UN CO RR EC TE D PR O O F 1 On Block Preconditioners for Generalized Saddle 2 Point Problems
نویسنده
چکیده
We assume that A is n×n and C is an m×m matrix. Many such systems arise from 9 the discretization of (systems of) partial differential equations. For example, Stokes 10 equations discretized with stable finite elements or a mixed finite element method 11 for second order elliptic PDEs lead to a positive definite matrix A and to C = 0, so 12 that (1) has a genuine saddle point structure. Certain other PDE problems may result 13 in an indefinite matrix A, or a semidefinite matrix A with a large kernel, which gives 14 (1) the structure of a so called generalized saddle point problem. Linear elasticity 15 equations modelling nearly incompressible materials discretized with mixed finite 16 elements result in both matrices A and C being positive definite, having thus a nature 17 of a penalized saddle point problem. All systems mentioned above have a common 18 feature that the matrix of (1) is indefinite. 19
منابع مشابه
UN CO RR EC TE D PR O O F 1 Penalty Robin - Robin Domain Decomposition Schemes 2 for Contact Problems of Nonlinear Elastic Bodies 3
متن کامل
UN CO RR EC TE D PR O O F 1 Mesh Regularization in Bank - Holst Parallel 2 hp - Adaptive Meshing 3 Randolph
متن کامل
UN CO RR EC TE D PR O O F 1 A Hybrid Discontinuous Galerkin Method 2 for Darcy - Stokes Problems 3
We propose and analyze a hybrid discontinuous Galerkin method for the solution 10 of incompressible flow problems, which allows to deal with pure Stokes, pure Darcy, and 11 coupled Darcy-Stokes flow in a unified manner. The flexibility of the method is demonstrated 12 in numerical examples.
متن کاملUN CO RR EC TE D PR O O F 1 Stable BETI Methods in Electromagnetics
In this paper we present a stable boundary element tearing and interconnecting 6 domain decomposition method for the parallel solution of the electromagnetic wave equation 7 with piecewise constant wave numbers. In particular we consider stable boundary integral 8 formulations and generalized Robin type transmission conditions to ensure unique solvability 9 of the local subproblems. Numerical r...
متن کامل