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Mixed Boundary Conditions (mixed + boundary_condition)
Selected AbstractsA relation between the logarithmic capacity and the condition number of the BEM-matricesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2007W. Dijkstra Abstract We establish a relation between the logarithmic capacity of a two-dimensional domain and the solvability of the boundary integral equation for the Laplace problem on that domain. It is proved that when the logarithmic capacity is equal to one the boundary integral equation does not have a unique solution. A similar result is derived for the linear algebraic systems that appear in the boundary element method. As these systems are based on the boundary integral equation, no unique solution exists when the logarithmic capacity is equal to one. Hence, the system matrix is ill-conditioned. We give several examples to illustrate this and investigate the analogies between the Laplace problem with Dirichlet and mixed boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Transient scattering of SH waves from an inclusion with a unilateral frictional interface,a 2D time domain boundary element analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2003Yang-De Feng Abstract This paper develops a 2D time domain boundary element method (BEM) to solve the transient SH-wave scattering from an inclusion with a unilateral frictional interface. The incident SH-wave is assumed strong enough to break friction so that localized slip takes place along the interface. The present problem is indeed a non-linear boundary value problem since the mixed boundary conditions involve unknown intervals (the slip and stick zones). In order to determine the intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embedded in an infinite solid. The numerical results of the interface traction and relative slip velocity are presented. Copyright © 2003 John Wiley & Sons, Ltd. [source] A Cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2010Phong B. H. Le Abstract In this paper, high-order systems are reformulated as first-order systems, which are then numerically solved by a collocation method. The collocation method is based on Cartesian discretization with 1D-integrated radial basis function networks (1D-IRBFN) (Numer. Meth. Partial Differential Equations 2007; 23:1192,1210). The present method is enhanced by a new boundary interpolation technique based on 1D-IRBFN, which is introduced to obtain variable approximation at irregular points in irregular domains. The proposed method is well suited to problems with mixed boundary conditions on both regular and irregular domains. The main results obtained are (a) the boundary conditions for the reformulated problem are of Dirichlet type only; (b) the integrated RBFN approximation avoids the well-known reduction of convergence rate associated with differential formulations; (c) the primary variable (e.g. displacement, temperature) and the dual variable (e.g. stress, temperature gradient) have similar convergence order; (d) the volumetric locking effects associated with incompressible materials in solid mechanics are alleviated. Numerical experiments show that the proposed method achieves very good accuracy and high convergence rates. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical modelling of elastic wave scattering in frequency domain by the partition of unity finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2009A. El Kacimi Abstract In this paper, we investigate a numerical approach based on the partition of unity finite element method, for the time-harmonic elastic wave equations. The aim of the proposed work is to accurately model two-dimensional elastic wave problems with fewer elements, capable of containing many wavelengths per nodal spacing, and without refining the mesh at each frequency. The approximation of the displacement field is performed via the standard finite element shape functions, enriched by superimposing pressure and shear plane wave basis, which incorporate knowledge of the wave propagation. A variational framework able to handle mixed boundary conditions is described. Numerical examples dealing with the radiation and the scattering of elastic waves by a circular body are presented. The results show the performance of the proposed method in both accuracy and efficiency. Copyright © 2008 John Wiley & Sons, Ltd. [source] On the a priori and a posteriori error analysis of a two-fold saddle-point approach for nonlinear incompressible elasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006Gabriel N. Gatica Abstract In this paper, we reconsider the a priori and a posteriori error analysis of a new mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions. The approach, being based only on the fact that the resulting variational formulation becomes a two-fold saddle-point operator equation, simplifies the analysis and improves the results provided recently in a previous work. Thus, a well-known generalization of the classical Babu,ka,Brezzi theory is applied to show the well-posedness of the continuous and discrete formulations, and to derive the corresponding a priori error estimate. In particular, enriched PEERS subspaces are required for the solvability and stability of the associated Galerkin scheme. In addition, we use the Ritz projection operator to obtain a new reliable and quasi-efficient a posteriori error estimate. Finally, several numerical results illustrating the good performance of the associated adaptive algorithm are presented. Copyright © 2006 John Wiley & Sons, Ltd. [source] Resolvent estimates in W,1,p related to strongly coupled-linear parabolic systems with coupled nonsmooth capacitiesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2007Annegret Glitzky Abstract We investigate linear parabolic systems with coupled nonsmooth capacities and mixed boundary conditions. We prove generalized resolvent estimates in W,1, p spaces. The method is an appropriate modification of a technique introduced by Agmon to obtain Lp estimates for resolvents of elliptic differential operators in the case of smooth boundary conditions. Moreover, we establish an existence and uniqueness result. Copyright © 2007 John Wiley & Sons, Ltd. [source] Determining the temperature from incomplete boundary dataMATHEMATISCHE NACHRICHTEN, Issue 16 2007B. Tomas Johansson Abstract An iterative procedure for determining temperature fields from Cauchy data given on a part of the boundary is presented. At each iteration step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. A convergence proof of this method in a weighted L2 -space is included, as well as a stopping criteria for the case of noisy data. Moreover, a solvability result in a weighted Sobolev space for a parabolic initial boundary value problem of second order with mixed boundary conditions is presented. Regularity of the solution is proved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A fourth-order compact algorithm for nonlinear reaction-diffusion equations with Neumann boundary conditionsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2006Wenyuan Liao Abstract In this article, we discuss a scheme for dealing with Neumann and mixed boundary conditions using a compact stencil. The resulting compact algorithm for solving systems of nonlinear reaction-diffusion equations is fourth-order accurate in both the temporal and spatial dimensions. We also prove that the standard second-order approximation to zero Neumann boundary conditions provides fourth-order accuracy when the nonlinear reaction term is independent of the spatial variables. Numerical examples, including an application of this algorithm to a mathematical model describing frontal polymerization process, are presented in the article to demonstrate the accuracy and efficiency of the scheme. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source] On the mixed finite element method with Lagrange multipliersNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003Ivo Babu Abstract In this note we analyze a modified mixed finite element method for second-order elliptic equations in divergence form. As a model we consider the Poisson problem with mixed boundary conditions in a polygonal domain of R2. The Neumann (essential) condition is imposed here in a weak sense, which yields the introduction of a Lagrange multiplier given by the trace of the solution on the corresponding boundary. This approach allows to handle nonhomogeneous Neumann boundary conditions, theoretically and computationally, in an alternative and usually easier way. Then we utilize the classical Babu,ka-Brezzi theory to show that the resulting mixed variational formulation is well posed. In addition, we use Raviart-Thomas spaces to define the associated finite element method and, applying some elliptic regularity results, we prove the stability, unique solvability, and convergence of this discrete scheme, under appropriate assumptions on the mesh sizes. Finally, we provide numerical results illustrating the performance of the algorithm for smooth and singular problems. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 192,210, 2003 [source] | |||||||||||||