Domain decomposition in conjunction with sinc methods for Poisson's equation

Abstract

Efforts to develop sinc domain decomposition methods for second-order two-point boundary-value problems have been successful, thus warranting further development of these methods. A logical first step is to thoroughly investigate the extension of these methods to Poisson's equation posed on a rectangle. The Sinc-Galerkin and sinc-collocation methods are, for appropriate weight choices, identical for Poisson's equation, and thus only the Sinc-Galerkin system is discussed here. Both the Sincaalerkin patching method and the Sincaalerkin overlapping method are presented in the simple case of decomposition into two subdomains. Numerical results are presented for each of these methods, showing the convergence. As an indication of the capabilities of these domain d e c o m psition techniques, they are applied to Poisson's equation on an L-shaped domain. Restrictions due to the method by which the discrete system is developed require that this problem be solved using nonoverlapping subdomains. Thus only the Sinc-Galerkin patching method is presented. Numerical results are presented that show the convergence of the approximate solutions, even in the presence of boundary singularities. 0 1996 John Wiley & Sons, Inc.

On bivariate poly-sinc collocation applied to patching domain decomposition

“…Sinc methods in connection with domain decompositions were used during the 90ies by Lybeck [13]. Her work includes Sinc-Galerkin and Sinc collocation methods connected to a direct domain decompositions, too [13,14]. It turned out during the years that a direct domain decomposition has some advantages over an iterative domain decomposition.…”

On bivariate poly-sinc collocation applied to patching domain decomposition

“…Sinc methods in connection with domain decompositions were used during the 90ies by Lybeck [13]. Her work includes Sinc-Galerkin and Sinc collocation methods connected to a direct domain decompositions, too [13,14]. It turned out during the years that a direct domain decomposition has some advantages over an iterative domain decomposition.…”

Navier-Stokes Solution of the Driven-Cavity Problem Using Sinc-Collocation Elements

“…In the same context, the Poisson equation was solved using domain decomposition by Lybeck and Bowers. 18,19 For the purpose of achieving higher-order precision, the Sinc-function approximation has also been used in heat transfer problems by Narasimhan, Chen and Stenger, 20,21 Lippke, 22 and others. In Chen and Stenger, 20 the two-dimensional, steady-state heat conduction problems in both a square and a semiinfinite rectangular cavity were considered.…”

On bivariate poly-sinc collocation applied to patching domain decomposition

“…Sinc methods in connection with domain decompositions were used during the 90ies by Lybeck [13]. Her work includes Sinc-Galerkin and Sinc collocation methods connected to a direct domain decompositions, too [13,14]. It turned out during the years that a direct domain decomposition has some advantages over an iterative domain decomposition.…”

Navier-Stokes Solution of the Driven-Cavity Problem Using Sinc-Collocation Elements

“…In the same context, the Poisson equation was solved using domain decomposition by Lybeck and Bowers. 18,19 For the purpose of achieving higher-order precision, the Sinc-function approximation has also been used in heat transfer problems by Narasimhan, Chen and Stenger, 20,21 Lippke, 22 and others. In Chen and Stenger, 20 the two-dimensional, steady-state heat conduction problems in both a square and a semiinfinite rectangular cavity were considered.…”

On bivariate poly-sinc collocation applied to patching domain decomposition

“…Sinc methods in connection with domain decompositions were used during the 90ies by Lybeck [13]. Her work includes Sinc-Galerkin and Sinc collocation methods connected to a direct domain decompositions, too [13,14]. It turned out during the years that a direct domain decomposition has some advantages over an iterative domain decomposition.…”

Navier-Stokes Solution of the Driven-Cavity Problem Using Sinc-Collocation Elements

“…In the same context, the Poisson equation was solved using domain decomposition by Lybeck and Bowers. 18,19 For the purpose of achieving higher-order precision, the Sinc-function approximation has also been used in heat transfer problems by Narasimhan, Chen and Stenger, 20,21 Lippke, 22 and others. In Chen and Stenger, 20 the two-dimensional, steady-state heat conduction problems in both a square and a semiinfinite rectangular cavity were considered.…”