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Analysis of Preconditioning and Relaxation Operators for the Discontinuous Galerkin Method Applied to Diffusion
- Publication Year :
- 2001
- Publisher :
- United States: NASA Center for Aerospace Information (CASI), 2001.
-
Abstract
- The explicit stability constraint of the discontinuous Galerkin method applied to the diffusion operator decreases dramatically as the order of the method is increased. Block Jacobi and block Gauss-Seidel preconditioner operators are examined for their effectiveness at accelerating convergence. A Fourier analysis for methods of order 2 through 6 reveals that both preconditioner operators bound the eigenvalues of the discrete spatial operator. Additionally, in one dimension, the eigenvalues are grouped into two or three regions that are invariant with order of the method. Local relaxation methods are constructed that rapidly damp high frequencies for arbitrarily large time step.
- Subjects :
- Theoretical Mathematics
Subjects
Details
- Language :
- English
- Database :
- NASA Technical Reports
- Publication Type :
- Report
- Accession number :
- edsnas.20010086238
- Document Type :
- Report