An Algorithm Using the Finite Volume Element Method and Its Splitting Extrapolation
Efendiev, Y. and Goovaerts, M. J. and Mitsui, T. and Ng, M. and Tsuchiya, T. and Wuytack, L.
This paper is to present a new efficient algorithm by using the finite volume element method and its splitting extrapolation. This method combines the local conservation property of the finite volume element method and the advantages of splitting extrapolation, such as a high order of accuracy, a high degree of parallelism, less computational complexity and more flexibility than a Richardson extrapolation. Because the splitting extrapolation formulas only require us to solve a set of smaller discrete subproblems on different coarser grids in parallel instead of on the globally fine grid, a large scale multidimensional problem is turned into a set of smaller discrete subproblems. Additionally, this method is efficient for solving interface problems if we regard the interfaces of the problems as the interfaces of the initial domain decomposition.
Y. Cao et al., "An Algorithm Using the Finite Volume Element Method and Its Splitting Extrapolation," Journal of Computational and Applied Mathematics, vol. 235, no. 13, pp. 3734-3742, Elsevier, Jan 2011.
The definitive version is available at https://doi.org/10.1016/j.cam.2011.01.019
Mathematics and Statistics
Keywords and Phrases
Extrapolation; Finite Volume Element Method; Parallel Algorithm; Domain Decomposition
Article - Journal
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