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Vietnam Journal of Mathematics 39:4 (2011) 485-497

 

Domain Decompositon Method for Elliptic Interface Problems

Dang Quang A1, Truong Ha Hai2 and Vu Vinh Quang2

1Institute of Information Technology, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam

2Faculty of Information Technology, Thai Nguyen University, Thai Nguyen, Vietnam

 

Abstract. Interface problems arise in setting of various physical and engineering problems, where the governing differential equations have discontinuous across an interface. For solving them in recent years there are intensively developed immersed finite difference/ finite element methods which draw attention to discretization of the equations nearly the interface for ensuring accuracy. Differently from these methods in this paper we use a domain decomposition method based on updating of derivative of unknown function on interface to problem considered. It reduces the interface problem to a sequence of problems in subdomains that are easily solved by available softwares. The convergence of the iterative process is proved. Many numerical examples for rectangular and L-shape domains demonstrate the fast convergence of the method. The method can be applied especially efficiently for domains consisting of rectangles.

2000 Mathematics Subject Classification: 35J25, 65N55.

Keywords: Interface problems; domain decomposition; iterative method.

 

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