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Recently, the original Wavenumber approach was introduced for dynamic analysis of dam-reservoir systems in frequency domain in the context of pure finite element programming. But its main disadvantages are that it cannot be implemented in time domain. The purpose of this paper is to propose an approximation to the original approach which enables one to carry out this effective method in time domain as well as in frequency domain. Based on the present investigation, it is proven that the Approximate Wavenumber approach has inherent characteristics, which allows it to be envisaged as an effective technique for calculating the response of concrete gravity dam-reservoir systems in time domain.

The method is described initially. Subsequently, the response of an idealized triangular dam-reservoir system is obtained by the proposed approach as well as by applying two other well-known absorbing conditions which are widely utilized in practice. The results are also controlled against the corresponding exact responses. It should be emphasized that all results presented herein are obtained by the FE-FE method under different absorbing conditions applied on the truncation boundary. These include two well-known absorbing conditions referred to as Sommerfeld and Sharan as well as the proposed approach of the present study (i.e. Approximate Wavenumber condition).

It is concluded that the maximum error for the Approximate Wavenumber approach is in the range of 10 percent at the major peaks of the response. This occurs mainly for the very low reservoir lengths under full reflective reservoir base condition and vertical excitation. This is a remarkable result for any kind of robust truncation boundary simulation that one may expect. The fundamental frequency of the system is captured correctly for the Approximate Wavenumber approach, even in cases of low reservoir length.

Based on this investigation, it is proven that the Approximate Wavenumber approach has inherent characteristics, which allows it to be envisaged as an effective technique for calculating the response of concrete gravity dam-reservoir systems in time domain. It is concluded that the maximum error for the Approximate Wavenumber approach is in the range of 10 percent at the major peaks of the response. This occurs mainly for the very low reservoir lengths under full reflective reservoir base condition and vertical excitation. This is a remarkable result for any kind of robust truncation boundary simulation that one may expect.

The finite element method (FEM) is used to calculate the two-dimensional anti-plane dynamic response of structure embedded in D’Alembert viscoelastic multilayered soil on the rigid bedrock. This paper aims to research a time-domain absorbing boundary condition (ABC), which should be imposed on the truncation boundary of the finite domain to represent the dynamic interaction between the truncated infinite domain and the finite domain.

A high-order ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. A new operator separation method and the mode reduction are adopted to construct the time-domain ABC.

The derivation of the ABC is accurate for the single layer but less accurate for the multilayer. To achieve high accuracy, therefore, the distance from the truncation boundary to the region of interest can be zero for the single layer but need to be about 0.5 times of the total layer height of the infinite domain for the multilayer. Both single-layered and multilayered numerical examples verify that the accuracy of the ABC is almost the same for both cases of only using the modal number excited by dynamic load and using the full modal number of infinite domain. Using the ABC with reduced modes can not only reduce the computation cost but also be more friendly to the stability. Numerical examples demonstrate the superior properties of the proposed ABC with stability, high accuracy and remarkable coupling with the FEM.

A high-order time-domain ABC for scalar wave propagation in the D’Alembert viscoelastic multilayered media is proposed. The proposed ABC is suitable for both linear elastic and D’Alembert viscoelastic media, and it can be coupled seamlessly with the FEM. A new operator separation method combining mode reduction is presented with better stability than the existing methods.

The purpose of this paper is to propose a stable high-order absorbing boundary condition (ABC) based on new continued fraction for scalar wave propagation in 2D and 3D unbounded layers.

The ABC is obtained based on continued fraction (CF) expansion of the frequency-domain dynamic stiffness coefficient (DtN kernel) on the artificial boundary of a truncated infinite domain. The CF which has been used to the thin layer method in [69] will be applied to the DtN method to develop a time-domain high-order ABC for the transient scalar wave propagation in 2D. Furthermore, a new stable composite-CF is proposed in this study for 3D unbounded layers by nesting the above CF for 2D layer and another CF.

The ABS has been transformed from frequency to time domain by using the auxiliary variable technique. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the ABC-FEM coupled system is discussed and cured.

This manuscript establishes a stable high-order time-domain ABC for the scalar wave equation in 2D and 3D unbounded layers, which is based on the new continued fraction. The high-order time-domain ABC can couple seamlessly with the finite element method. The instability of the coupled system is discussed and cured.

The paper has the purpose of proposing a new open boundary condition to be used in conjunction with the finite integration technique (FIT) for the modelling of passive on‐chip components.

This boundary condition is ensured by using a virtual layer that surrounds the computational domain.

The paper proves which are the optimal material properties of the equivalent layer of open boundary.

When modelling passive on‐chip components with FIT, the method proposed is more efficient than the strategic dual image technique.

The paper shows the advantage of this approach – that the analysis algorithm remains unchanged, while saving the field‐circuit compatibility properties, such as current conservation.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The response of an idealized triangular concrete gravity dam is studied due to horizontal and vertical ground motions for both fully reflective and absorptive reservoir bottom conditions. For each combination, in this paper different orders of Givoli-Neta (G-N) high-order truncation condition are aimed to be evaluated from accuracy point of view by comparing the results against corresponding exact solutions which relies on utilizing a two-dimensional fluid hyper-element.

In present study, the dynamic analysis of concrete gravity dam-reservoir systems is formulated by Finite Element (FE)-(FE-TE) approach. In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the G-N high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.

It was observed that trend in gaining accuracy with increase in the order of G-N condition were basically the same for both horizontal and vertical ground motions under full reflective reservoir bottom condition. Moreover, convergence rate increases for absorptive reservoir bottom condition cases in comparison with fully reflective cases. It is also noticed that in certain cases, the responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on G-N condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete gravity dam-reservoir systems.

Dynamic analysis of concrete gravity dam-reservoir systems are formulated by a new method. The salient aspect of the technique is that it utilizes G-N high-order condition at the truncation boundary. This is achieved by developing a special truncation element which its generalized matrices are derived for Finite Element Method (FEM) programmers. The method is discussed for all types of excitation and reservoir bottom conditions. It must be emphasized that although time harmonic analysis is considered in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Subsequently, the response of idealized Morrow Point arch dam is studied due to stream, vertical and cross-stream ground motions for reservoir bottom/sidewalls conditions of both fully reflective and absorptive. For each combination, different orders of Hagstrom–Warburton (HW) condition are evaluated from accuracy point of view by comparing them against exact solutions. It should be emphasized that normalized length of reservoir near-field region is taken as a very low value of L/H = 0.2 during this process which makes it a very challenging test for any kind of truncation boundary condition.

In present study, dynamic analysis of concrete arch dam-reservoir systems is formulated by FE-(FE-TE) approach [i.e. finite element-(finite element-truncation element)]. In this technique, dam and reservoir are discretized by solid and fluid finite elements. Moreover, the HW high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially explained in details.

The trend in gaining accuracy with increase in order of HW condition were basically the same for all three types of excitations under both full reflective and absorptive reservoir bottom/sidewalls conditions. The only exception was for cross-stream excitation response which was showing less accurate results near the first major peak for moderate orders of HW (e.g. O3-2) in comparison to what was observed for responses due to symmetric excitations (stream and vertical). This is mainly attributed to the selection of evanescent-type parameters of HW condition which is based on the first symmetric mode of reservoir. However, it is noted that error diminishes even for cross-stream excitation as order increases. High orders of HW condition, such as O5-5 considered herein, generate highly accurate responses for all three possible excitations under both types of full reflective and absorptive reservoir bottom/sidewalls conditions. It is such that responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on HW condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete arch dam-reservoir systems.

Dynamic analysis of concrete arch dam-reservoir system is formulated by new method. HW high-order condition is applied for a very low and challenging reservoir length. Different orders are evaluated against exact solution with excellent agreement. Generalized matrices of truncation element are derived for FEM programmers. The method is discussed for all types of excitation and reservoir base conditions.

The design of microwave circuits requires detailed knowledge on the electromagnetic properties of the transmission lines used. This can be obtained by applying Maxwell’s equations to a longitudinally homogeneous waveguide structure, which results in an eigenvalue problem for the propagation constant. Special attention is paid to the so‐called perfectly matched layer boundary conditions (PML). Using the finite integration technique we get an algebraic formulation. The finite volume of the PML introduces additional modes that are not an intrinsic property of the waveguide. In the presence of losses or absorbing boundary conditions the matrix of the eigenvalue problem is complex. A method which avoids the computation of all eigenvalues is presented in an effort to find the few propagating modes one is interested in. This method is an extension of a solver presented by the authors in a previous paper which analyses the lossless case. Using mapping relations between the planes of eigenvalues and propagation constants a strip in the complex plane is determined containing the desired propagation constants and some that correspond to the PML modes. In an additional step the PML modes are eliminated.The numerical effort of the presented method is reduced considerably compared to a full calculation of all eigenvalues.

A basic difficulty encountered in applying the finite element method to unbounded wave problems is that the domain in which the field is to be computed is unbounded, while finite element models are of finite size. There are several ways to overcome this difficulty. The widely used method is to truncate the finite element model at a finite position and apply suitable boundary conditions there. The relevant boundary conditions must absorb the outgoing wave and have been called absorbing boundary conditions (ABC's).

This work is concerned with the development and the numerical investigation of a hybridizable discontinuous Galerkin (HDG) method for the simulation of two‐dimensional time‐harmonic electromagnetic wave propagation problems.

The proposed HDG method for the discretization of the two‐dimensional transverse magnetic Maxwell equations relies on an arbitrary high order nodal interpolation of the electromagnetic field components and is formulated on triangular meshes. In the HDG method, an additional hybrid variable is introduced on the faces of the elements, with which the element‐wise (local) solutions can be defined. A so‐called conservativity condition is imposed on the numerical flux, which can be defined in terms of the hybrid variable, at the interface between neighbouring elements. The linear system of equations for the unknowns associated with the hybrid variable is solved here using a multifrontal sparse LU method. The formulation is given, and the relationship between the considered HDG method and a standard upwind flux‐based DG method is also examined.

The approximate solutions for both electric and magnetic fields converge with the optimal order of p+1 in L₂ norm, when the interpolation order on every element and every interface is p and the sought solution is sufficiently regular. The presented numerical results show the effectiveness of the proposed HDG method, especially when compared with a classical upwind flux‐based DG method.

The work described here is a demonstration of the viability of a HDG formulation for solving the time‐harmonic Maxwell equations through a detailed numerical assessment of accuracy properties and computational performances.