A fast algorithm for volume integral equation using interpolative decomposition and multilevel fast multipole algorithm

The fast algorithm which combines interpolative decomposition (ID) and the multilevel fast multipole algorithm (MLFMA) is extended to the method of moments (MoM) solution of volume integral equations (VIE) from that of surface integral equations (SIE). Boxes in the finest level in MLFMA are further divided and the rank-deficient submatrices of the near-field interactions are approximated by the data sparse representation through the ID. Numerical experiments are conducted to study the performance of the fast solver.