Direct and iterative solution of the generalized Dirichlet-Neumann map for elliptic PDEs on square domains

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:227

Article; Proceedings Paper

Sifalakis, A. G.¹  Fulton, S. R.²  Papadopoulou, E. P.¹  Saridakis, Y. G.¹ 

[1] Tech Univ Crete, Dept Sci, Appl Math & Comp Lab, Khania 73100, Greece

[2] Clarkson Univ, Dept Math & Comp Sci, Potsdam, NY 13699 USA

关键词: Elliptic PDEs;    Dirichlet-Neumann map;    Global relation;    Collocation;    Iterative methods;    Jacobi;    Gauss-Seidel;    GMRES;    Bi-CGSTAB;   

DOI  :  10.1016/j.cam.2008.07.025

来源: Elsevier

【 摘 要 】

In this work we derive the Structural properties of the Collocation coefficient matrix associated with the Dirichlet-Neumann map for Laplace's equation on a square domain. The analysis is independent of the choice of basis functions and includes the case involving the same type of boundary conditions on all sides, as well as the case where different boundary conditions are used on each side of the square domain. Taking advantage of said properties, we present efficient implementations of direct factorization and iterative methods, including classical SOR-type and Krylov subspace (Bi-CGSTAB and GMRES) methods appropriately preconditioned, for both Sine and Chebyshev basis functions. Numerical experimentation, to verify our results, is also included. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free