Spectral, Tensor and Domain Decomposition Methods for Fractional PDEs
Abstract
Fractional PDEs have recently found several geophysics and imaging science applications due to their nonlocal nature and their flexibility in capturing sharp transitions across interfaces. However, this nonlocality makes it challenging to design efficient solvers for such problems. In this paper, we introduce a spectral method based on an ultraspherical polynomial discretization of the Caffarelli–Silvestre extension to solve such PDEs on rectangular and disk domains. We solve the discretized problem using tensor equation solvers and thus can solve higher-dimensional PDEs. In addition, we introduce both serial and parallel domain decomposition solvers. We demonstrate the numerical performance of our methods on a 3D fractional elliptic PDE on a cube as well as an application to optimization problems with fractional PDE constraints.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Feb 12, 2022
- Source ID
- 10.1515/cmam-2021-0118
Entities
People
- Drew Kouri
- Harbir Antil
- Tianyi Shi
Organizations
- Air Force Office of Scientific Research
- Cornell University
- George Mason University
- National Nuclear Security Administration
- National Science Foundation
- Sandia National Laboratories