Eigenvalues and Eigenmodes for the Homogeneous Helmholtz Equation for Arbitrary Domains.
Abstract
An integral equation technique is employed to obtain eigenvalues and eigenmodes for a homogeneous Helmholtz equation for a two-dimensional or three-dimensional arbitrary closed region with arbitrary first order homogeneous boundary conditions. The integral approach has one dimension less than corresponding finite difference and finite element approaches. To demonstrate the method, an analytic solution is given for circular and spherical regions with a Dirichlet boundary condition and a Neumann boundary condition, and a solution procedure valid for any separable geometry is indicated. For an application to a non-separable boundary, a right triangle is considered as a two dimensional example. (Modified author abstract)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1973
- Accession Number
- AD0774464
Entities
People
- George R. C. Tai
- Richard Paul Shaw
Organizations
- University at Buffalo