Adaptive, scalable domain decomposition methods for surface integral equations

The objective of this research is to investigate scalable, high-performance surface integral equation solvers for geometrically large, multi-scale electromagnetics problems. There are three key components of this work: adaptive discontinuous Galerkin non-conformal discretizations, geometry-aware domain decomposition, and parallel computational algorithms that are scalable. Non-conformal discretization permits the mixing of different types of elements to dramatically improve mesh generation for high-definition objects. The enhanced domain decomposition method aids in capturing the geometric complexity of an object, so that it can be decomposed into smaller components, which are commonly referred to as sub-domains. The new computational algorithms will reduce the time complexity of the problems through the use of high performance computing. An alternative view of the proposed work is as an effective preconditioner to reduce the condition number. The mathematical advancements made through this work will result in high performance simulation tools with improved parallel efficiency and scalability.