Effective precondition technique to solve a full linear system for the fast multipole method

The fast multipole method (FMM) is an O(N) solver of a full linear system appearing in integral equation methods. We propose a precondition technique for the FMM using the Bi-CGSTAB2 method, which employs a nested FMM having intentionally deteriorated precision. This enables us to utilize the global information residing in the system matrix.