A Direct Integral-Equation Solver of Linear Complexity for Large-Scale 3D Capacitance and Impedance Extraction

Provided by: Association for Computing Machinery
Topic: Hardware
Format: PDF
State-of-the-art integral-equation-based solvers rely on techniques that can perform a matrix-vector multiplication in O (N) complexity. In this work, a fast inverse of linear complexity was developed to solve a dense system of linear equations directly for the capacitance extraction of any arbitrary shaped 3D structure. The proposed direct solver has demonstrated clear advantages over state-of-the-art solvers such as FastCap and HiCap; with fast CPU time and modest memory consumption, and without sacrificing accuracy. It successfully inverts a dense matrix that involves more than one million unknowns associated with a large-scale on-chip 3D interconnect embedded in inhomogeneous materials.

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