Boundary-distribution solution of the Helmholtz equation for a region with corners

Journal Article · Sun Apr 01 04:00:00 EST 1979 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(79)90060-3· OSTI ID:5985084

Riddell, Jr, R J

A technique is described for the solution of the Helmholtz equation together with associated boundary conditions based on a generalization of a method used for the solution of the Dirichlet problem of potential theory, in which a dipole distribution is introduced on the boundary of a region to generate the potential inside. In order that the boundary conditions be satisfied, the distribution must be found as the solution of an integral equation. If the boundary is smooth, the equation is of Fredholm type, but if it has a corner the equation is singular. The problem of a sharp corner is analyzed, and properties of the solution are developed using the theory of singular integral equations. Direct use of the technique can be made impossible in some cases by the presence of ''partner problem'' eigenvalues. A simple method for avoiding this difficulty is presented.

• Research Organization: Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
• OSTI ID: 5985084
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 31:1; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
INTEGRAL EQUATIONS
NUMERICAL SOLUTION
SINGULARITY