Accelerating solution of volume-surface integral equations with multiple right-hand sides by improved skeletonization techniques

Skeletonization is an effective method to accelerate the solution of linear systems with multiple right-hand sides (RHSs) by exploiting the rank-deficiency property of the RHS matrix. However, when the size of the RHS matrix is very large, the memory requirement would become a bottleneck of the skeletonization technique. To reduce the memory cost, this letter presents the theoretical basis of how to find out the skeleton basis functions (SBFs) to construct the skeleton RHS matrix more efficiently from a purely algebraic point of view and proposes a multilevel algorithm to figure out the SBFs for solving the integral equations with multiple RHSs. The numerical results show that the proposed method accelerates the solution of the volume-surface integral equation with multiple RHSs and reduces the memory cost significantly.