Displaying similar documents to “Resilient asynchronous primal Schur method”

Numerical comparison of different choices of interface weights in the BDDC method

Čertíková, Marta, Burda, Pavel, Šístek, Jakub

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Balancing Domain Decomposition by Constraints (BDDC) belongs to the class of primal substructuring Domain Decomposition (DD) methods. DD methods are iterative methods successfully used in engineering to parallelize solution of large linear systems arising from discretization of second order elliptic problems. Substructuring DD methods represent an important class of DD methods. Their main idea is to divide the underlying domain into nonoverlapping subdomains and solve many relatively...

A new block triangular preconditioner for three-by-three block saddle-point problem

Jun Li, Xiangtuan Xiong (2024)

Applications of Mathematics

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In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties...

Parallel solution of elasticity problems using overlapping aggregations

Roman Kohut (2018)

Applications of Mathematics

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The finite element (FE) solution of geotechnical elasticity problems leads to the solution of a large system of linear equations. For solving the system, we use the preconditioned conjugate gradient (PCG) method with two-level additive Schwarz preconditioner. The preconditioning is realised in parallel. A coarse space is usually constructed using an aggregation technique. If the finite element spaces for coarse and fine problems on structural grids are fully compatible, relations between...

On conditioning of Schur complements of H-TFETI clusters for 2D problems governed by Laplacian

Petr Vodstrčil, Jiří Bouchala, Marta Jarošová, Zdeněk Dostál (2017)

Applications of Mathematics

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Bounds on the spectrum of the Schur complements of subdomain stiffness matrices with respect to the interior variables are key ingredients in the analysis of many domain decomposition methods. Here we are interested in the analysis of floating clusters, i.e. subdomains without prescribed Dirichlet conditions that are decomposed into still smaller subdomains glued on primal level in some nodes and/or by some averages. We give the estimates of the regular condition number of the Schur...

On selection of interface weights in domain decomposition methods

Čertíková, Marta, Šístek, Jakub, Burda, Pavel

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Different choices of the averaging operator within the BDDC method are compared on a series of 2D experiments. Subdomains with irregular interface and with jumps in material coefficients are included into the study. Two new approaches are studied along three standard choices. No approach is shown to be universally superior to others, and the resulting recommendation is that an actual method should be chosen based on properties of the problem.

Multigrid Methods for (Multilevel) Structured Matrices Associated with a Symbol and Related Application

Marco Donatelli, Stefano Serra Capizzano (2013)

Bollettino dell'Unione Matematica Italiana

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When dealing with large linear systems with a prescribed structure, two key ingredients are important for designing fast solvers: the first is the computational analysis of the structure which is usually inherited from an underlying infinite dimensional problem, the second is the spectral analysis which is often deeply related to a compact symbol, again depending on the infinite dimensional problem of which the linear system is a given approximation. When considering the computational...

Domain decomposition methods for solving the Burgers equation

Robert Cimrman (1999)

Applications of Mathematics

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This article presents some results of numerical tests of solving the two-dimensional non-linear unsteady viscous Burgers equation. We have compared the known convergence and parallel performance properties of the additive Schwarz domain decomposition method with or without a coarse grid for the model Poisson problem with those obtained by experiments for the Burgers problem.

A numerical study on Neumann-Neumann methods for approximations on geometrically refined boundary layer meshes II. Three-dimensional problems

Andrea Toselli, Xavier Vasseur (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we present extensive numerical tests showing the performance and robustness of a Balancing Neumann-Neumann method for the solution of algebraic linear systems arising from finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in three dimensions. The numerical results are in good agreement with the theoretical bound for the condition number of the preconditioned operator derived in [Toselli and Vasseur, ...

Numerical Study of Two Sparse AMG-methods

Janne Martikainen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A sparse algebraic multigrid method is studied as a cheap and accurate way to compute approximations of Schur complements of matrices arising from the discretization of some symmetric and positive definite partial differential operators. The construction of such a multigrid is discussed and numerical experiments are used to verify the properties of the method.