Abstract: A natural boundary reduction initiated and developed by Feng Kang and Yu Dehao^[1~4] is applied to solve the exterior initial boundary value problem of 2D parabolic equation, and a new coupled method of the natural boundary element method(NBEM) and finite element method(FEM) is suggested. The governing equation is first discretized in time, leading to a time-stepping scheme. Second, the natural integral equation over circular domain is given, and the coupling of the NBEM and FEM for the parabolic equation with unbounded domain is studied. Finally, a numerical example is devoted to illustrate this new method.

Key words: parabolic equation, natural boundary reduction, coupled method, numerical implementation