Related papers: Generating Equidistributed Meshes in 2D via Domain…
We propose a new numerical domain decomposition method for solving elliptic equations on compact Riemannian manifolds. One advantage of this method is its ability to bypass the need for global triangulations or grids on the manifolds.…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
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…
We present a Schur complement Domain Decomposition (DD) algorithm for the solution of frequency domain multiple scattering problems. Just as in the classical DD methods we (1) enclose the ensemble of scatterers in a domain bounded by an…
In this paper we are concerned with restricted additive Schwarz with local impedance transformation conditions for a family of Helmholtz problems in two dimensions. These problems are discretized by the finite element method with conforming…
This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov-Poincar\'e operator and the…
We investigate the application of the additive overlapping Schwarz domain decomposition method as a preconditioner for the large sparse linear systems arising in graph-based nonlinear least-squares problems, specifically the pose-graph…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
We propose new domain decomposition methods for systems of partial differential equations in two and three dimensions. The algorithms are derived with the help of the Smith factorization of the operator. This could also be validated by…
We present in this paper the results of a research motivated by the need of a very fast solution of thermal flow in solar receivers. These receivers are composed by a large number of parallel pipes with the same geometry. We have introduced…
Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution of Maxwell's equations is evaluated using…
This paper introduces a novel, robust, and computationally efficient framework for high-quality quadrilateral mesh generation on general two-dimensional domains. The core of the proposed approach is a novel method for computing cross fields…
In this paper, we study the stability of the non symmetric version of the Nitsche's method without penalty for domain decomposition. The Poisson problem is considered as a model problem. The computational domain is divided into two…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
We present an analysis of the additive average Schwarz preconditioner with two newly proposed adaptively enriched coarse spaces which was presented at the 23rd International conference on domain decomposition methods in Korea, for solving…
A new functional is presented for variational mesh generation and adaptation. It is formulated based on combining the equidistribution and alignment conditions into a single condition with only one dimensionless parameter. The functional is…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
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…
The presented article contains a 3D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes of a prescribed volume V_0 of elements. The finite volume meshes are used with the Finite Element…
In this paper, we partially answer open questions about the convergence of overlapping Schwarz methods. We prove that overlapping Schwarz methods with Dirichlet transmission conditions for semilinear elliptic and parabolic equations always…