Fast Multiscale Algorithms for Wave Propagation in Heterogeneous Environments
Abstract
The objective of this research project was to further develop and integrate numerical methods for the fast and accurate simulation of wave propagation problems in the time domain. In support of the long-term goal of creating high-quality software for simulating waves, we seek methods which are not only efficient, but which are reliable in that both their stability and the accuracy of the results are essentially guaranteed. In support of this goal we have developed: (i.) convenient implementations of optimal local radiation boundary sequences for isotropic waves, with implementations in a wide variety of popular discretization schemes for Maxwell's equations; (ii.) extensions of these sequences to more complex systems arising in linear elasticity; (iii.) new highly efficient energy-stable discretization schemes on structured grids - these include methods based on Hermite interpolation and compact difference schemes constructed using Galerkin techniques; (iv.)stable coupling of the efficient structured grid methods with upwind discontinuous Galerkin methods defined on unstructured grids - using hybrid grids allows us to treat very complex geometry with efficency comparable to simple domains; (v.) natural upwind discontinuous Galerkin discretizations for wave equations in second order form - using the second order form for complex systems results in fewer dependent variables.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 07, 2016
- Accession Number
- AD1006842
Entities
People
- Thomas Hagstrom
Organizations
- Southern Methodist University