The Finite Element Method in Electromagnetics, 3rd Edition

CHAPTER 14DOMAIN DECOMPOSITION FOR LARGE-SCALE ANALYSIS

Because of its unmatched capabilities in modeling highly complicated geometries and materials, the finite element method is often the method of choice for dealing with real-life engineering problems. However, because many engineering electromagnetic problems are electrically very large and the finite element method requires a volumetric discretization, the number of unknowns or the dimension of the linear system in their finite element analysis can easily reach the order of millions or even billions. Solving such a large numerical system, whether directly or iteratively, can be technically very challenging even though the finite element matrices are very sparse. A direct solver based on matrix decomposition would require excessive computation time and computer memory, and an iterative solver, because of the poor condition of the finite element matrices, would converge very slowly if at all. Fortunately, while engineering problems for the finite element analysis are becoming larger and more complicated, computer technologies have been advancing at an extraordinary speed. In particular, the technology of parallel computing has made tremendous progress in both hardware and software. Today’s parallel computers are often equipped with hundreds or thousands of multicore computing processing units (CPUs). Computer architectures have also been developed to accelerate massive computation using general-purpose graphics processing ...