期刊
ADVANCES IN WATER RESOURCES
卷 38, 期 -, 页码 92-101出版社
ELSEVIER SCI LTD
DOI: 10.1016/j.advwatres.2011.12.013
关键词
Richards' equation; Modified Picard iteration; Anderson acceleration; Acceleration methods; Newton's method
资金
- United States Department of Energy Office of Advanced Scientific Computing Research
- Department of Energy SciDAC
- NSF [DMS 0915183]
- DOE [DE-SC0004880]
- US Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344]
- U.S. Department of Energy (DOE) [DE-SC0004880] Funding Source: U.S. Department of Energy (DOE)
In this paper, we investigate the effectiveness of the Anderson acceleration method applied to modified Picard iteration for nonlinear problems arising in variably saturated flow modeling. While many authors have studied the relative merits of Newton's method and modified Picard iteration in this context, the combination of Anderson acceleration and modified Picard iteration has not been investigated for these problems until recently. Since modified Picard iteration can be slow to converge, we investigate the use of Anderson acceleration to provide faster convergence while maintaining the robustness and lower memory requirements of modified Picard iteration relative to Newton's method. Results indicate that Anderson acceleration significantly improves not only convergence speed but also robustness of modified Picard iteration and can often provide faster solutions than Newton's method without the need for derivative computations. (C) 2012 Elsevier Ltd. All rights reserved.
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