Fast meshfree methods for nonlinear radiation diffusion equation

Abstract

Radiation diffusion is a phenomenon of interest in the field of astrophysics, inertial confinement fusion and so on. Since it is modeled by nonlinear equations that are usually solved in complex domains, it is difficult to solve by means of finite element method and finite difference method and so on. In the paper, we will provide a kind of new fast meshfree methods based on radial basis functions. At first, the part of diffusion terms for 1D and 2D radiation diffusion equations are linearized directly on time to form the new implicit schemes, and Kansa’s non-symmetric collocation method with the compactly supported radial basis function is used to solve the radiation diffusion problem. Second, the successive permutation iterative algorithms for full-implicit discretization on time are constructed furtherly, which are more efficient than the former algorithm. In the end, the accuracy and efficiency of the presented algorithms are verified by 1D and 2D numerical experiments. The new meshfree methods not only avoid the complexity of mesh generation, but also solve the radiation diffusion problem with high accuracy.