Explicit Evaluation of Hypersingular Boundary Integral Equation for 3-D Helmholtz Equation Discretized with Constant Triangular Element

• DOI: 10.1299/jcst.4.194
• Publication Date: 2010-09-24T06:53:51Z
• Authors: Toshiro MATSUMOTO; Changjun ZHENG; Shinya HARADA; Toru TAKAHASHI
• Keywords: Helmholtz equation; Helmholtz free energy; Constant (computer programming)

It is well known that the solution of an exterior acoustic problem governed by Helmholtz equation violated at eigenfrequencies associated interior when boundary element method (BEM) based on conventional integral (CBIE) applied without any special treatment to solve it. To tackle this problem, Burton-Miller formulation using a linear combination CBIE and its normal derivative (NDBIE) emerges as effective efficient formula which proved yield unique for all frequencies if imaginary part coupling constant two equations nonzero. The most difficult in implementing NDBIE hypersingular type, it often regularized fundamental Laplace's equation. But various regularization procedures literature give rise integrals are still and/or extremely time consuming evaluate general. However, triangular elements used discretize boundary, strongly-singular can be evaluated finite-part sense explicitly difficulty, numerical computation becomes more than other singularity-subtraction technique. Therefore, paper, these singular rigorously finite parts divergent canceling out terms appears limiting process explicitly. correctness also demonstrated through some test examples.