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Vietnam
Journal of Mathematics 39:4 (2011) 485-497
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Domain Decompositon Method for Elliptic
Interface Problems
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Dang Quang A1, Truong Ha Hai2
and Vu Vinh Quang2
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1Institute of Information
Technology, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
2Faculty of Information
Technology, Thai Nguyen University,
Thai Nguyen, Vietnam
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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.
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2000 Mathematics Subject Classification: 35J25, 65N55.
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Keywords: Interface
problems; domain decomposition; iterative method.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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