Hybrid matrix-decomposition-based fast direct solver of integral equations

Our numerical experiments show that the hierarchical matrix (H-matrix) solver is more efficient than the butterfly solver for electrically small problems, although the converse is true for sufficiently large problems. In this communication, we propose a hybrid matrix decomposition algorithm (HMDA) that combines the H-matrix and butterfly algorithms. In the HMDA, the H-matrix algorithm is employed to compress the lower-upper decomposition matrix in the lower levels, whereas the butterfly algorithm is adopted at the higher levels. Numerical examples demonstrate that the performance of the HMDA is similar to that of the H-matrix for electrically small problems and higher than the butterfly algorithm for electrically large problems.