurate scheme is combined with a deferred correction or Richardson extrapolation method to increase the accuracy. The Dirichlet condition is approximated by a method suggested by Heinz-Otto Kreiss. A convergence proof of his, previously not published, is given which shows that, for the interval size h, one of the methods has an accuracy of at least 0(h) in ¿j. The linear systems of algebraic equations are solved by a capacitance matrix method. The results of our numerical experiments show that highly accurate solutions are obtained with only a slight additional use of computer time when compared to the results obtained by second order accurate methods.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalMathematics of Computation
Volume31
Issue number137
DOIs
StatePublished - 1977

Fingerprint

Laplace equation
Laplace
Extrapolation
Dirichlet Problem
Linear systems
Capacitance
Boundary conditions
Higher Order
Deferred Correction
Richardson Extrapolation
Extrapolation Method
Dirichlet conditions
Experiments
Matrix Method
Laplace's equation
Finite Difference Scheme
Algebraic Equation
Dirichlet Boundary Conditions
Linear Systems
Numerical Experiment

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Cite this

High order fast laplace solvers for the dirichlet problem on general regions. / Pereyra, Victor; Proskurowski, Wtodzimierz; Widlund, Olof.

In: Mathematics of Computation, Vol. 31, No. 137, 1977, p. 1-16.

Research output: Contribution to journalArticle

Pereyra, Victor ; Proskurowski, Wtodzimierz ; Widlund, Olof. / High order fast laplace solvers for the dirichlet problem on general regions. In: Mathematics of Computation. 1977 ; Vol. 31, No. 137. pp. 1-16.
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