Imaging and Sensing Waves seminar (contact Chrysoula Tsogka)
2pm-3pm in ACS 362B (Zoom option)
Speaker: Pierre-David Letourneau (Reservoir Labs)
Title: Fast Multipole Method (FMM) for simulation of electromagnetic waves in 3D complex media
Abstract: In this talk, I will provide an overview of the Fast Multipole Method (FMM) algorithm and will discuss its use for the simulation of electromagnetic waves in 3D complex media. I will also discuss some recent results obtained in collaboration with UC Merced and Stanford demonstrating how such algorithms can be used for simulating the macroscopic response of materials directly from microstructure. FMMs represent a family of powerful algorithms that allow for the solution of N-body problems in optimal linear time (O(N)). The FMM was originally designed to address the Laplace potential (e.g. gravitational, 1/r) and has since been generalized in various ways. In this presentation, I will focus on the use of the FMM for simulating electromagnetic waves in 3D media consisting of a large number of disparate discrete scatterers. The talk will begin with an overview of tree-based FMM codes, followed by a description of its specialization to scalar waves and, finally, vector waves (Maxwell's equations). I will also introduce the concept of T-matrix and Foldy-Lax system for the efficient treatment of multiple scattering. Numerical results will demonstrate the advantageous empirical scaling of our implementation in practice, and examples will be provided that demonstrate how it is now possible to capture the macroscopic and asymptotic behaviors of electromagnetic waves from first principles, including in the effective medium and diffusion regimes.