Recent advances have shown that block recursive approximate factorizations provide among the best preconditioners for solving elasticity equations on large 3D meshes such as arising in geomechanical applications. However, to get full efficiency of these methods, a wide range of implementation...

In this paper, to obtain an efficient parallel algorithm to solve sparse block-tridiagonal linear systems, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are suitable when the desired goal is to maximize parallelism....

We consider the discrete system resulting from mixed finite element approximation of a second-order elliptic boundary value problem with Crouzeix–Raviart non-conforming elements for the vector valued unknown function and piece-wise constants for the scalar valued unknown function. Since the...

In this paper we analyze a preconditioner for mixed finite element systems arising in the approximation of a second order elliptic problem with Neumann boundary conditions by triangular non-conforming elements. This problem stems from the so called projection methods for the unsteady...

We develop numerical methods for the computer simulation and modeling of a three dimensional heat transfer problem in biological bodies. The technique is intended for the temperature predications and parameter measurements in thermal medical practices and for the studies of thermomechanical...

A non-overlapping domain decomposition algorithm of Neumann–Neumann type for solving variational inequalities arising from the elliptic boundary value problems in two dimensions with unilateral boundary condition is presented. We suppose that boundary with inequality condition is...

Separate displacement preconditioners are studied in the context of outer–inner iterations for a model in 3D nonlinear elasticity. Such a preconditioner, already known to be efficient for linear models, arises as the discretization of three independent Laplacian operators. In this paper the...