An Element-based Spectrally-optimized Approximate Inverse Preconditioner for the Euler Equations
Abstract
We introduce a method for constructing an element-by-element sparse approximate inverse (SAI) preconditioner designed to fully exploit the maximum degree of parallelism available in a spectral element modeling environment. This new preconditioning approach is based on a spectral optimization of a low-resolution preconditioned system matrix rather than on a Frobenius norm optimization (FNO) of the full-resolution preconditioned system matrix. We show that the local preconditioning matrices obtained via this element-based, spectrum-optimized (ESBO) 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 2-D spectral element method (SEM) formulations for a simple linear conservation law and for the fully-compressible 2-D Euler equations with various boundary conditions. For the latter model, the EBSO approach outperforms the FNO approach and, for sufficiently large Courant Number, model wall-clock time is reduced by a factor of 2.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2011
- Accession Number
- ADA547034
Entities
People
- Carlos F. Borges
- F. X. Giraldo
- L. E. Carr Iii
Organizations
- Naval Postgraduate School