An efficient high order multilevel fast multipole algorithm for electromagnetic scattering analysis

An effcient higher order MLFMA is developed by using an "extended-tree". With this extended-tree, the size of the box at the finest level is reduced, and the cost associated with the aggregation and disaggregation operations is significantly decreased. The sparse approximate inverse (SAI) preconditioner is utilized to accelerate the convergence of iterative solutions. The Cholesky factorization, instead of the often used QR factorization, is employed to construct the SAI preconditioner for cavity scattering analysis, by taking advantage of the symmetry of the matrix arising from electric field integral equation. Numerical experiments show that the higher order MLFMA is more effcient than its low-order counterpart.