A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite Elements
Nonlinear elliptic partial differential equations are important to many large scale engineering and science problems. For this kind of equations, this article discusses a splitting extrapolation which possesses a high order of accuracy, a high degree of parallelism, less computational complexity and more flexibility than Richardson extrapolation. According to the problems, some domain decompositions are constructed and some independent mesh parameters are designed. Multi-parameter asymptotic expansions are proved for the errors of approximations. Based on the expansions, splitting extrapolation formulas are developed to compute approximations with high order of accuracy on a globally fine grid. Because these 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.
Y. Cao et al., "A Splitting Extrapolation for Solving Nonlinear Elliptic Equations with D-quadratic Finite Elements," Journal of Computational Physics, Elsevier, Jan 2009.
The definitive version is available at https://doi.org/10.1016/j.jcp.2008.09.003
Mathematics and Statistics
Keywords and Phrases
extrapolation; asymptotic expansion; parallel algorithm; finite elements; Domain decomposition; A posteriori error estimate
International Standard Serial Number (ISSN)
Article - Journal
© 2009 Elsevier, All rights reserved.