101. Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm.
- Author
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Yu, Bing, Zheng, Xiangcheng, Zhang, Pingwen, and Zhang, Lei
- Subjects
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NONLINEAR equations , *APPROXIMATION algorithms , *DIFFUSION coefficients - Abstract
The nonlinear space-fractional problems often allow multiple stationary solutions, which can be much more complicated than the corresponding integer-order problems. In this paper, we systematically compute the solution landscapes of nonlinear constant/variable-order space-fractional problems on one- and two-dimensional rectangular domains. A fast approximation algorithm is developed to deal with the variable-order spectral fractional Laplacian by approximating the variable-indexing Fourier modes, and then combined with saddle dynamics to construct the solution landscape of variable-order space-fractional phase field model. Numerical experiments are performed to substantiate the accuracy and efficiency of fast approximation algorithm and elucidate essential features of the stationary solutions of space-fractional phase field model. Furthermore, we demonstrate that the solution landscapes of spectral fractional Laplacian problems can be reconfigured by varying the diffusion coefficients in the corresponding integer-order problems. • A fast approximation algorithm for variable-order spectral fractional Laplacian. • Construction of solution landscapes of space-fractional phase field models. • Reconfiguration of fractional Laplacian problems by integer-order problems. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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