Applied Interdisciplinary Mathematics

We demonstrate a new direct integral equation solver for high-frequency electromagnetic analysis that derives from butterfly, a.k.a. multilevel matrix decomposition algorithm, compression schemes. The solver uses butterfly schemes for compressing the LU factors and HOLDR decompositions of discretized integral operators. The solver requires O(N^1.5 Log N) CPU resources and O(N log N) memory, and operates directly on butterfly-compressed blocks of the interaction matrix. To this end, it uses new randomized schemes for rapidly adding and multiplying butterfly-compressed operators. The solver has been applied to the analysis of large-scale 2D and 3D scattering phenomena involving both perfectly conducting as well as penetrable scatterers. Joint work with Yang Liu and Han Guo. Speaker(s): Eric Michielssen (EECS, University of Michigan)