A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation

doi:10.13371/j.cnki.chin.q.j.m.2017.04.002

Chinese Quarterly Journal of Mathematics ›› 2017, Vol. 32 ›› Issue (4): 345-354.doi: 10.13371/j.cnki.chin.q.j.m.2017.04.002

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A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation

1. School of Mathematics and Statistics, Henan University2. Institute of AppliedMathematics, Henan University3. Laboratory of Data Analysis Technology,Henan University4. School of Mathematical Sciences, Queensland University of Technology

Received:2016-12-16 Online:2017-12-30 Published:2020-10-20
About author:CHEN Ai-min(corresponding author)(1981-), female, native of Xinye, Henan, an associate professor of Henan University, Ph.D., engages in nonlinear dynamics.
Supported by:
Supported by the National Natural Science Foundation of China(11105040,61773153)； Supported by the Foundation of Henan Educational Committee(18B110003,15A110015)； Supported by the Excellent Young Scientific Talents Cultivation Foundation of Henan University(yqpy20140037)； Supported by the Science and Technology Program of Henan Province(162300410061)；

Abstract

Abstract:

Fractional-in-space Allen-Cahn equation containing a very strong nonlinear source term and small perturbation shows metastability and a quartic double well potential.Using a finite volume unstructured triangular mesh method, the present paper solves the twodimensional fractional-in-space Allen-Cahn equation with homogeneous Neumann boundary condition on different irregular domains. The efficiency of the method is presented through numerical computation of the two-dimensional fractional-in-space Allen-Cahn equation on different domains.

Key words: fractional-in-space Allen-Cahn equation, finite volume method, matrix transfer technique, preconditioned Lanczos method

CLC Number:

O241.8

CHEN Ai-min, , LIU Fa-wang. A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(4): 345-354.

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A Finite Volume Unstructured Mesh Method for Fractional-in-space Allen-Cahn Equation

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