This proposal requests support to advance research on a novel and efficient method for approximation and solution of partial differential equations (PDEs) on spherical domains and other manifolds. The scheme relies on windowed Fourier approximations and domain decomposition. Objectives include the design of algorithms for solving time-dependent PDEs on spherical geometries; the development of a rigorous mathematical analysis of convergence and stability for such algorithms; the implementation of high performance and scalable solvers, including adaptive algorithms that are able to handle multi-scale problems; and to make software available that can be used and disseminated by the scientific community.
|Effective start/end date||9/15/15 → 7/31/19|
- National Science Foundation (NSF): $150,001.00
Partial differential equations