A Schwarz Alternating Algorithm For The Kardar-Parisi-Zhang Equation Over An Exterior Two Dimensional Domain

In this thesis, by the theory of the natural boundary reduction and the key idea of domain decomposition method, we study a Schwarz alternating algorithm based on the natural boundary reduction for the Kardar-Parisi-Zhang (K-P-Z) equation over an exterior two dimen-sional domain.Firstly, the K-P-Z equation is transformed by the Cole-Hopf transformation, and then resulting equation is discretized in time by the Newmark method, which leads to a time-stepping scheme (i.e.,an exterior elliptic problem). Secondly, two artificial boundaries are introduced, and the Poisson integral formula and the natural integral equation of the problem in an exterior domain are obtained by the theory of the natural boundary reduction. Thirdly, by means of the results of the natural boundary reduction,the Schwarz alternating al-gorithm is proposed. The convergence of the algorithm is analyzed.Finally, some numerical experiments are presented to illustrate the feasibility and effectiveness of the method.