A Randomized Low-Rank Decomposition Based Method for Solving Volume-Surface Integral Equation

A new method for solving volume-surface integral equation is proposed. The four sub-blocks of the impedance matrix are compressed in a form of hierarchical semi-separable (HSS) structure by randomized low-rank decompositions. To accelerate the convergence of the iterative solution, an HSS-based preconditioner is also proposed. Numerical experiments are conducted on an on-chip power grid model to study the performance of the method. This method can be further extended to the multilevel fast multipole algorithm for solving large-scale problems.