Multigrid Methods for Time-Fractional Evolution Equations: A Numerical Study

AbstractIn this work, we develop an efficient iterative scheme for a class of nonlocal evolution models involving a Caputo fractional derivative of order\(\alpha (0,1)\) in time. The fully discrete scheme is obtained using the standard Galerkin method with conforming piecewise linear finite elements in space and corrected high-order BDF convolution quadrature in time. At each time step, instead of solving the linear algebraic system exactly, we employ a multigrid iteration with a Gauss –Seidel smoother to approximate the solution efficiently. Illustrative numerical results for nonsmooth problem data are presented to demonstrate the approach.

Source: European Journal of Applied Physiology - February 11, 2020 Category: Physiology Source Type: research