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

Integral equation based approaches are popular for extracting the capacitance of integrated circuit struc-tures. Typically, rst-order collocation or Galerkin methods are used. The resulting dense system of equations is eciently solved by combining matrix sparsi cation with an iterative solver. While the speed-up over direct factorization is substantial, the rst-order methods still lead to large systems even for simple problems. In this paper we introduce a high-order Nyström scheme. For the same level of discretization, the high-order schemes can be an or-der of magnitude more accurate than the rst-order approaches at the same computational cost. As a con-sequence, we obtain the same level of accuracy with a much smaller matrix.