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Domain Method (domain + method)
Selected AbstractsA continuum-to-atomistic bridging domain method for composite latticesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Mei Xu Abstract The bridging domain method is an overlapping domain decomposition approach for coupling finite element continuum models and molecular mechanics models. In this method, the total energy is decomposed into atomistic and continuum parts by complementary weight functions applied to each part of the energy in the coupling domain. To enforce compatibility, the motions of the coupled atoms are constrained by the continuum displacement field using Lagrange multipliers. For composite lattices, this approach is suboptimal because the internal modes of the lattice are suppressed by the homogeneous continuum displacement field in the coupling region. To overcome this difficulty, we present a relaxed bridging domain method. In this method, the atom set is divided into primary and secondary atoms; the relative motions between them are often called the internal modes. Only the primary atoms are constrained in the coupling region, which succeed in allowing these internal modes to fully relax. Several one- and two-dimensional examples are presented, which demonstrate improved accuracy over the standard bridging domain method. Copyright © 2009 John Wiley & Sons, Ltd. [source] A parallel implicit/explicit hybrid time domain method for computational electromagneticsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2009Z. Q. Xie Abstract The numerical solution of Maxwell's curl equations in the time domain is achieved by combining an unstructured mesh finite element algorithm with a cartesian finite difference method. The practical problem area selected to illustrate the application of the approach is the simulation of three-dimensional electromagnetic wave scattering. The scattering obstacle and the free space region immediately adjacent to it are discretized using an unstructured mesh of linear tetrahedral elements. The remainder of the computational domain is filled with a regular cartesian mesh. These two meshes are overlapped to create a hybrid mesh for the numerical solution. On the cartesian mesh, an explicit finite difference method is adopted and an implicit/explicit finite element formulation is employed on the unstructured mesh. This approach ensures that computational efficiency is maintained if, for any reason, the generated unstructured mesh contains elements of a size much smaller than that required for accurate wave propagation. A perfectly matched layer is added at the artificial far field boundary, created by the truncation of the physical domain prior to the numerical solution. The complete solution approach is parallelized, to enable large-scale simulations to be effectively performed. Examples are included to demonstrate the numerical performance that can be achieved. Copyright © 2009 John Wiley & Sons, Ltd. [source] Bridging domain methods for coupled atomistic,continuum models with L2 or H1 couplingsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009P.-A. Guidault Abstract A bridging domain method for coupled atomistic,continuum models is proposed that enables to compare various coupling terms. The approach does not require the finite element mesh to match the lattice spacing of the atomic model. It is based on an overlapping domain decomposition method that makes use of Lagrange multipliers and weight functions in the coupling zone in order to distribute the energy between the two competing models. Two couplings are investigated. The L2 coupling enforces the continuity of displacements between the two models directly. The H1 coupling involves the definition of a strain measure. For this purpose, a moving least-square interpolant of the atomic displacement is defined. The choice of the weight functions is studied. Patch tests and a graphene sheet with a crack are studied. It is shown that both continuous and discontinuous weight functions can be used with the H1 coupling whereas the L2 coupling requires continuous weight functions. For the examples developed herein, the L2 coupling produces less error in the zone of interest. The flexibility of the H1 coupling with constant weight function may be beneficial but the results may be affected depending on the topology of the bridging zone. Copyright © 2008 John Wiley & Sons, Ltd. [source] A fast multi-level convolution boundary element method for transient diffusion problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005C.-H. Wang Abstract A new algorithm is developed to evaluate the time convolution integrals that are associated with boundary element methods (BEM) for transient diffusion. This approach, which is based upon the multi-level multi-integration concepts of Brandt and Lubrecht, provides a fast, accurate and memory efficient time domain method for this entire class of problems. Conventional BEM approaches result in operation counts of order O(N2) for the discrete time convolution over N time steps. Here we focus on the formulation for linear problems of transient heat diffusion and demonstrate reduced computational complexity to order O(N3/2) for three two-dimensional model problems using the multi-level convolution BEM. Memory requirements are also significantly reduced, while maintaining the same level of accuracy as the conventional time domain BEM approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Adaptive embedded unstructured grid methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Rainald Löhner Abstract A simple embedded domain method for node-based unstructured grid solvers is presented. The key modification of the original, edge-based solver is to remove all geometry-parameters (essentially the normals) belonging to edges cut by embedded surface faces. Several techniques to improve the treatment of boundary points close to the immersed surfaces are explored. Alternatively, higher-order boundary conditions are achieved by duplicating crossed edges and their endpoints. Adaptive mesh refinement based on proximity to or the curvature of the embedded CSD surfaces is used to enhance the accuracy of the solution. User-defined or automatic deactivation for the regions inside immersed solid bodies is employed to avoid unnecessary work. Several examples are included that show the viability of this approach for inviscid and viscous, compressible and incompressible, steady and unsteady flows, as well as coupled fluid,structure problems. Copyright © 2004 John Wiley & Sons, Ltd. [source] Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Gang-Won Jang Abstract One major hurdle in developing an efficient wavelet-based numerical method is the difficulty in the treatment of general boundaries bounding two- or three-dimensional domains. The objective of this investigation is to develop an adaptive multiscale wavelet-based numerical method which can handle general boundary conditions along curved boundaries. The multiscale analysis is achieved in a multi-resolution setting by employing hat interpolation wavelets in the frame of a fictitious domain method. No penalty term or the Lagrange multiplier need to be used in the present formulation. The validity of the proposed method and the effectiveness of the multiscale adaptive scheme are demonstrated by numerical examples dealing with the Dirichlet and Neumann boundary-value problems in quadrilateral and quarter circular domains. Copyright © 2003 John Wiley & Sons, Ltd. [source] A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2003Part 2: Neumann boundary conditions Abstract We present a fictitious domain decomposition method for the fast solution of acoustic scattering problems characterized by a partially axisymmetric sound-hard scatterer. We apply this method to the solution of a mock-up submarine problem, and highlight its computational advantages and intrinsic parallelism. A key component of our method is an original idea for addressing a Neumann boundary condition in the general framework of a fictitious domain method. This idea is applicable to many other linear partial differential equations besides the Helmholtz equation. Copyright © 2003 John Wiley & Sons, Ltd. [source] A two-grid fictitious domain method for direct simulation of flows involving non-interacting particles of a very small sizeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010A. Dechaume Abstract The full resolution of flows involving particles whose scale is hundreds or thousands of times smaller than the size of the flow domain is a challenging problem. A naive approach would require a tremendous number of degrees of freedom in order to bridge the gap between the two spatial scales involved. The approach used in the present study employs two grids whose grid size fits the two different scales involved, one of them (the micro-scale grid) being embedded into the other (the macro-scale grid). Then resolving first the larger scale on the macro-scale grid, we transfer the so obtained data to the boundary of the micro-scale grid and solve the smaller size problem. Since the particle is moving throughout the macro-scale domain, the micro-scale grid is fixed at the centroid of the moving particle and therefore moves with it. In this study we combine such an approach with a fictitious domain formulation of the problem resulting in a very efficient algorithm that is also easy to implement in an existing CFD code. We validate the method against existing experimental data for a sedimenting sphere, as well as analytical results for motion of an inertia-less ellipsoid in a shear flow. Finally, we apply the method to the flow of a high aspect ratio ellipsoid in a model of a human lung airway bifurcation. Copyright © 2009 John Wiley & Sons, Ltd. [source] Absorbing boundary condition on elliptic boundary for finite element analysis of water wave diffraction by large elongated bodiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2001Subrata Kumar Bhattacharyya Abstract In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modelling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers of first- and second-orders, which require a circular cylindrical truncation boundary in the diffraction-radiation problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic cylindrical truncation boundary has the potential to reduce the modelling domain and hence the computational effort. Grote and Keller [On non-reflecting boundary conditions. Journal of Computational Physics 1995; 122: 231,243] proposed extension of the first- and second-order BGT dampers for the elliptic radiation boundary and used these conditions to the acoustic scattering by an elliptic scatterer using the finite difference method. In this paper, these conditions are implemented for the problem of diffraction of water waves using the finite element method. Also, it is shown that the proposed extension works well only for head-on wave incidence. To remedy this, two new elliptic dampers are proposed, one for beam-on incidence and the other for general wave incidence. The performance of all the three dampers is studied using a numerical example of diffraction by an elliptic cylinder. Copyright © 2001 John Wiley & Sons, Ltd. [source] Some new algebraic criteria for chaos synchronization of Chua's circuits by linear state error feedback controlINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2006Xiaofeng Wu Abstract The research on the sufficient criterion for chaos synchronization of the master,slave Chua's circuits by linear state error feedback control has received much attention and some synchronization criteria for special control matrix were proposed. In this paper, the above synchronization issue is investigated in the situation of general linear state error feedback controller with propagation delay of control signals from the master Chua's circuit. First of all, a master,slave synchronization scheme for Chua's circuits with propagation delay is given and the relevant error system is derived. Using a quadratic Lyapunov function and frequency domain method, three new algebraic synchronization criteria for the synchronization scheme with general control matrix are proven. They are applied to derive the synchronization criteria for simple control matrices. Some examples are given to show the sharpness of these new criteria compared with the known criteria. Copyright © 2006 John Wiley & Sons, Ltd. [source] Characteristic analysis of reverse-L-shaped microstrip-fed large-bandwidth printed slot antennaINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 6 2002Yong-Woong Jang Abstract The characteristics of a reverse-L-shaped microstrip-fed structure is analyzed using the finite difference time domain method, and the characteristics of the proposed antenna are compared with a conventional antenna. The return loss, radiation resistance, and voltage,standing wave ratio in the frequency domain are calculated by Fourier transforming the time domain results. When the proposed feed structure is used, the bandwidth is extended in proportion to the slot width and the radiation resistance has the low value. When the slot width is 16 mm, the experimental bandwidth is approximately 50% (,10 dB , S11) at the center frequency of 2.3 GHz. In addition, the experimental data for the impedance and radiation pattern of the antenna are described. They are in good agreement with the calculated results. © 2002 Wiley Periodicals, Inc. Int J RF and Microwave CAE 12, 496,502, 2002. Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mmce.10055 [source] Difference Equations for the Higher Order Moments and Cumulants of the INAR(p) ModelJOURNAL OF TIME SERIES ANALYSIS, Issue 1 2005Maria Eduarda Silva Abstract., Here we obtain difference equations for the higher order moments and cumulants of a time series {Xt} satisfying an INAR(p) model. These equations are similar to the difference equations for the higher order moments and cumulants of the bilinear time series model. We obtain the spectral and bispectral density functions for the INAR(p) process in state,space form, thus characterizing it in the frequency domain. We consider a frequency domain method , the Whittle criterion , to estimate the parameters of the INAR(p) model and illustrate it with the series of the number of epilepsy seizures of a patient. [source] | ||||||||||