Seminar Series - 2000-2001

Infinite Element Methods for Helmholtz Equation Problems on Unbounded Domains

Michael Newman
Department of Engineering Mechanics
University of Nebraska - Lincoln
Lincoln, NE  68588
Advisor:  Professor Andrzej J. Safjan

Date: Wednesday, December 6, 2000
Time: 3:30 p.m.
Place: W185 Nebraska Hall


Two methods for improving the conditioning and convergence properties of infinite elements are proposed and examined for one-dimensional, two-dimensional and three-dimensional infinite elements. The first method is a preconditioning technique which is based on a Gram-Schmidt-like transformation induced by general bilinear and sesquilinear forms. This preconditioning method can be applied to many types of infinite elements including the popular multipole infinite element of Burnett.

The second method improves the conditioning and convergence properties of infinite elements by replacing the characteristic (eigenfunction) basis functions which have global support with basis functions with local support. These new infinite elements employing basis functions with compact support produce very good results for a wide range of nondimensional wave numbers ka, and, unlike the global infinite elements, have the property of being h-p-r adaptive.

The conditioning and convergence properties of these new infinite elements are presented in solving two-dimensional and three-dimensional exterior problems for the Helmholtz equation.


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