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Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations

Antoine Gloria (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice ℤ d with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...

Numerical approximation of effective coefficients in stochastic homogenization of discrete elliptic equations

Antoine Gloria (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice ℤ d with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...

Numerical study of two sparse AMG-methods

Janne Martikainen (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

Janne Martikainen (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Observations Regarding Algorithms Required for Robust CFD Codes

F. T. Johnson, D. S. Kamenetskiy, R. G. Melvin, V. Venkatakrishnan, L. B. Wigton, D. P. Young, S. R. Allmaras, J. E. Bussoletti, C. L. Hilmes (2011)

Mathematical Modelling of Natural Phenomena

Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD has had its most favorable impact on the aerodynamic design of the high-speed cruise configuration of a transport. This success has raised expectations among aerodynamicists that the applicability of CFD can be extended to the full flight envelope. However, the complex nature...

On a construction of fast direct solvers

Milan Práger (2003)

Applications of Mathematics

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.

On iterative solution of nonlinear heat-conduction and diffusion problems

Herbert Gajewski (1977)

Aplikace matematiky

The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.

On the choice of iteration parameters in the Stone incomplete factorization

Karel Segeth (1983)

Aplikace matematiky

The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values...

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