A fast algorithm for multiscale electromagnetic problems using interpolative decomposition and multilevel fast multipole algorithm

The interpolative decomposition (ID) is combined with the multilevel fast multipole algorithm (MLFMA), denoted by ID-MLFMA, to handle multiscale problems. The ID-MLFMA first generates ID levels by recursively dividing the boxes at the finest MLFMA level into smaller boxes. It is specifically shown that near-field interactions with respect to the MLFMA, in the form of the matrix vector multiplication (MVM), are efficiently approximated at the ID levels. Meanwhile, computations on far-field interactions at the MLFMA levels remain unchanged. Only a small portion of matrix entries are required to approximate coupling among well-separated boxes at the ID levels, and these submatrices can be filled without computing the complete original coupling matrix. It follows that the matrix filling in the ID-MLFMA becomes much less expensive. The memory consumed is thus greatly reduced and the MVM is accelerated as well. Several factors that may influence the accuracy, efficiency and reliability of the proposed ID-MLFMA are investigated by numerical experiments. Complex targets are calculated to demonstrate the capability of the ID-MLFMA algorithm.