Examination and Significance of Sparse Preconditioners for High-Order Finite Element Systems
Today, higher-order polynomials are being employed more frequently in finite element discretizations, used in the simulation of previÂ¬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. PrecondiÂ¬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 preconditionÂ¬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 polynoÂ¬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 Â¿nite elements to achieve greater efficiency in their simulations on todayÂ¿s supercomputers. As users begin to employ these preconditioners in their codes, consulting opportunities would be expected to arise.
Small Business Information at Submission:
5621 Arapahoe Avenue Suite A Boulder, CO 80303
Number of Employees: