A Novel Approach for Volume-Integral Evaluation in the BEM
J. Ding and W. Ye
Georgia Institute of Technology, US
Keywords: Poisson equation, BEM, volume integral, fast algorithm
The need for efficient solutions to problems with complex 3-D geometries, such as those encountered in micro-electro-mechanical systems (MEMS), has led to the development of fast algorithms. Based on the accelerated Boundary Element Method (BEM), fast solvers for electrostatic problems, Stokes problems, etc. have been developed and applied successfully in solving practical problems. However, to date most applications of the BEM have been limited to linear and homogeneous problems. For non-homogeneous or nonlinear problems, a major difficulty in applying the BEM is the presence of volume integrals in the boundary integral formulation. One common approach for treating the volume integrals is to perform a volume discretization. Unless the nonlinearity exists only in a small region, such an approach loses the major advantage of the BEM the need of only surface discretization. In this paper, we describe a novel approach for evaluating volume integrals resulted from either a nonlinear problem or a non-homogeneous problem without volume discretization of the problem domain. Based on this approach, an accelerated BEM solver for Poisson equations using only surface discretization has been developed. Case studies have been performed and results have been compared with analytical solutions.
Nanotech 2004 Conference Technical Program Abstract