A Domain Decomposition Method for Strongly Mixed Boundary Value Problems for the Poisson Equation
Recently we proposed a domain decomposition method (DDM) for solving a Dirichlet problem for a second order elliptic equation, where differently from other DDMs, the value of the normal derivative on an interface is updated from iteration to iteration. In this paper we develop a method for solving strongly mixed boundary value problems (BVPs), where boundary conditions are of different type on different sides of a rectangle and the transmission of boundary conditions occurs not only in vertices but also in one or several inner points of a side of the rectangle. Such mixed problems often arise in mechanics and physics. Our method reduces these strongly mixed BVPs to sequences of weakly mixed problems for the Poisson equation in the sense that on each side of the rectangle there is given only one type of boundary condition, which are easily solved by a program package, constructed recently by Vu (see ). The detailed investigation of the convergence of the method for a model problem is carried out. After that the method is applied to a problem of semiconductors. The convergence of the method is proved and numerical experiments confirm the efficiency of the method.
KeywordsDomain decomposition method Poisson equation strongly mixed boundary conditions
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