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Examination and Significance of Sparse Preconditioners for High-Order Finite…

Award Information

Department of Energy
Award ID:
Program Year/Program:
2008 / SBIR
Agency Tracking Number:
Solicitation Year:
Solicitation Topic Code:
Solicitation Number:
Small Business Information
Tech-X Corporation
5621 Arapahoe Ave, Suite A Boulder, CO -
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Woman-Owned: No
Minority-Owned: No
HUBZone-Owned: No
Phase 1
Fiscal Year: 2008
Title: Examination and Significance of Sparse Preconditioners for High-Order Finite Element Systems
Agency: DOE
Contract: DE-FG02-08ER85154
Award Amount: $99,781.00


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.

Principal Investigator:

Travis Austin

Business Contact:

Laurence D. Nelson
Small Business Information at Submission:

Tech-x Corporation
5621 Arapahoe Avenue Suite A Boulder, CO 80303

EIN/Tax ID: 841256533
Number of Employees:
Woman-Owned: No
Minority-Owned: No
HUBZone-Owned: No