Fast algorithms and parallel computing: solution of extremely large integral equations in computational electromagnetics

Abstract

Accurate simulations of real-life electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved easily, even when using the most powerful computers with state-of-the-art technology. Some of the world’s largest integral-equation problems in computational electromagnetics have been solved at Bilkent University Computational Electromagnetics Research Center (BiLCEM). Most recently, we have achieved the solution of 550,000,000×550,000,000 dense matrix equations! This achievement is an outcome of a multidisciplinary study involving physical understanding of electromagnetics problems, novel parallelization strategies (computer science), constructing parallel clusters (computer architecture), advanced mathematical methods for integral equations, fast solvers, iterative methods, preconditioners, and linear algebra. In this seminar, following a general introduction to our work in computational electromagnetics, I will continue to present fast and accurate solutions of large-scale electromagnetic modeling problems involving three-dimensional geometries with arbitrary shapes using the multilevel fast multipole algorithm (MLFMA) and parallel MLFMA. Some of the complicated real-life problems (such as, scattering from a realistic aircraft) involve geometries that are larger than 1000 wavelengths. Accurate solutions of such problems can be used as reference data for high-frequency techniques. Solutions of extremely large canonical benchmark problems involving sphere and NASA Almond geometries will be presented, in addition to the solution of complicated objects, such as metamaterial problems, red blood cells, and dielectric photonic crystals. Solving the world’s largest computational electromagnetics problems has important implications in terms of obtaining the solution of previously intractable physical, real-life, and scientific problems in various areas, such as (subsurface) scattering, optics, bioelectromagnetics, metamaterials, nanotechnology, remote sensing, etc.