A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions. (English) Zbl 1302.35005

Reimer, Ashton S.; Cheviakov, Alexei F.

Comput. Phys. Commun. 184, No. 3, 783-798 (2013); corrigendum ibid. 209, 200-201 (2016).

Summary: A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers.

MSC:

35-04	Software, source code, etc. for problems pertaining to partial differential equations
35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations

Keywords:

Poisson problem; mixed boundary conditions; finite-difference solver; Matlab; mean first passage time

Software:

Matlab; FDMRP

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