Trimmed Multilevel Fast Multipole Algorithm for D-Type Volume Integral Equations

In this work, we present a trimming scheme for the multilevel tree structure of multilevel fast multipole algorithm (MLFMA), which is applied on D-type volume integral equations. With this approach, the number of iterations and the durations of matrix-vector multiplications are significantly reduced for the solution of multi-scale volumetric problems. The trimming operation is performed on rows and columns of the impedance matrix. In order to eliminate the matrix columns, the current coefficients are estimated via machine learning techniques. The implementation particularly provides significant acceleration for the iterative solutions of electrically large volumetric problems.