Numerical solution of the Helmholtz equation for two-dimensional polygonal regions

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

DOI:https://doi.org/10.1016/0021-9991(79)90061-5· OSTI ID:6210099

Riddell, Jr, R J

The Helmholtz equation together with associated boundary conditions can be solved using a dipole distribution on the boundary of any region of interest. If the region has corners, the distribution satisfies a singular integral equation. In this paper numerical techniques for the solution of this equation which take into account the analytic properties of the solution are discussed. Although a complete error analysis has not been developed, some indicators of the errors generated are considered. The technique is illustrated by comparing the numerical solution of the eigenvalue problem associated with various two-dimensional polygonal regions with exact solutions. Numerical solutions of the Dirichlet problem for the Helmholtz equation are also obtained. A method for eliminating difficulties arising from nearby singularities is also implemented, and sample results given.

• Research Organization: Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
• OSTI ID: 6210099
• 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
DIRICHLET PROBLEM
EIGENVALUES
EQUATIONS
NUMERICAL SOLUTION