A Generalization of the Schwarz Alternating Method to an Arbitrary Number of Subdomains.
A generalization of the steepest descent method for matrix functions.
A generalized ADI iterative method.
A Generalized Conjugate Gradient, Least Square Method.
A hierarchical preconditioner for the mortar finite element method.
A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations.
A Kaczmarz-Kovarik algorithm for symmetric ill-conditioned matrices.
A Legendre spectral collocation method for the biharmonic Dirichlet problem
A Legendre Spectral Collocation Method for the Biharmonic Dirichlet Problem
A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacian of the solution on the two vertical sides of the square. The Schur complement system is solved by a...
A linear acceleration row action method for projecting onto subspaces.
A modification of minimal residual iterative method to solve linear systems.
A modification of the two-level algorithm with overcorrection
In this paper we analyse an algorithm which is a modification of the so-called two-level algorithm with overcorrection, published in [2]. We illustrate the efficiency of this algorithm by a model example.
A moving mesh fictitious domain approach for shape optimization problems
A new numerical method based on fictitious domain methods for shape optimization problems governed by the Poisson equation is proposed. The basic idea is to combine the boundary variation technique, in which the mesh is moving during the optimization, and efficient fictitious domain preconditioning in the solution of the (adjoint) state equations. Neumann boundary value problems are solved using an algebraic fictitious domain method. A mixed formulation based on boundary Lagrange multipliers is...
A multigrid algorithm for higher order finite elements on sparse grids.
A Multigrid Method for a Parameter Dependent Problem in Solid Mechanics.
A multigrid method for a Petrov-Galerkin discretization of the Stokes equations.
A multilevel method with correction by aggregation for solving discrete elliptic problems
The author studies the behaviour of a multi-level method that combines the Jacobi iterations and the correction by aggragation of unknowns. Our considerations are restricted to a simple one-dimensional example, which allows us to employ the technique of the Fourier analysis. Despite of this restriction we are able to demonstrate differences between the behaviour of the algorithm considered and of multigrid methods employing interpolation instead of aggregation.
A multilevel preconditioner for the mortar method for nonconforming P1 finite element
A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming P1 finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some numerical results confirming...
A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices
A necessary and sufficient to guarantee feasibility of the interval Gaussian algorithms for a class of matrices. We apply the interval Gaussian algorithm to an interval matrix the comparison matrix of which is irreducible and diagonally dominant. We derive a new necessary and sufficient criterion for the feasibility of this method extending a recently given sufficient criterion.
A network programming approach in solving Darcy's equations by mixed finite-element methods.