Natural Boundary Element Method for ParabolicEquations in an Unbounded Domain

Abstract:

      In this paper we introduce an implementation for the etfficient numerical solution of exterior initial boundary value problem for parabolic equation. The problem is reformulated as an equivalent one on a boundary Γ using natural boundary reduction.The governing equation is first discretized in tine, leading to a time-stepping scheme,where an exterior elliptic problem has to be solved in each time step. By Fourier expansion, we derive a natural integral equation of the elliptic problem related to time step and Poisson integral integral formula over exterior circular domain. Finite element discretization of the natural integral equation is employed to solve this problem. The computational aspects of this method are discussed. Numerical results are presented to illustrate feasibility and efficiency of our method.