Accession Number:

ADA604707

Title:

A Polynomial-Based Nonlinear Least Squares Optimized Preconditioner for Continuous and Discontinuous Element-Based Discretizations of the Euler Equations

Descriptive Note:

Journal article preprint

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CA DEPT OF APPLIED MATHEMATICS

Report Date:

2014-01-01

Pagination or Media Count:

23.0

Abstract:

We introduce a method for constructing a polynomial preconditioner using a nonlinear least squares NLLS algorithm. We show that this polynomial-based NLLS-optimized PBNO preconditioner significantly improves the performance of 2-D continuous Galerkin CG and discontinuous Galerkin DG fluid dynamical research models when run in an implicit-explicit time integration mode. When employed in a serially computed Schur-complement form of the 2-D CG model with positive definite spectrum, the PBNO preconditioner achieves greater reductions in GMRES iterations and model wall-clock time compared to the analogous linear least-squares-derived Chebyshev polynomial preconditioner. Whereas constructing a Chebyshev preconditioner to handle the complex spectrum of the DG model would introduce an element of arbitrariness in selecting the appropriate convex hull construction of a PBNO preconditioner for the 2-D DG model utilizes precisely the same objective NLLS algorithm as for the CG model. As in the CG model, the PBNO preconditioner achieves significant reduction in GMRES iteration counts and model wall-clock time. Comparisons of the ability of the PBNO preconditioner to improve CG and DG model performance when employing the Stabilized Biconjugate Gradient algorithm BICGS and the basic Richardson RICH iteration are also included. In particular, we show that higher order PBNO preconditioning of the Richardson iteration which is run in a dot product free mode makes the algorithm competitive with GMRES and BICGS in a serial computing environment, especially when employed in a DG model. Because the NLLS-based algorithm used to construct the PBNO preconditioner can handle both positive definite and complex spectra without any need for algorithm modification, we suggest that the PBNO preconditioner is, for certain types of problems, an attractive alternative to existing polynomial preconditioners based on linear least-squares methods.

Subject Categories:

  • Atmospheric Sciences
  • Numerical Mathematics
  • Operations Research
  • Fluid Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE