Reduced basis approximations of the solutions to spectral fractional diffusion problems
-
Andrea Bonito
and
Ashley R. Zhang
Abstract
We consider the numerical approximation of the spectral fractional diffusion problem based on the so called Balakrishnan representation. The latter consists of an improper integral approximated via quadratures. At each quadrature point, a reaction–diffusion problem must be approximated and is the method bottle neck. In this work, we propose to reduce the computational cost using a reduced basis strategy allowing for a fast evaluation of the reaction–diffusion problems. The reduced basis does not depend on the fractional power s for 0 < smin ⩽ s ⩽ smax < 1. It is built offline once for all and used online irrespectively of the fractional power. We analyze the reduced basis strategy and show its exponential convergence. The analytical results are illustrated with insightful numerical experiments.
Funding: This research was supported by the NSF grant DMS-1817691 (AB-DG-AZ); DG was supported by the Swiss National Science Foundation grant P2ELP2-175056 and IAMCS at TAMU.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- The deal.II library, Version 9.2
- Reduced basis approximations of the solutions to spectral fractional diffusion problems
- Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems
- Doubly-adaptive artificial compression methods for incompressible flow
Articles in the same Issue
- Frontmatter
- The deal.II library, Version 9.2
- Reduced basis approximations of the solutions to spectral fractional diffusion problems
- Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems
- Doubly-adaptive artificial compression methods for incompressible flow
