Efficient Strong Stability Preserving Time Discretizations and Robust Automated Splitting for Time Evolution of Problems with Multiple Time-Scales
Abstract
Strong stability preserving (SSP) high order time discretizations were developed to ensure non-linear stability properties necessary in the numerical solution of hyperbolic partial differential equa-tions with discontinuous solutions. The research in the field of SSP methods centers around thesearch for high order SSP methods where the allowable time-step is as large as possible, per function evaluation required in each time-step.Of particular interest to us are equations that can be additively split into non-stiff (slow time-scale) and stiff (fast time-scale) components, where the stiff component is linear. In typical cases we find that when the SSP property is to be preserved, the overall time-step is limited by the stiff component even when specially designed methods such as implicit-explicit (IMEX) are used. The goal of this project is to develop efficient high order SSP time-stepping methods for multi-scale timestepping and also to develop efficient and automated optimal splitting to preserve stability.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 28, 2018
- Source ID
- FA95501810383
Entities
People
- Sigal Gottlieb
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Massachusetts