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Toward robust scalable algebraic multigrid solvers

Tuminaro, Raymond S.; Siefert, Christopher S.; Hu, Jonathan J.; Gaidamour, Jeremie G.

This talk highlights some multigrid challenges that arise from several application areas including structural dynamics, fluid flow, and electromagnetics. A general framework is presented to help introduce and understand algebraic multigrid methods based on energy minimization concepts. Connections between algebraic multigrid prolongators and finite element basis functions are made to explored. It is shown how the general algebraic multigrid framework allows one to adapt multigrid ideas to a number of different situations. Examples are given corresponding to linear elasticity and specifically in the solution of linear systems associated with extended finite elements for fracture problems.

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TYPE Conference YEAR 2010
OSTI

A fully implicit method for 3D quasi-steady state magnetic advection-diffusion

Siefert, Christopher S.; Robinson, Allen C.

We describe the implementation of a prototype fully implicit method for solving three-dimensional quasi-steady state magnetic advection-diffusion problems. This method allows us to solve the magnetic advection diffusion equations in an Eulerian frame with a fixed, user-prescribed velocity field. We have verified the correctness of method and implementation on two standard verification problems, the Solberg-White magnetic shear problem and the Perry-Jones-White rotating cylinder problem.

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TYPE SAND Report YEAR 2009
OSTIDOI

Highly scalable linear solvers on thousands of processors

Siefert, Christopher S.; Tuminaro, Raymond S.; Domino, Stefan P.; Robinson, Allen C.

In this report we summarize research into new parallel algebraic multigrid (AMG) methods. We first provide a introduction to parallel AMG. We then discuss our research in parallel AMG algorithms for very large scale platforms. We detail significant improvements in the AMG setup phase to a matrix-matrix multiplication kernel. We present a smoothed aggregation AMG algorithm with fewer communication synchronization points, and discuss its links to domain decomposition methods. Finally, we discuss a multigrid smoothing technique that utilizes two message passing layers for use on multicore processors.

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TYPE SAND Report YEAR 2009
OSTIDOI
Results 76–100 of 114
Results 76–100 of 114