Advancing analysis capabilities in ANSYS through solver technology.
Algorithmes de calcul du maximum des formes quadratiques sur la boule unité de la norme du maximum.
An additive Schwarz method for mortar Morley finite element discretizations of 4th order elliptic problem in 2D.
An Algorithm for Scaling Matrices and Computing the Minimum Cycle Mean in a Digraph.
An analysis of the pole placement problem I: The single-input case.
An analysis of the pole placement problem. II: The multi-input case.
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 incomplete-factorization preconditioning using repeated red-black ordering.
An optimum iteration for the matrix polar decomposition.
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...
Applications of Shortest Path Algorithms to Matrix Scalings.
Block triangular preconditioners for -matrices and Markov chains.
Circulant preconditioners for convolution-like integral equations with higher-order quadrature rules.
Combining the preconditioned conjugate gradient method and a matrix iterative method
The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.
Comparing multilevel coarsening strategies.
Concerning decomposition of a system of linear algebraic equations
Condition numbers of the Krylov bases and spaces associated with the truncated iteration.
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.