Singularity-treated quadrature-evaluated method of moments solver for 3-D capacitance extraction

While research work on fast integral equation solver has resulted in several algorithms of similar linear equation solving performance, it has been well observed that the convergence of capacitance versus discretization is rather slow due to the most commonly used first-order collocation or Galerkin methods. This paper reports a new high-order scheme, Quadrature-evaluated Method of Moments Solver (QMMS), that uses high-order weighting and Gaussian quadrature to optimally handle the singularities at the edges and corners. For practical interconnect extraction problems, singularities at edges are analytically known and the corresponding Gaussian nodes allocation affords a near optimal discretization scheme. The new formulation avoids the special position-dependent quadrature rules, and surprisingly, provides a well-behaved matrix that converges rapidly without any pre-conditioning. Combining the high-order scheme with a kernel-independent fast solver yields an efficient algorithm for 3-D capacitance extraction.