Accession Number:

AD0774464

Title:

Eigenvalues and Eigenmodes for the Homogeneous Helmholtz Equation for Arbitrary Domains.

Descriptive Note:

Summary rept.,

Corporate Author:

STATE UNIV OF NEW YORK BUFFALO DEPT OF ENGINEERING SCIENCE

Personal Author(s):

• Tai,George R. C.
• Shaw,Richard Paul

Report Date:

1973-08-01

Pagination or Media Count:

54.0

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

Descriptors:

• *INTEGRAL EQUATIONS
• *EIGENVECTORS
• *BOUNDARY VALUE PROBLEMS
• ANALYTIC FUNCTIONS
• NUMERICAL ANALYSIS

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE