Examination and Significance of Sparse Preconditioners for High-Order Finite Element Systems

Award Information
Agency: Department of Energy
Branch: N/A
Contract: DE-FG02-08ER85154
Agency Tracking Number: N/A
Amount: $99,781.00
Phase: Phase I
Program: SBIR
Awards Year: 2008
Solicitation Year: 2008
Solicitation Topic Code: 39 b
Solicitation Number: DE-PS02-07ER07-36
Small Business Information
Tech-x Corporation
5621 Arapahoe Avenue, Suite A, Boulder, CO, 80303
DUNS: 806486692
HUBZone Owned: N
Woman Owned: N
Socially and Economically Disadvantaged: N
Principal Investigator
 Travis Austin
 Dr.
 (303) 996-2038
 austin@txcorp.com
Business Contact
 Laurence Nelson
Title: Mr.
Phone: (720) 974-1856
Email: lnelson@txcorp.com
Research Institution
N/A
Abstract
Today, higher-order polynomials are being employed more frequently in finite element discretizations, used in the simulation of previ¬ously intractable problems of importance to the DOE. The use of higher-order polynomials creates new challenges in efficiently solving the corresponding finite element matrix problems. Precondi¬tioners are used to achieve good convergence behavior; however, the design of preconditioners with minimal memory usage and minimal application cost is not trivial. Sparser precondition¬ers are needed that significantly reduce the overall memory consumption, but still maintain good convergence behavior. This project will develop preconditioners for high-order polynomials that have sparsity patterns equivalent to those generated by first-order polyno¬mials. These sparse preconditioners will be matrices of the same rank developed on a finite element mesh constructed from the Gauss nodes of the high-order polynomials. Commercial Applications and other Benefits as described by the awardee: The new preconditioners should enable DOE projects employing high-order ¿nite elements to achieve greater efficiency in their simulations on today¿s supercomputers. As users begin to employ these preconditioners in their codes, consulting opportunities would be expected to arise.

* information listed above is at the time of submission.

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