Development of 3D Parallelized CMPS Method with Optimized Domain Decomposition

Optimized Entire-domain Moment-method Analysis of 3d Dielectric Scatterers

When compared with commonly used subdomain moment-method analysis, entire-domain analysis of 3D dielectric scatterers results in a greatly reduced number of unknowns. Unfortunately, the expressions for matrix elements tend to be quite complicated and their calculation extremely time-consuming if evaluated directly. It is shown in the paper that, in a Galerkin-type solution with large trilinear ...

Optimized Overlapping Domain Decomposition: Convergence Proofs

During the last two decades many domain decomposition algorithms have been constructed and lot of techniques have been developed to prove the convergence of the algorithms at the continuous level. Among the techniques used to prove the convergence of classical Schwarz algorithms, the first technique is the maximum principle used by Schwarz. Adopting this technique M. Gander and H. Zhao proved a...

Optimized Schwarz method with two-sided transmission conditions in an unsymmetric domain decomposition

Domain decomposition (DD) methods are important techniques for designing parallel algorithms for solving partial differential equations. Since the decomposition is often performed using automatic mesh partitioning tools, one can in general not make any assumptions on the shape or physical size of the subdomains, especially if local mesh refinement is used. In many of the popular domain decompos...

Optimized Schwarz methods with nonoverlapping circular domain decomposition

While the classical Schwarz method can only be used with overlap, optimized Schwarz methods can also be used without overlap, which can be an advantage when simulating heterogeneous problems, problems with jumping coefficients, or also for independent mesh generation per subdomain. The analysis of nonoverlapping optimized Schwarz methods has so far been restricted to the case of straight interf...

Development of a Domain Decomposition Method for Computational Aeroacoustics