High-Order Nyström Schemes for Efficient 3-D Capacitance Extraction

Integral equation based approaches are popular for extracting the capacitance of integrated circuit structures. Typically, first-order collocation or Galerkin methods are used. The resulting dense system of equations is e#ciently solved by combining matrix sparsification with an iterative solver. While the speed-up over direct factorization is substantial, the first-order methods still lead to large systems even for simple problems. In this paper we introduce a high-order Nystrom scheme. For the same level of discretization, the high-order schemes can be an order of magnitude more accurate than the first-order approaches at the same computational cost. As a consequence, we obtain the same level of accuracy with a much smaller matrix. 1 Introduction With decreasing feature sizes and increasing frequencies, accurate and e#cient capacitance extraction has become critical for design. In recent years, capacitance extractors based on integral equations [3, 7] have become popular. Integral ..