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Absorbing Boundary Conditions (absorbing + boundary_condition)
Selected AbstractsAbsorbing 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] Lagrangian finite element treatment of transient vibration/acoustics of biosolids immersed in fluidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008P. Krysl Abstract Superposition principle is used to separate the incident acoustic wave from the scattered and radiated waves in a displacement-based finite element model. An absorbing boundary condition is applied to the perturbation part of the displacement. Linear constitutive equation allows for inhomogeneous, anisotropic materials, both fluids and solids. Displacement-based finite elements are used for all materials in the computational volume. Robust performance for materials with limited compressibility is achieved using assumed-strain nodally integrated simplex elements or incompatible-mode brick elements. A centered-difference time-stepping algorithm is formulated to handle general damping accurately and efficiently. Verification problems (response of empty steel cylinder immersed in water to a step plane wave, and scattering of harmonic plane waves from an elastic sphere) are discussed for assumed-strain simplex and for voxel-based brick finite element models. A voxel-based modeling scheme for complex biological geometries is described, and two illustrative results are presented from the bioacoustics application domain: reception of sound by the human ear and simulation of biosonar in beaked whales. Copyright © 2007 John Wiley & Sons, Ltd. [source] Fast direct solution of the Helmholtz equation with a perfectly matched layer or an absorbing boundary conditionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Erkki Heikkola Abstract We consider the efficient numerical solution of the Helmholtz equation in a rectangular domain with a perfectly matched layer (PML) or an absorbing boundary condition (ABC). Standard bilinear (trilinear) finite-element discretization on an orthogonal mesh leads to a separable system of linear equations for which we describe a cyclic reduction-type fast direct solver. We present numerical studies to estimate the reflection of waves caused by an absorbing boundary and a PML, and we optimize certain parameters of the layer to minimize the reflection. Copyright © 2003 John Wiley & Sons, Ltd. [source] On the development of efficient FDTD-PML formulations for general dispersive mediaINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2008Konstantinos P. Prokopidis Abstract A novel implementation of the perfectly matched layer (PML) absorbing boundary condition (ABC) to terminate the finite-difference time-domain (FDTD) algorithm for general dispersive and negative index materials is presented. The proposed formulation also adopts the complex frequency-shifted (CFS) approach, involves simple FDTD expressions and avoids complex arithmetic. Several FDTD-PML simulations with different parameters are conducted for the termination of various dispersive media validating the stability, accuracy and effectiveness of the schemes and indicating the advantage of the CFS-PML. Copyright © 2008 John Wiley & Sons, Ltd. [source] A compact one-dimensional modal FDTD methodINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1-2 2008Shuiping Luo Abstract The finite-difference time-domain (FDTD) method is an effective technique for computing wideband electrical parameters such as scattering parameters of waveguide structures. in the computations, a known incident is normally required and is usually obtained with a simulation of a long uniform structure. For a three-dimensional problem, simulation of a long structure can be very memory- and CPU time-intensive. In addition, effective absorbing boundary conditions are needed to effectively terminate the structure even at and below the cutoff frequencies. To address these issues, many one-dimensional FDTD methods and absorbing schemes were proposed. However, they all have dispersion characteristics different from those of the conventional FDTD method, leading to undesired errors or reflections. In this paper, a new one-dimensional scheme is developed that has numerical dispersion characteristics very similar to that of the conventional FDTD method. When used as the absorbing boundary condition, it generates reflections of less than ,200,dB even at and below the cutoff frequencies for the considered modes. When used to obtain the incident wave, its results have difference of less than ,200,dB from that produced by the conventional FDTD method. Copyright © 2007 John Wiley & Sons, Ltd. [source] Nonconforming Galerkin methods for the Helmholtz equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2001Jim Douglas Jr. Abstract Nonconforming Galerkin methods for a Helmholtz-like problem arising in seismology are discussed both for standard simplicial linear elements and for several new rectangular elements related to bilinear or trilinear elements. Optimal order error estimates in a broken energy norm are derived for all elements and in L2 for some of the elements when proper quadrature rules are applied to the absorbing boundary condition. Domain decomposition iterative procedures are introduced for the nonconforming methods, and their convergence at a predictable rate is established. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 475,494, 2001 [source] Improved accuracy for the Helmholtz equation in unbounded domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Eli Turkel Abstract Based on properties of the Helmholtz equation, we derive a new equation for an auxiliary variable. This reduces much of the oscillations of the solution leading to more accurate numerical approximations to the original unknown. Computations confirm the improved accuracy of the new models in both two and three dimensions. This also improves the accuracy when one wants the solution at neighbouring wavenumbers by using an expansion in k. We examine the accuracy for both waveguide and scattering problems as a function of k, h and the forcing mode l. The use of local absorbing boundary conditions is also examined as well as the location of the outer surface as functions of k. Connections with parabolic approximations are analysed. Copyright © 2004 John Wiley & Sons, Ltd. [source] A compact one-dimensional modal FDTD methodINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1-2 2008Shuiping Luo Abstract The finite-difference time-domain (FDTD) method is an effective technique for computing wideband electrical parameters such as scattering parameters of waveguide structures. in the computations, a known incident is normally required and is usually obtained with a simulation of a long uniform structure. For a three-dimensional problem, simulation of a long structure can be very memory- and CPU time-intensive. In addition, effective absorbing boundary conditions are needed to effectively terminate the structure even at and below the cutoff frequencies. To address these issues, many one-dimensional FDTD methods and absorbing schemes were proposed. However, they all have dispersion characteristics different from those of the conventional FDTD method, leading to undesired errors or reflections. In this paper, a new one-dimensional scheme is developed that has numerical dispersion characteristics very similar to that of the conventional FDTD method. When used as the absorbing boundary condition, it generates reflections of less than ,200,dB even at and below the cutoff frequencies for the considered modes. When used to obtain the incident wave, its results have difference of less than ,200,dB from that produced by the conventional FDTD method. Copyright © 2007 John Wiley & Sons, Ltd. [source] An alternative analytical reduction scheme in the time-domain layered finite element reduction recovery method for high-frequency IC designMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 9 2008Houle Gan Abstract An alternative analytical reduction scheme was proposed in the time-domain layered finite element reduction recovery (LAFE-RR) method for the analysis of high-frequency integrated circuits. This alternative reduction scheme permits the use of general absorbing boundary conditions in the framework of a time-domain LAFE-RR method. In addition, it allows for an application of the LAFE-RR method to circuit problems in which the system matrices in multiple regions need to be reduced separately. Numerical and experimental results are given to demonstrate its validity. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 2337,2341, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23630 [source] Assessment of the performances of first- and second-order time-domain ABC's for the truncation of finite element gridsMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 1 2003Salvatore Caorsi Abstract In this paper we investigate the performances of first- and second-order time-domain absorbing boundary conditions (ABCs) when introduced in a finite-element algorithm to solve electromagnetic scattering problems. Attention is focused on the analysis of the ABC's absorbing characteristics when different geometries are considered for the truncation of the computational domain. Numerical results will be given by considering, as a first analysis, two-dimensional scattering problems. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 38: 11,16, 2003 [source] Analysis of a corrugated horn with the use of the BOR-FDTD methodMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2002Christopher P. Johnson Abstract The derivation of the body-of-revolution finite-difference,time-domain (BOR-FDTD) technique is presented and used to determine the return loss and radiation patterns of a corrugated horn. The perfectly matched layer (PML) absorbing boundary conditions are used for the computation. The source excitation is a sine-modulated Gaussian pulse, spatially weighted with the cylindrical TE11 mode fields. The results for the return loss and radiation patterns are compared with those obtained using a commercial package based on a mode- matching/method-of-moments technique. The results show excellent agreement. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 452,457, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10348 [source] Numerical solution to a linearized KdV equation on unbounded domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Chunxiong Zheng Abstract Exact absorbing boundary conditions for a linearized KdV equation are derived in this paper. Applying these boundary conditions at artificial boundary points yields an initial-boundary value problem defined only on a finite interval. A dual-Petrov-Galerkin scheme is proposed for numerical approximation. Fast evaluation method is developed to deal with convolutions involved in the exact absorbing boundary conditions. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] Coupling 3D and 1D fluid-structure interaction models for blood flow simulationsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006L. Formaggia Three-dimensional (3D) simulations of blood flow in medium to large vessels are now a common practice. These models consist of the 3D Navier-Stokes equations for incompressible Newtonian fluids coupled with a model for the vessel wall structure. However, it is still computationally unaffordable to simulate very large sections, let alone the whole, of the human circulatory system with fully 3D fluid-structure interaction models. Thus truncated 3D regions have to be considered. Reduced models, one-dimensional (1D) or zero-dimensional (0D), can be used to approximate the remaining parts of the cardiovascular system at a low computational cost. These models have a lower level of accuracy, since they describe the evolution of averaged quantities, nevertheless they provide useful information which can be fed to the more complex model. More precisely, the 1D models describe the wave propagation nature of blood flow and coupled with the 3D models can act also as absorbing boundary conditions. We consider in this work the coupling of a 3D fluid-structure interaction model with a 1D hyperbolic model. We study the stability of the coupling and present some numerical results. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||