Neumann-Neumann algorithms for spectral elements in three dimensions
Neumann-Neumann methods for vector field problems.
Norm Bounds for Rational Matrix Functions.
Norm Estimates for Inverses of Vandermonde Matrices.
Numerical experiments with algebraic multilevel preconditioners.
Numerical experiments with parallel orderings for ILU preconditioners.
Numerical stability of the cyclic Richardson iteration.
Numerical study of two sparse AMG-methods
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.
Numerical Study of Two Sparse AMG-methods
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.
Obtaining bounds on the two norm of a matrix from the splitting lemma.
On a hierarchical basis multilevel method with nonconforming P1 elements.
On a parallel implementation of the mortar element method
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
On additive scharz preconditioners for sparse grid discretizations.
On Asymptotically Best Norms for Powers of Operators.
On block diagonal and Schur complement preconditioning.
On Condition Numbers and the Distance to the Nearest Ill-posed Problem.
On generalized methods of the transfer of conditions
The methods of the transfer of conditions are generalized so that they also cover the direct methods leading to the diagonalization of the original matrix of a system with a band matrix. Part 3 is devoted to the numerical stability of methods of the transfer of conditions described in author's previous paper. Finally, it is shown how to obtain a particular method by the choice parameters of the general algorithm.
On parallel two-stage methods for Hermitian positive definite matrices with applications to preconditioning.
On perfect conditioning of Vandermonde matrices on the unit circle.