Space-Time Discretizations Enabling Parallel-in-Time Simulations (Section 3.4 Numerical Analysis)
Abstract
The objective of the proposed research is to develop finite element upscaling techniques for broad classes of nonstationary and nonlinear PDEs, discretized in a combined space-time domain with the goal to achieve substantial savings in memory. Finite element upscaling techniques are most directly accessible when employing discretizations that lead to either symmetric positive definite or symmetric saddle-point problems. To meet this requirement, a least-squares discretization approach augmented with constraints will be attempted. The constraints will be imposed to ensure conservation of certain quantities of physical interest (depending on the application). For time-dependent problems, two approaches will be tried: to discretize in time and then apply at every time-step discretization in space and then utilize an upscaling technique developed previously by the PI, whereas in the second approach discretization in the combined space-time domain will be used. In both cases, least-squares formulation will be used. Both strategies are expected to achieve at least some measure of dimension reduction, and perhaps a significant amount. In the time-stepping case with dimension reduction in space, existing parallel-in-time techniques will be used which will still save memory and hence can allow for larger time slabs which will increase the effect of parallelization. The effort will focus on the combined space-time approach since it offers more uniform treatment and in particular offers the additional potential for utilizing existing parallel discretization and solvers libraries.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510590
Entities
People
- Panayot Vassilevski
Organizations
- Army Contracting Command
- Portland State University
- United States Army