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Interface Problems (interface + problem)
Selected AbstractsNumerical simulation of non-isothermal phase change problem using ADRBEM with augmented itemsHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 7 2007Jie Liu Abstract In this paper, the phase change moving interface problem along the axial direction of the cylinder in the lead alloys containing tin is simulated by the axisymmetric dual reciprocity boundary element method (ADRBEM) with augmented items. The numerical method is verified by comparing with the analytical solution under a certain condition. The calculating results show that the ADRBEM with augmented items is an effective numerical method to solve the analogous problem of non-isothermal phase change, which occurs in the crystal growth process. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(7): 408, 416, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20173 [source] Computational methods for optical molecular imagingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2009Duan Chen Abstract A new computational technique, the matched interface and boundary (MIB) method, is presented to model the photon propagation in biological tissue for the optical molecular imaging. Optical properties have significant differences in different organs of small animals, resulting in discontinuous coefficients in the diffusion equation model. Complex organ shape of small animal induces singularities of the geometric model as well. The MIB method is designed as a dimension splitting approach to decompose a multidimensional interface problem into one-dimensional ones. The methodology simplifies the topological relation near an interface and is able to handle discontinuous coefficients and complex interfaces with geometric singularities. In the present MIB method, both the interface jump condition and the photon flux jump conditions are rigorously enforced at the interface location by using only the lowest-order jump conditions. This solution near the interface is smoothly extended across the interface so that central finite difference schemes can be employed without the loss of accuracy. A wide range of numerical experiments are carried out to validate the proposed MIB method. The second-order convergence is maintained in all benchmark problems. The fourth-order convergence is also demonstrated for some three-dimensional problems. The robustness of the proposed method over the variable strength of the linear term of the diffusion equation is also examined. The performance of the present approach is compared with that of the standard finite element method. The numerical study indicates that the proposed method is a potentially efficient and robust approach for the optical molecular imaging. Copyright © 2008 John Wiley & Sons, Ltd. [source] Variational approach to the free-discontinuity problem of inverse crack identificationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008R. TsotsovaArticle first published online: 17 DEC 200 Abstract This work presents a computational strategy for identification of planar defects (cracks) in homogenous isotropic linear elastic solids. The underlying strategy is a regularizing variational approach based on the diffuse interface model proposed by Ambrosio and Tortorelli. With the help of this model, the sharp interface problem of crack identification is split into two coupled elliptic boundary value problems solved using the finite element method. Numerical examples illustrate the application of the proposed approach for effective reconstruction of the position and the shape of a single crack using only the information collected on the surface of the analyzed body. Copyright © 2007 John Wiley & Sons, Ltd. [source] Approximation capability of a bilinear immersed finite element spaceNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2008Xiaoming He Abstract This article discusses a bilinear immersed finite element (IFE) space for solving second-order elliptic boundary value problems with discontinuous coefficients (interface problem). This is a nonconforming finite element space and its partition can be independent of the interface. The error estimates for the interpolation of a Sobolev function indicate that this IFE space has the usual approximation capability expected from bilinear polynomials. Numerical examples of the related finite element method are provided. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] A discontinuous Galerkin method for elliptic interface problems with application to electroporationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009Grégory Guyomarc'h Abstract We solve elliptic interface problems using a discontinuous Galerkin (DG) method, for which discontinuities in the solution and in its normal derivatives are prescribed on an interface inside the domain. Standard ways to solve interface problems with finite element methods consist in enforcing the prescribed discontinuity of the solution in the finite element space. Here, we show that the DG method provides a natural framework to enforce both discontinuities weakly in the DG formulation, provided the triangulation of the domain is fitted to the interface. The resulting discretization leads to a symmetric system that can be efficiently solved with standard algorithms. The method is shown to be optimally convergent in the L2 -norm. We apply our method to the numerical study of electroporation, a widely used medical technique with applications to gene therapy and cancer treatment. Mathematical models of electroporation involve elliptic problems with dynamic interface conditions. We discretize such problems into a sequence of elliptic interface problems that can be solved by our method. We obtain numerical results that agree with known exact solutions. Copyright © 2008 John Wiley & Sons, Ltd. [source] A fast implementation of the FETI-DP method: FETI-DP-RBS-LNA and applications on large scale problems with localized non-linearitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2005Jun Sun Abstract As parallel and distributed computing gradually becomes the computing standard for large scale problems, the domain decomposition method (DD) has received growing attention since it provides a natural basis for splitting a large problem into many small problems, which can be submitted to individual computing nodes and processed in a parallel fashion. This approach not only provides a method to solve large scale problems that are not solvable on a single computer by using direct sparse solvers but also gives a flexible solution to deal with large scale problems with localized non-linearities. When some parts of the structure are modified, only the corresponding subdomains and the interface equation that connects all the subdomains need to be recomputed. In this paper, the dual,primal finite element tearing and interconnecting method (FETI-DP) is carefully investigated, and a reduced back-substitution (RBS) algorithm is proposed to accelerate the time-consuming preconditioned conjugate gradient (PCG) iterations involved in the interface problems. Linear,non-linear analysis (LNA) is also adopted for large scale problems with localized non-linearities based on subdomain linear,non-linear identification criteria. This combined approach is named as the FETI-DP-RBS-LNA algorithm and demonstrated on the mechanical analyses of a welding problem. Serial CPU costs of this algorithm are measured at each solution stage and compared with that from the IBM Watson direct sparse solver and the FETI-DP method. The results demonstrate the effectiveness of the proposed computational approach for simulating welding problems, which is representative of a large class of three-dimensional large scale problems with localized non-linearities. Copyright © 2005 John Wiley & Sons, Ltd. [source] Pressure relaxation procedures for multiphase compressible flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005M.-H. Lallemand Abstract This paper deals with pressure relaxation procedures for multiphase compressible flow models. Such models have nice mathematical properties (hyperbolicity) and are able to solve a wide range of applications: interface problems, detonation physics, shock waves in mixtures, cavitating flows, etc. The numerical solution of such models involves several ingredients. One of those ingredients is the instantaneous pressure relaxation process and is of particular importance. In this article, we present and compare existing and new pressure relaxation procedures in terms of both accuracy and computational efficiency. Among these procedures we enhance an exact one in the particular case of fluids governed by the stiffened gas equation of state, and approximate procedures for general equations of state, which are particularly well suited for problems with large pressure variations. We also present some generalizations of these procedures in the context of multiphase flows with an arbitrary number of fluids. Some tests are provided to illustrate these comparisons. Copyright © 2005 John Wiley & Sons, Ltd. [source] A simple method for compressible multiphase mixtures and interfacesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2003Nikolai Andrianov Abstract We develop a Godunov-type scheme for a non-conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial differential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and non-equilibrium thermodynamics (two pressures, two temperatures, two densities, etc.).Its numerical resolution poses several difficulties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non-conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions. Copyright © 2003 John Wiley & Sons, Ltd. [source] Wave front sets of the Riemann function of elastic interface problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2004Senjo Shimizu Abstract We obtain an inner and an outer estimates of wave front sets and analytic wave front sets of the Riemann function of elastic interface problems by using the localization method due to Wakabayashi. In our problem the outer estimate of wave front sets and analytic wave front sets of the Riemann function coincides with the inner estimate of those. The strong point of our results is to catch the lateral wave as well as the incident, the reflected, and the refracted waves. Copyright © 2004 John Wiley & Sons, Ltd. [source] Introduction to the Special Issue on Marketing and Operations Management Interfaces and CoordinationPRODUCTION AND OPERATIONS MANAGEMENT, Issue 4 2009Teck H. Ho In this special issue, the contributing authors address several emerging marketing and operations interface problems and develop innovative approaches for solving them. Specifically, by explicitly modeling active consumer behavior under different pricing schemes, the papers in this special issue examine how firms can coordinate their marketing and operations to improve their competitiveness and profit. The papers also provide insights on how to develop and operate new and innovative market mechanisms. [source] A priori estimates for fluid interface problemsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2008Jalal Shatah We consider the regularity of an interface between two incompressible and inviscid fluid flows in the presence of surface tension. We obtain local-in-time estimates on the interface in H(3/2)k + 1 and the velocity fields in H(3/2)k. These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation. © 2007 Wiley Periodicals, Inc. [source] | |||||||||||||