A robust and parallel multigrid method for convection diffusion equations.
A subspace correction method for discontinuous Galerkin discretizations of linear elasticity equations
We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued piecewise linear discontinuous finite element space, that are optimal with respect to the mesh size and the Lamé parameters. The pure displacement, the mixed and the traction free problems are discussed in detail. We present a convergence analysis of the proposed...
A theory for ungrounded electrical grids and its application to the geophysical exploration of layered strata
A two parameter iterative method for solving algebraic systems of domain decomposition type
An iterative procedure containing two parameters for linear algebraic systems originating from the domain decomposition technique is proposed. The optimization of the parameters is investigated. A numeric example is given as an illustration.
Adaptive algorithm for stochastic Galerkin method
We introduce a new tool for obtaining efficient a posteriori estimates of errors of approximate solutions of differential equations the data of which depend linearly on random parameters. The solution method is the stochastic Galerkin method. Polynomial chaos expansion of the solution is considered and the approximation spaces are tensor products of univariate polynomials in random variables and of finite element basis functions. We derive a uniform upper bound to the strengthened Cauchy-Bunyakowski-Schwarz...
Adaptive data distribution for concurrent continuation.
Adaptive reduction-based multigrid for nearly singular and highly disordered physical systems.
Advances techniques for the direct, numerical solution of Poisson's equation
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
An implicit approximate inverse preconditioner for saddle point problems.
An incomplete-factorization preconditioning using repeated red-black ordering.
An introduction to hierarchical matrices
Analysis of a Damped Nonlinear Multilevel Method.
Analysis of the Du Fort-Frankel method for linear systems
Application of relaxation scheme to degenerate variational inequalities
In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.
Approximation of Hopf Bifurcation.
Approximation of the scattering amplitude and linear systems.
Axissymmetric Free Surface Seepage
Comparison of Vlasov solvers for spacecraft charging simulation
The modelling and the numerical resolution of the electrical charging of a spacecraft in interaction with the Earth magnetosphere is considered. It involves the Vlasov-Poisson system, endowed with non standard boundary conditions. We discuss the pros and cons of several numerical methods for solving this system, using as benchmark a simple 1D model which exhibits the main difficulties of the original models.
Composite grid finite element method: Implementation and iterative solution with inexact subproblems
This paper concerns the composite grid finite element (FE) method for solving boundary value problems in the cases which require local grid refinement for enhancing the approximating properties of the corresponding FE space. A special interest is given to iterative methods based on natural decomposition of the space of unknowns and to the implementation of both the composite grid FEM and the iterative procedures for its solution. The implementation is important for gaining all benefits of the described...