A memory‐efficient finite volume method for advection‐diffusion‐reaction systems with nonsmooth sources |
| |
Authors: | Jonas Schäfer Xuan Huang Stefan Kopecz Philipp Birken Matthias K Gobbert Andreas Meister |
| |
Institution: | 1. Institute of Mathematics, University of Kassel, Kassel, Germany;2. Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland |
| |
Abstract: | We present a parallel matrix‐free implicit finite volume scheme for the solution of unsteady three‐dimensional advection‐diffusion‐reaction equations with smooth and Dirac‐Delta source terms. The scheme is formally second order in space and a Newton–Krylov method is employed for the appearing nonlinear systems in the implicit time integration. The matrix‐vector product required is hardcoded without any approximations, obtaining a matrix‐free method that needs little storage and is well‐suited for parallel implementation. We describe the matrix‐free implementation of the method in detail and give numerical evidence of its second‐order convergence in the presence of smooth source terms. For nonsmooth source terms, the convergence order drops to one half. Furthermore, we demonstrate the method's applicability for the long‐time simulation of calcium flow in heart cells and show its parallel scaling. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq31: 143–167, 2015 |
| |
Keywords: | calcium waves Dirac delta distribution finite volume method matrix‐free Newton– Krylov method parallel computing |
|
|