Sparse boundary conditions on artificial boundaries for three-dimensional potential problems

Journal Article · Fri Nov 01 04:00:00 EST 1996 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1996.0237· OSTI ID:478600

Deakin, A S; Rasmussen, H ^[1]

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1. Univ. of Western Ontario, London (Canada)

We consider Laplace`s equation in three dimensions where the domain is restricted to a finite region with the introduction of an artificial boundary B on which a boundary condition is imposed. The finite difference method is employed to compare the solution at the nodes inside and on the surface B for four different boundary conditions of which two are local and two are nonlocal. The standard nonlocal (DtN) boundary condition is derived from the solution of the exterior Dirichlet problem, and a discretized (DDtN) version is derived that applies at the nodes on B. However, the coefficients associated with the nodes on B in the system of linear equations for the solution is not sparse. This lack of sparsity is acute for three-dimensional problems owing to the large number of equations. The DDtN boundary condition is approximated to obtain a sparse nonlocal boundary condition, where the coefficients associated with the nodes on Bare relatively sparse. We show that the DDtN solution is very accurate. In addition, we present results which indicate that the difference between the DDtN solution and the solution for each of the other three boundary conditions has the correct behavior when the artificial boundary is enlarged. 11 refs., 6 figs., 2 tabs.

• OSTI ID: 478600
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 129; ISSN 0021-9991; ISSN JCTPAH
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
BOUNDARY CONDITIONS
DIRICHLET PROBLEM
FINITE DIFFERENCE METHOD
LAPLACE EQUATION
POTENTIALS
THREE-DIMENSIONAL CALCULATIONS