Skeletonization Accelerated Solution of Crank-Nicolson Method for Solving Three-Dimensional Parabolic Equation

Parabolic equation models discretized with the finite difference method have been extensively studied for a long time. However, several explicit and implicit schemes exist in the literature. The advantage in explicit schemes is its simplicity, while its disadvantage is conditional stability. On the...

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Bibliographic Details
Published in:Applied Computational Electromagnetics Society journal 2020-09, Vol.35 (9), p.1006-1011
Main Authors: Rasool, Hafiz, Jun, Chen, Pan, Xiao-Min, Sheng, Xin-Qing
Format: Article
Language:English
Subjects:
Accuracy
Boundary conditions
Computing costs
Crank-Nicholson method
Decomposition
Efficiency
Finite difference method
Geometrical optics
Methods
Partial differential equations
Propagation
Sparsity
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Summary:Parabolic equation models discretized with the finite difference method have been extensively studied for a long time. However, several explicit and implicit schemes exist in the literature. The advantage in explicit schemes is its simplicity, while its disadvantage is conditional stability. On the other hand, implicit schemes are unconditionally stable but require special treatment for a fast and accurate solution such as the Crank-Nicolson (CN) method. This method becomes computationally intensive for problems with dense meshes. The resulting matrix from the CN in two and three-dimensional cases requires high computational resources. This paper applies hierarchical interpolative factorization (HIF) to reduce the computational cost of the CN method. Numerical experiments are conducted to validate the proposed HIF acceleration.
ISSN:1054-4887
1054-4887
1943-5711
DOI:10.47037/2020.ACES.J.350905