Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 75, Issue 6, Pages 2031-2043Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2017.09.003
Keywords
Finite difference method for fractional differential equation on convex domain; Multi-term fractional differential equation; Distributed-order fractional differential equation
Categories
Funding
- OSD/ARO MURI Grant [W911NF-15-1-0562]
- National Science Foundation [DMS-1620194]
- National Natural Science Foundation of China [11471194, 11571115, 91630207]
- China Postdoctoral Science Foundation [KLH1411044]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1620194] Funding Source: National Science Foundation
Ask authors/readers for more resources
Fractional partial differential equations (PDEs) provide a powerful and flexible tool for modeling challenging phenomena including anomalous diffusion processes and long-range spatial interactions, which cannot be modeled accurately by classical second-order diffusion equations. However, numerical methods for space-fractional PDEs usually generate dense or full stiffness matrices, for which a direct solver requires O(N-3) computations per time step and O(N-2) memory, where N is the number of unknowns. The significant computational work and memory requirement of the numerical methods makes a realistic numerical modeling of three-dimensional space -fractional diffusion equations computationally intractable. Fast numerical methods were previously developed for space-fractional PDEs on multidimensional rectangular domains, without resorting to lossy compression, but rather, via the exploration of the tensor-product form of the Toeplitz-like decompositions of the stiffness matrices. In this paper we develop a fast finite difference method for distributed order space-fractional PDEs on a general convex domain in multiple space dimensions. The fast method has an optimal order storage requirement and almost linear computational complexity, without any lossy compression. Numerical experiments show the utility of the method. (C) 2017 Elsevier Ltd. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available