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

有限体积方法非结构网格方法解分数阶Allen-Cahn程（英文）

作　　者：CHEN Ai-min LIU Fa-wang 

机构地区：[1]School of Mathematics and Statistics, Henan University, Kaifeng,475004, China Institute of Applied Mathematics, Henan University, Kaifeng, 475004, China Laboratory of Data Analysis Technology, Henan University, Kaifeng, 475004, China [2]School of Mathematical Sciences, Queensland Universityof Technology, GPO Box 2434, Brisbane, Qld. 4001, Australia

出　　处：《Chinese Quarterly Journal of Mathematics》2017年第4期345-354,共10页数学季刊（英文版）

基　　金：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)

摘　　要：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.

关 键 词：fractional-in-space Allen-Cahn equation finite volume METHOD matrix transfertechnique preconditioned LANCZOS METHOD 

分 类 号：O242.21[理学—计算数学]