Krylov Implicit Integration Factor Discontinuous Galerkin Methods on Sparse Grids for High Dimensional Reaction-diffusion Equations
Loading...
Can’t use the file because of accessibility barriers? Contact us with the title of the item, permanent link, and specifics of your accommodation need.
Date
2019
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Permanent Link
Abstract
Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving effcient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high spatial dimensions. The key ingredient of spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG spatial operator in discretizing reaction-diffusion equations, we apply the efficient
IIF time discretization methods, which are a class of exponential integrators. Krylov
subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained.
Key words: Sparse grid; Discontinuous Galerkin methods; Implicit integration factor methods; Krylov subspace approximation; Reaction-diffusion equations
Description
Keywords
Citation
Liu, Yuan, et al. “Krylov Implicit Integration Factor Discontinuous Galerkin Methods on Sparse Grids for High Dimensional Reaction-diffusion Equations.” Journal of Computational Physics, vol. 388, 2019, pp. 90–102.
Journal
DOI
Link(s) to data and video for this item
Relation
Rights
Type
Article