Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Friday, January 24th, 1997

BEM Solution of Laplace's Equation in Multi-Layered Media with High Permittivity Ratios}

A boundary integral formulation for Laplace's equation \nabla \cdot a \nabla u = 0 with piecewise constant coefficients a is discussed. Although the arising integral operator and its inverse can be bounded independently of the coefficients, numerical problems occur when the dynamic range of the coefficients is large. This is due to different scaling of the solution of the integral equation which results in large discretization errors of the flux a \nabla u. We will discuss a novel two step technique to avoid different scaling. The analysis of this approach shows that the discretization error and the condition of the discretized linear system can be bounded independently of the coefficients. Numerical experiments concerning the three-dimensional capacitance extraction of structures with multiple dielectrics will demonstrate the accuracy and efficiency of the method.