相关论文: Coarse spaces for non-symmetric two-level precondi…

Coarse spaces are essential to ensure robustness w.r.t. the number of subdomains in two-level overlapping Schwarz methods. Robustness with respect to the coefficients of the underlying partial differential equation (PDE) can be achieved by…

This paper proposes a two-level restricted additive Schwarz (RAS) method for multiscale PDEs, built on top of a multiscale spectral generalized finite element method (MS-GFEM). The method uses coarse spaces constructed from optimal local…

In this paper, we design and analyze two new methods based on additive average Schwarz -- AAS method introduced in \cite{MR1943457}. The new methods design for elliptic problems with highly heterogeneous coefficients. The methods are of the…

Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. The GenEO coarse space has been shown to lead to a fully robust two-level Schwarz preconditioner which scales well over…

The additive Schwarz method is usually presented as a preconditioner for a PDE linearization based on overlapping subsets of nodes from a global discretization. It has previously been shown how to apply Schwarz preconditioning to a…

We propose a simple domain decomposition method for $d$-dimensional elliptic PDEs which involves an overlapping decomposition into local subdomain problems and a global coarse problem. It relies on a space-filling curve to create equally…

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…

In this paper we consider Schwarz domain decomposition applied to the generation of 2D spatial meshes by a local equidistribution principle. We briefly review the derivation of the local equidistribution principle and the appropriate choice…

Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…

In this paper, we are interested in scalable Domain Decomposition Methods (DDM). To this end, we introduce and study a new Coarse Space Correction algorithm for Optimized Schwarz Methods(OSM) : the DCS-DGLC algorithm. The main idea is to…

In this paper, we extend the additive average Schwarz method to solve second order elliptic boundary value problems with heterogeneous coefficients inside the subdomains and across their interfaces by the mortar technique, where the mortar…

In this article, we analyse the convergence behaviour and scalability properties of the one-level Parallel Schwarz method (PSM) for domain decomposition problems in which the boundaries of many subdomains lie in the interior of the global…

A non-intrusive proper generalized decomposition (PGD) strategy, coupled with an overlapping domain decomposition (DD) method, is proposed to efficiently construct surrogate models of parametric linear elliptic problems. A parametric…

We analyze the convergence of the one-level overlapping domain decomposition preconditioner SORAS (Symmetrized Optimized Restricted Additive Schwarz) applied to a generic linear system whose matrix is not necessarily symmetric/self-adjoint…

We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for example, when a (partial) differential equation is posed and…

Additive overlapping Schwarz Methods are iterative methods of the domain decomposition type for the solution of partial differential equations. Numerical and parallel scalability of these methods can be achieved by adding coarse levels. A…

The Helmholtz equation poses significant computational challenges due to its oscillatory solutions, particularly for large wavenumbers. Inspired by the Schur complement system for elliptic problems, this paper presents a novel…

This paper introduces the multiplicative variant of the recently proposed asynchronous additive coarse-space correction method. Definition of an asynchronous extension of multiplicative correction is not straightforward, however, our…

Motivated by recent work on coarse spaces for Helmholtz problems, we provide in this paper a comparative study on the use of spectral coarse spaces of GenEO type for heterogeneous indefinite elliptic problems within an additive overlapping…

The oscillatory waves require sufficient degrees of freedom to resolve. That restriction usually applies also to coarse problems for Schwarz methods. The resulting coarse problem is then too large. To address the issue, a new form of…