Domain Decomposition Method

Integral equation based optimized Schwarz method for electromagnetics

GetDDM

GetDDM is an open-source framework for testing Schwarz-type domain decomposition methods for time-harmonic wave problems.

GetDDM: an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems

We present an open finite element framework, called GetDDM, for testing optimized Schwarz domain decomposition techniques for time-harmonic wave problems. After a review of Schwarz domain decomposition methods and associated transmission conditions, …

A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations

This paper presents a new non-overlapping domain decomposition method for the time harmonic Maxwell's equations, whose effective convergence is quasi-optimal. These improved properties result from a combination of an appropriate choice of …

GetDDM: an Open Framework for Testing Optimized Schwarz Methods for Time-Harmonic Wave Problems

This talk presents the parallel domain decomposition solver GetDDM, integrated in the open-source finite element solver GetDP. This add-on has proved to be efficient on 3D large scale problems, while staying relatively easy-to-use, by, e.g. managing automatically the iterative solver, arising from the DDM, and the communication between processes. It is moreover versatile, e.g, it can consider scalar or vector problems, one-, two- or three-dimensional problems, mixed formulations and preconditionners. Available with ready-to-use examples for Helmholtz and Maxwell’s equations, GetDDM aims to be a framework to test and develop optimized Schwarz methods for time-harmonic wave problems.

Open-source finite element solver for domain decomposition problems

Improved Domain Decomposition Method for the Helmholtz Equation

In this talk we will present recent improvements to the quasi-optimal domain decomposition method for the Helmholtz equation presented in 1. The key point of the method is the construction of an accurate local approximation of the exact Dirichlet-to-Neumann operator which leads to a new transmission operator between sub-domains. We will show that this local approximation, based on complex Pad approximants, is well-suited for large scale parallel finite element simulations of high frequency scattering problems, with either manual or automatic mesh partitioning.

A quasi-optimal non-overlapping domain decomposition algorithm for the Helmholtz equation