A Mixed Potential MLFMA for Higher Order Moment Methods With Application to the Generalized Method of Moments

The application of the multilevel fast multipole algorithm (MLFMA) to higher order moment method discretizations is a continuing open problem. Herein, we present a point-based mixed potential variant of the MLFMA algorithm that exhibits an MLFMA tree of arbitrary height with no restriction related to basis function support size, efficient nearfield precomputation, and that maintains favorable scaling for any mixture of low- and high-order bases. The flexibility of the algorithm is also leveraged to accelerate the precomputation of algebraic preconditioners. We demonstrate the method through application to the generalized method of moments (GMM), a recently introduced moment method discretization capable of combining both low- and high-order bases and geometries in the same simulation; however, the method may be used to accelerate other higher order moment methods as well.