ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

Abstract

Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

Fast finite element electrostatic analysis with domain decomposition method

“…When the traditional finite element method is used in large-scale and multi-scale electromagnetic analysis, the computational efficient is reduced and the resource consumption is increased [13]. As an efficient numerical algorithm, domain decomposition (DD) method can decompose the big problem into several smaller ones, and can use various parallel solving techniques to accelerate the calculation [14], which has great advantages for solving large-scale and multi-scale electromagnetic problems [15]. Therefore, the DD method is adopted to solve the electrostatic problems.…”

A Parallel 3D Spatial Spectral Volume Integral Equation Method for Electromagnetic Scattering from Finite Scatterers

“…Exploiting the increasing capabilities of modern computational hardware in combination with computationally efficient algorithms has resulted in the possibility of simulating large-scale electromagnetic problems faster in terms of wall-clock time, e.g., [14][15][16][17][18][19][20]. Inspired by these techniques, we investigate converting the Maxwell solver of [6,7] from a single-core algorithm to a multi-core algorithm, to achieve a significant reduction in wall-clock time.…”

Tear-and-Interconnect Domain Decomposition Scheme for Solving Multiscale Composite Penetrable Objects

“…The transmission conditions preventing unphysical reflections from the subdomain interfaces, which is essential to achieve good convergence, are then enforced along the tearing contours between subdomains. In some cases using overlapping regions to couple adjacent subdomains [20], [22], and in some other without auxiliar unknowns at all, directly enforcing the current continuity through an interior penalty formulation [23], [24]. The primarily advantage of the T&I scheme is the absence of fictitious surfaces to close the open subdomains, thus preventing the use of large numbers of redundant unknowns.…”