High-order Nystrom 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 efficiently 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. 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.