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Title: Accurate gradient approximation for complex interface problems in 3D by an improved coupling interface method

Most 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 gradientmore » 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.« less
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6] ;  [4]
  1. Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan (China)
  2. (South), Tainan 701, Taiwan (China)
  3. Department of Applied Mathematics, National Chiao Tung University, Hsin Chu 300, Taiwan (China)
  4. (China)
  5. (Taipei Office), Taipei 106, Taiwan (China)
  6. Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan (China)
Publication Date:
OSTI Identifier:
22382134
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 275; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; APPROXIMATIONS; ATOMS; COUPLING; FINITE DIFFERENCE METHOD; INTERFACES; INTERPOLATION; MOLECULES; PROCESSING