to be developed in order to allow an efficient solution of even larger problems. This paper gives a review of the first hierarchical and purely matrix-based approach, algebraic multigrid (AMG). AMG can directly be applied, for instance, to efficiently solve various types of elliptic partial differential equations

itself across F is allowed. It is shown that it is possible to modify the standard centered difference approximation to maintain second order accuracy on the uniform grid even when F is not aligned with the grid. This approach is also compared with a discrete delta function approach to handling singular

Abstract. We consider a second-order parabolic equation in R d+1 with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally Hölder continuous in the space variables. We show that global Schauder estimates hold even

Implicit-explicit (IMEX) schemes have been widely used, especially in conjunction with spectral methods, for the time integration of spatially discretized PDEs of diffusion-convection type. Typically, an implicit scheme is used for the diffusion term and an explicit scheme is used

-called ‘repeated ’ or ‘recursive ’ red– black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by �(n 1 2 log2 (√5−1) ) where

We consider Quadratic Spline Collocation (QSC) methods for solving systems of two coupled linear second-order PDEs in two dimensions. The system of PDEs is treated as one entity; no decoupling is applied. Optimal order approximation to the solution is obtained, in the sense that the convergence

A digital signal processing (DSP) approach is used to study numerical methods for discretizing and solving linear elliptic par-tial differential equations (PDEs). Whereas conventional PDE anal-ysis techniques rely on matrix analysis and on a space-domain point of view to study the performance

We consider algebraic multilevel preconditioning methods based on the recursive use of a 2 × 2 block incomplete factorization procedure in which the Schur complement is approximated by a coarse grid matrix. As is well known, for discrete second-order elliptic PDEs, optimal convergence properties

We have observed Bose-Einstein condensation of sodium atoms. The atoms were trapped in a novel trap that employed both magnetic and optical forces. Evaporative cooling increased the phase-space density by 6 orders of magnitude within seven seconds. Condensates contained up to 5 3 10 5 atoms

set of coupled second order elliptic partial di#erential equations #PDEs# in two dimensions....