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Coupled Problem (coupled + problem)

Distribution by Scientific Domains

Engineering	75%
Mathematics and Statistics	25%

Selected Abstracts

Modelling and optimal control of coupled structural acoustic systems with piezoelectric elements

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2003
W. G. Litvinov
Abstract We construct a model of a shell with piezoelectric elements (patches) that take into account the mutual influence of deformations and electric fields. Coupled problems for the shell with piezoelectric patches and an acoustic field, are studied and results on the existence and the uniqueness are obtained. For this system we consider an optimal control problem on noise attenuation and obtain results on the existence, the uniqueness, necessary and sufficient conditions of optimality. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Coupled simulation of wave propagation and water flow in soil induced by high-speed trains

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2008
P. Kettil
Abstract The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water-saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Analysis of coupled seepage and temperature fields in concrete dam

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 6 2002
Article first published online: 28 MAR 200, Chai Junrui
Abstract It is very important to investigate the coupled problem and solution of seepage and temperature fields in the concrete dam. Seepage through the concrete dam influences the distribution of the temperature field in the dam by heat exchange. The temperature field in the dam also influences the hydraulic conductivity and seepage through the dam. The mechanism of the action and reaction between the seepage and temperature fields in the concrete dam is analysed according to the seepage characteristics of the concrete dam. The continuum mathematical model for coupled seepage and temperature fields in the concrete dam is presented, and the iterative steps and the finite element numerical solution method for the coupled model are proposed. An engineering example is also given to show the applicability of the proposed model and numerical solution method. It can be shown from the example that the difference between the coupled and uncoupled solution to the two fields in the dam is about 4,5%. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Parallel numerical simulation for the coupled problem of continuous flow electrophoresis

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2007
M. Chau
Abstract The performance of parallel subdomain method with overlapping is analysed in the case of the 3D coupled boundary-value problem of continuous flow electrophoresis which is governed by Navier,Stokes equations coupled with convection,diffusion and potential equations. Convergence of parallel synchronous and asynchronous iterative algorithms is studied. Comparison between implemented explicit and implicit schemes for the transport equation is made using these algorithms and shows that both methods provide similar results and comparable performances. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Unified finite element discretizations of coupled Darcy,Stokes flow

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2009
Trygve Karper
Abstract In this article, we discuss some new finite element methods for flows which are governed by the linear stationary Stokes system on one part of the domain and by a second order elliptic equation derived from Darcy's law in the rest of the domain, and where the solutions in the two domains are coupled by proper interface conditions. All the methods proposed here utilize the same finite element spaces on the entire domain. In particular, we show how the coupled problem can be solved by using standard Stokes elements like the MINI element or the Taylor,Hood element in the entire domain. Furthermore, for all the methods the handling of the interface conditions are straightforward. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

Electromechanics of Cardiac Tissue: A Unified Approach to the Fully Coupled Excitation-Contraction Problem

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Serdar Göktepe
This contribution is concerned with a new, unified finite element approach to the fully coupled problem of cardiac electromechanics. In contrast to the existing numerical approaches suggested in the literature; to the best of our knowledge, for the first time, we propose a fully implicit, purely finite-element-based approach to the coupled problem. The system of coupled algebraic equations obtained by simultaneous linearization of non-linear weighted residual terms is solved monolithically. The put forward modular algorithmic framework leads to an unconditionally stable and geometrically flexible structure that can readily be extended towards complex ionic models of cardiac electrophysiology. The performance of the proposed approach is illustrated by the coupled electromechanical analysis of a biventricular generic heart model. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Theory and Numerics of Rate-Dependent Incremental Variational Formulations in Ferroelectricity

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008
Daniele Rosato
This paper is concerned with macroscopic continuous and discrete variational formulations for domain switching effects at small strains, which occur in ferroelectric ceramics. The developed new three,dimensional model is thermodynamically,consistent and determined by two scalar,valued functions: the energy storage function (Helmholtz free energy) and the dissipation function, which is in particular rate,dependent. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butterfly hysteresis for ferroelectric ceramics. The rate,dependent character of the dissipation function allows us also to reproduce the experimentally observed rate dependency of the above mentioned hysteresis phenomena. An important aspect is the numerical implementation of the coupled problem. The discretization of the two,field problem appears, as a consequence of the proposed incremental variational principle, in a symmetric format. The performance of the proposed methods is demonstrated by means of a benchmark problem. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Galerkin-type space-time finite elements for volumetrically coupled problems

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Holger Steeb Dipl.-Ing.
The study focuses on error estimation techniques for a coupled problem with two constituents based on the Theory of Porous Media. After developing space-time finite elements for this mixed problem, we extend the numerical scheme to a coupled space-time adaptive strategy. Therefore, an adjoint or dual problem is formulated and discussed, which is solved lateron numerically. One advantage of the presented technique is the high flexibility of the error indicator with respect to the error measure. [source]

Direct, partitioned and projected solution to finite element consolidation models

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2002
Giuseppe Gambolati
Abstract Direct, partitioned, and projected (conjugate gradient-like) solution approaches are compared on unsymmetric indefinite systems arising from the finite element integration of coupled consolidation equations. The direct method is used in its most recent and computationally efficient implementations of the Harwell Software Library. The partitioned approach designed for coupled problems is especially attractive as it addresses two separate positive definite problems of a smaller size that can be solved by symmetric conjugate gradients. However, it may stagnate and when converging it does not prove competitive with a global projection method such as Bi-CGSTAB, which may take full advantage of its flexibility in working on scaled and reordered equations, and thus may greatly improve its computational performance in terms of both robustness and convergence rate. The Bi-CGSTAB superiority to the other approaches is discussed and demonstrated with a few representative examples in two-dimensional (2-D) and three-dimensional (3-D) coupled consolidation problems. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A framework for fracture modelling based on the material forces concept with XFEM kinematics

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005
Ragnar Larsson
Abstract A theoretical and computational framework which covers both linear and non-linear fracture behaviour is presented. As a basis for the formulation, we use the material forces concept due to the close relation between on one hand the Eshelby energy,momentum tensor and on the other hand material defects like cracks and material inhomogeneities. By separating the discontinuous displacement from the continuous counterpart in line with the eXtended finite element method (XFEM), we are able to formulate the weak equilibrium in two coupled problems representing the total deformation. However, in contrast to standard XFEM, where the direct motion discontinuity is used to model the crack, we rather formulate an inverse motion discontinuity to model crack development. The resulting formulation thus couples the continuous direct motion to the inverse discontinuous motion, which may be used to simulate linear as well as non-linear fracture in one and the same formulation. In fact, the linear fracture formulation can be retrieved from the non-linear cohesive zone formulation simply by confining the cohesive zone to the crack tip. These features are clarified in the two numerical examples which conclude the paper. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Mathematical analysis of some new Reynolds-rod elastohydrodynamic models

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 15 2001
G. Bayada
In this paper, some new elastohydrodynamic Reynolds-rod models are posed to obtain the existence of solution (the lubricant pressure and the elastic rod displacement). More precisely, a sign restriction on fluid pressure for cavitation modelling and different unilateral conditions on the rod displacement associated with a rigid structure coating are formulated in terms of coupled variational inequalities. The particular hinged or clamped boundary conditions on the rod displacement require different techniques to prove the existence of solution. Besides nearly linear coupled problems, two non-linear rod problems including curvature effects are analysed. Mainly, regularity results and L, estimates for the solution of variational inequalities and fixed-point theorems lead to the existence results for the various coupled models. Copyright © 2001 John Wiley & Sons, Ltd. [source]