Additive Schwarz method

The additive Schwarz method is an algorithm used in domain decomposition methods, specifically in the finite element method, that involves solving subdomains of a larger problem independently and then combining the solutions using an additive approach. It is characterized by the use of the Jacobi algorithm and is contrasted with the multiplicative Schwarz method, which uses the Gauss-Seidel algorithm.From: Computational Partial Differential Equations Using MATLAB [2019]

Meshless Methods with Radial Basis Functions

View Chapter

Purchase Book

Published in Jichun Li, Yi-Tung Chen, Computational Partial Differential Equations Using MATLAB®, 2019

Jichun Li, Yi-Tung Chen

Tables 10.5 and 10.6 show that the number of iterations for the multiplicative Schwarz method is roughly half of that needed for the additive version. These phenomena have also been observed in our earlier work [68], and more examples were provided there. Note that such features are also observed for the FEM domain decomposition method [60, p. 25] due to the fact that Gauss-Seidel (resp. Jacobi) algorithm is formally a multiplicative (resp. additive) Schwarz method [41, p. 134].

Sound shielding simulation by coupled discontinuous Galerkin and fast boundary element methods

View Article

Journal Information

Published in Engineering Applications of Computational Fluid Mechanics, 2022

S. Proskurov, R. Ewert, M. Lummer, M. Mößner, J. W. Delfs

Many details and methodologies have to be taken into account for an efficient numerical implementation of the MLFMM which cannot be covered in this paper. Since the FMCAS code is almost a standard implementation it is possible to refer to the literature (Sylvand, 2003; Wolf & Lele, 2009, 2010). In our version of the MLFMM the iterative solvers from the Portable Extensible Toolkit for Scientific Computation (PETSc) library are used for improved performance and code optimisation. In particular, the GMRES solver was preferred for its superior convergence property that was employed together with the Generalised Additive Schwarz Method (GASM) (Goossens et al., 1996) to precondition the system of linear equations on a triangulated grid.

Additive Schwarz method

Explore chapters and articles related to this topic

Meshless Methods with Radial Basis Functions

Sound shielding simulation by coupled discontinuous Galerkin and fast boundary element methods