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Novel algebraic multigrid solver for real-life industrial applications

Project information

Grant agreement ID: 21927

  • Start date

    1 October 2006

  • End date

    31 December 2007

Funded under:

FP6-MOBILITY

Coordinated by:

TECHNISCHE UNIVERSITEIT DELFT

Netherlands

Objective

An important constraint on our ability to numerically simulate important physical processes is our ability to solve the linear and non-linear systems of equations that result from discretization of continuous mathematical models (partial differential equations). A useful computational model of a physical process is one that is accurate (includes features and scales that are important to the scientific goals) and that can be solved efficiently (acceptable computational solution time on available resources).

Multiscale methods, such as multigrid, provide optimal order solution techniques for a wide range of these discrete models; however, efficient modelling of many important physical phenomena remains intractable. We propose to continue the recent development of adaptive algebraic multigrid methods and, thus, develop efficient solvers for industrial applications, such as seismic wave migration, electromagnetics, and prosthesis design.

Recent advances in multigrid methodology, implemented in the adaptive algebraic multigrid algorithm, reduce the reliance of multigrid on limiting assumptions about the performance of its component parts. Complementarity between the chosen relaxation algorithm and the coarse-grid correction stage is, instead, achieved through a careful construction of the grid-transfer operators that explicitly depends on the discrete model and performance of relaxation. While this, in principle, allows efficient multigrid solution of a much larger class of problems, other challenges arise in the implementation of these ideas, particularly when the mathematical model includes complex-valued coefficients, a large near null space, or a system of PDEs. Such models, however, are ubiquitous in modern industrial applications, and so we seek to extend the adaptive algebraic multigrid algorithm to overcome such challenges.

Coordinator

TECHNISCHE UNIVERSITEIT DELFT

Address

Julianalaan 134
Delft

Netherlands

Project information

Grant agreement ID: 21927

  • Start date

    1 October 2006

  • End date

    31 December 2007

Funded under:

FP6-MOBILITY

Coordinated by:

TECHNISCHE UNIVERSITEIT DELFT

Netherlands