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Journal of Scientific Computing

Erschienen in:

19.05.2016

Krylov Integration Factor Method on Sparse Grids for High Spatial Dimension Convection–Diffusion Equations

verfasst von: Dong Lu, Yong-Tao Zhang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2016

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Abstract

Krylov implicit integration factor (IIF) methods were developed in Chen and Zhang (J Comput Phys 230:4336–4352, 2011) for solving stiff reaction–diffusion equations on high dimensional unstructured meshes. The methods were further extended to solve stiff advection–diffusion–reaction equations in Jiang and Zhang (J Comput Phys 253:368–388, 2013). Recently we studied the computational power of Krylov subspace approximations on dealing with high dimensional problems. It was shown that the Krylov integration factor methods have linear computational complexity and are especially efficient for high dimensional convection–diffusion problems with anisotropic diffusions. In this paper, we combine the Krylov integration factor methods with sparse grid combination techniques and solve high spatial dimension convection–diffusion equations such as Fokker–Planck equations on sparse grids. Numerical examples are presented to show that significant computational times are saved by applying the Krylov integration factor methods on sparse grids.

Vorheriger Artikel Symmetric Energy-Conserved S-FDTD Scheme for Two-Dimensional Maxwell’s Equations in Negative Index Metamaterials

Nächster Artikel Viscous Regularization for the Non-equilibrium Seven-Equation Two-Phase Flow Model

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Titel: Krylov Integration Factor Method on Sparse Grids for High Spatial Dimension Convection–Diffusion Equations
verfasst von: Dong Lu
Yong-Tao Zhang
Publikationsdatum: 19.05.2016
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2016
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0216-7

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