Advancing analysis capabilities in ANSYS through solver technology.
Algebraic approach to domain decomposition
An iterative procedure containing two parameters for solving linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numerical example is given as an illustration.
Algebraic domain decomposition solver for linear elasticity
We generalize the overlapping Schwarz domain decomposition method to problems of linear elasticity. The convergence rate independent of the mesh size, coarse-space size, Korn’s constant and essential boundary conditions is proved here. Abstract convergence bounds developed here can be used for an analysis of the method applied to singular perturbations of other elliptic problems.
Algebraic multigrid smoothing property of Kaczmarz's relaxation for general rectangular linear systems.
An additive Schwarz method for mortar Morley finite element discretizations of 4th order elliptic problem in 2D.
An aggregation-based algebraic multigrid method.
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab)...
An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems
This paper extends previous results on nonlinear Schwarz preconditioning (Cai and Keyes 2002) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The nonlocal finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in Jones...
An iterative method of alternating type for systems with special block matrices
An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.
An Iterative Substructuring Algorithm for Equilibrium Equations.
Analysis of domain decomposition for non symmetric problems : application to the Navier-Stokes equations
Analysis of multilevel decomposition iterative methods for mixed finite element methods
Analysis of patch substructuring methods
Patch substructuring methods are non-overlapping domain decomposition methods like classical substructuring methods, but they use information from geometric patches reaching into neighboring subdomains condensated, on the interfaces to enhance the performance of the method, while keeping it non-overlapping. These methods are very convenient to use in practice, but their convergence properties have not been studied yet. We analyze geometric patch substructuring methods for the special case of one...
Analysis of the Schwarz algorithm for mixed finite elements methods
Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework.
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a set of assumptions...
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a...
Application of the multigrid methods for solving Stefan problem
Asymptotic stability of a 9-point multigrid algorithm for convection-diffusion equations.
Behavior of plane relaxation methods as multigrid smoothers.