Accuracy Controlled $mathcal{H}^{2_{-}}$ Matrix-Matrix Product in Linear Complexity and Its Applications

摘要

Existing linear-complexity H^{2- matrix- matrix product lacks an explicit accuracy control. A new linear complexity algorithm is developed in this work to compute the product of two H2 matrices with controllable accuracy. The complexity of the algorithm for variable-rank H2 is also derived. Applications to both large-scale capacitance extraction and electromagnetic scattering problems involving millions of unknowns on a single core have demonstrated the accuracy and efficiency of the proposed algorithm.}