An Element-Based Spectrally Optimized Approximate Inverse Preconditioner for the Euler Equations
| Autor: | Francis X. Giraldo, Carlos F. Borges, Lester E. Carr |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Conservation law
Preconditioner Applied Mathematics Courant–Friedrichs–Lewy condition Mathematical analysis Spectral element method Inverse Computer Science::Numerical Analysis Mathematics::Numerical Analysis Euler equations Computational Mathematics symbols.namesake symbols Galerkin method Sparse matrix Mathematics |
| Zdroj: | SIAM Journal on Scientific Computing. 34:B392-B420 |
| ISSN: | 1095-7197 1064-8275 |
| Popis: | We introduce a method for constructing an element-by-element sparse approximate inverse (SAI) preconditioner designed to be effective in a massively parallel spectral element modeling environment involving nonsymmetric systems. This new preconditioning approach is based on a spectral optimization of a low-resolution preconditioned system matrix. We show that the local preconditioning matrices obtained via this element-based spectrum-optimized (EBSO) approach may be applied to arbitrarily high-resolution versions of the same system matrix without appreciable loss of preconditioner performance. We demonstrate the performance of the EBSO preconditioning approach using two-dimensional spectral element method formulations for a simple linear conservation law and for the fully compressible two-dimensional Euler equations with various boundary conditions. For the latter model running at sufficiently large Courant number, the EBSO preconditioner significantly reduces both iteration count and wall-clock time regar... |
| Databáze: | OpenAIRE |
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