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dc.contributor.authorShu, Yu-Chenen_US
dc.contributor.authorChern, I-Liangen_US
dc.contributor.authorChang, Chien C.en_US
dc.date.accessioned2014-12-08T15:36:40Z-
dc.date.available2014-12-08T15:36:40Z-
dc.date.issued2014-10-15en_US
dc.identifier.issn0021-9991en_US
dc.identifier.urihttp://dx.doi.org/10.1016/j.jcp.2014.07.017en_US
dc.identifier.urihttp://hdl.handle.net/11536/25020-
dc.description.abstractMost elliptic interface solvers become complicated for complex interface problems at those "exceptional points" where there are not enough neighboring interior points for high order interpolation. Such complication increases especially in three dimensions. Usually, the solvers are thus reduced to low order accuracy. In this paper, we classify these exceptional points and propose two recipes to maintain order of accuracy there, aiming at improving the previous coupling interface method [26]. Yet the idea is also applicable to other interface solvers. The main idea is to have at least first order approximations for second order derivatives at those exceptional points. Recipe 1 is to use the finite difference approximation for the second order derivatives at a nearby interior grid point, whenever this is possible. Recipe 2 is to flip domain signatures and introduce a ghost state so that a second-order method can be applied. This ghost state is a smooth extension of the solution at the exceptional point from the other side of the interface. The original state is recovered by a post-processing using nearby states and jump conditions. The choice of recipes is determined by a classification scheme of the exceptional points. The method renders the solution and its gradient uniformly second-order accurate in the entire computed domain. Numerical examples are provided to illustrate the second order accuracy of the presently proposed method in approximating the gradients of the original states for some complex interfaces which we had tested previous in two and three dimensions, and a real molecule (1D63) which is double-helix shape and composed of hundreds of atoms. (C) 2014 Elsevier Inc. All rights reserved.en_US
dc.language.isoen_USen_US
dc.subjectElliptic interface problemsen_US
dc.subjectCoupling interface methoden_US
dc.subjectExceptional pointsen_US
dc.subjectComplex interfacesen_US
dc.subjectSecond-order method for gradienten_US
dc.titleAccurate gradient approximation for complex interface problems in 3D by an improved coupling interface methoden_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.jcp.2014.07.017en_US
dc.identifier.journalJOURNAL OF COMPUTATIONAL PHYSICSen_US
dc.citation.volume275en_US
dc.citation.issueen_US
dc.citation.spage642en_US
dc.citation.epage661en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
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