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Computing solution landscape of nonlinear space-fractional problems via fast approximation algorithm
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DOI：10.1016/j.jcp.2022.111513.png)
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Abstract
En 中文
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.(c) 2022 Elsevier Inc. All rights reserved.
Keywords:
Solution landscape
Phase field
Variable -order
Fractional Laplacian
Saddle dynamics
Stationary solution
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