EFFICIENT AND ACCURATE STRUCTURE PRESERVING SCHEMES FOR COMPLEX NONLINEAR SYSTEMS
Abstract
The ability of fast and accurate simulation of complex phenomena governed by highly complex nonlinear systems is central to our understanding of many important issues which play critical roles to Air Force s mission, such as advanced materials, quantum mechanics, semiconductors, optimal transport, non-convex optimization, and machine learning. However, it is a tremendous challenge to design numerical schemes for highly complex nonlinear systems which preserve energy dissipation/conservation, and/or physical constraints such as positivity, mass conservation, etc, as simple fully implicit or explicit type approaches for the nonlinear terms will induce severe stability conditions on the time step so they are not efficient in practice. We propose to develop innovative, structure preserving schemes for a large class of complex nonlinear systems with structures such as energy dissipation/conservation, positivity, mass conservation. In particular, we aim to develop highly effcient time-marching schemes, which can be combined with any consistent Galerkin-type spatial discretization, are unconditionally energy stable, and preserve essential physical constraints such as positivity and/or mass conservation. The proposed methodology will lead to numerical predictive tools that extend the applicability of mathematical and experimental analysis, and contribute to better understanding of a number of pressing physics and engineering problems that are of critical importance to Air Force s mission.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010309
Entities
People
- Jie Shen
Organizations
- Air Force Office of Scientific Research
- Purdue University
- United States Air Force