Reduced basis approximations of the solutions to spectral fractional diffusion problems Academic Article uri icon

abstract

  • AbstractWe 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 reactiondiffusion 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 reactiondiffusion 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.

published proceedings

  • Journal of Numerical Mathematics

author list (cited authors)

  • Bonito, A., Guignard, D., & Zhang, A. R.

publication date

  • January 1, 2020 11:11 AM