Volume 6, pp. 1-34, 1997.

The Gauss Center research in multiscale scientific computation

Achi Brandt

Abstract

The recent research of the author and his collaborators on multiscale computational methods is reported, emphasizing main ideas and inter-relations between various fields, and listing the relevant bibliography. The reported areas include: top-efficiency multigrid methods in fluid dynamics; atmospheric data assimilation; PDE solvers on unbounded domains; wave/ray methods for highly indefinite equations; many-eigenfunction problems and ab-initio quantum chemistry; fast evaluation of integral transforms on adaptive grids; multigrid Dirac solvers; fast inverse-matrix and determinant updates; multiscale Monte-Carlo methods in statistical physics; molecular mechanics (including fast force summation, fast macromolecular energy minimization, Monte-Carlo methods at equilibrium and the combination of small-scale equilibrium with large-scale dynamics); image processing (edge detection and segmentation); and tomography.

Full Text (PDF) [263 KB]

Key words

Scientific computation, multiscale, multi-resolution, multigrid, fluid dynamics, atmospheric flows, data assimilation, wave problems, Dirac equations, inverse matrix, Schrödinger operator, Monte-Carlo algorithms, critical slowing down, molecular mechanics, fast force summation, energy minimization, integro-differential equations, tomography, image processing, edge detection, segmentation

AMS subject classifications

34A50, 35A40, 44–04, 45–04, 65C05, 65F10, 65F15, 65F40, 65K10, 65M30, 65M50, 65M55,65N22, 65N25, 65N38, 65N55, 65R10, 65R20, 65Y05, 68U10, 70-08, 76-04, 76M20, 81-08, 81T80, 82-08, 82B80, 82C80, 92E99

Links to the cited ETNA articles

[32]Vol. 6 (1997), pp. 162-181 A. Brandt and I. Livshits: Wave-ray multigrid method for standing wave equations
[50]Vol. 6 (1997), pp. 106-119 Boris Diskin: Multigrid algorithm with conditional coarsening for the non-aligned sonic flow

ETNA articles which cite this article

Vol. 10 (2000), pp. 1-20 Achi Brandt: General highly accurate algebraic coarsening

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