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Abstract This paper proposes a numerical method to model wave scattering by local inhomogeneities in elastic open waveguides. The damaged zone of the waveguide and its vicinity are described by a finite-element model. This model is coupled on the cross-section boundaries to a modal representation of the field propagating along the waveguide axis in the undamaged parts, yielding transparent boundary conditions. However, open waveguides are unbounded in the transverse direction, which complicates both the numerical resolution and the physical analysis. Theoretically, the wave fields are described by a discrete sum of trapped modes and two continuous sums on radiation modes. The latter is sometimes approximated by a discrete sum of leaky modes, which grow at infinity in the transverse direction. In this paper, a Perfectly Matched Layer (PML) of finite thickness is introduced to absorb outgoing waves in the transverse direction, yielding three types of discrete modes: trapped modes, leaky modes and PML modes (PML modes oscillate mainly inside the layer and are non-intrinsic to the physics). Two numerical test cases are considered: the scattering at the junction between a closed and an open cylindrical waveguides and the scattering by an axisymmetrical notch. Good agreement with literature results is found. In particular, the influence of PML modes on the scattered field is highlighted through numerical tests. Due to the lack of power orthogonality of leaky modes, it is also shown that the modal cross power can become significant, which complicates the scattering analysis of open waveguides. Finally, the generality of the proposed method is discussed through a three-dimensional test case considering an embedded bar with an oblique break. Graphical abstract Image 1 [ABSTRACT FROM AUTHOR]

Abstract Conventionally, the dynamic modeling of H-type gantry stage(HGS) assumes that the stiffness of mid-beam is extremely high so that its deformation is ignorable. This assumption apparently simplifies the study, but unavoidably compromises the modeling precision as it is not consistent with the real working status especially at high frequency motion. Comparing with similar studies on moving mass problems, the beam vibration of HGS is excited not only by the moving mass and system acceleration but also by the non-synchronized motion of the two moving ends of mid-beam. Therefore, the objective of this paper is to propose an assumed mode method based on simplified mode shapes(AMM-SMS) by simultaneously considering the lateral flexibility and the motion of the ends of mid-beam. The proposed AMM-SMS adopts the mode shapes of a simplified system, which has the same geometry boundary condition(BC) with the investigated system, to discretize the nonlinear kinematic equations of the proposed system. This method improves the modeling precision with low complexity, and can be applied in different BCs of FHGS. The proposed method is verified by various comparisons with the finite element method. Based on the AMM-SMS, the first three natural frequencies and mode shapes are studied. The open-loop responses of the system are obtained to analyze the effects of different BCs, of the motion of end-effector and of the external exciting force on the vibratory behavior. [ABSTRACT FROM AUTHOR]

Abstract Local artificial boundary conditions (ABCs) for the numerical simulation of waves have been successfully used for decades (most notably, the boundary conditions due to Engquist & Majda, Bayliss, Gunzburger & Turkel, and Higdon). The basic idea behind these boundary conditions is that they cancel several leading terms in an expansion of the solution. The larger the number of terms canceled, the higher the order of the boundary condition and, in turn, the smaller the reflection error due to truncation of the original unbounded domain by an artificial outer boundary. In practice, however, the use of local ABCs has been limited to low orders (first and second), because higher order boundary conditions involve higher order derivatives of the solution, which may harm well-posedness and cause numerical instabilities. They are also difficult to implement especially in finite elements. A prominent exception is the development of local high order ABCs based on auxiliary variables. In the current paper, we implement high order Bayliss–Turkel ABCs directly — with no auxiliary variables yet no discrete approximation of the constituent high order derivatives either. Instead, we represent the solution at the boundary as an expansion with respect to a continuous basis. For the spherical artificial boundary, the basis consists of eigenfunctions of the Beltrami operator (spherical harmonics), which enable replacing the high order derivatives in the ABCs with powers of the corresponding eigenvalues. The continuous representation at the boundary is coupled to higher order compact finite differences inside the domain by the method of difference potentials (MDP). It maintains high order accuracy even when the boundary is not aligned with the discretization grid. Highlights • Direct implementation of high order Bayliss–Gunzburger–Turkel (BGT) ABCs. • No auxiliary variables; no discretization of high order derivatives on the grid either. • Spectral representation of ABCs coupled with high order finite differences in the interior. • The method of difference potentials (MDP) renders the coupling most efficiently. • Numerical simulations fully corroborate the theoretical developments and expectations. [ABSTRACT FROM AUTHOR]

Abstract Large computation time is widely considered to be the most important issue in scientific research especially in solving structural evolution problems. Recent developments in this domain have shown that the use of non-incremental schemes through Model Order Reduction led to important results in saving time. Yet, the question arises here how to obtain more time-saving. This paper examines an approach based on a collection of significant modes given by Proper Generalized Decomposition (PGD) solution for different time scales in order to save more computation time. The dictionary of the significant modes allows to construct an accurate solution for different characteristic times and different boundary problems compared to the full solution with a relative error rate less than 5% and with a large time saving of order 50 compared to Finite Element Method (FEM). The ability of the approach with respect to cycle time is discussed. Highlights • A new approach is proposed to decrease computational time for cyclic problems involving different time scales. • The approach is based on the use of pre-computed space–time modes which are further collected in a dictionary. • For a physical time belonging to the range of the dictionary, the solution can be accurately predicted. • For a given cycle time, the dictionary leads to an accurate if it contains the modes associated with this specific time. [ABSTRACT FROM AUTHOR]

Highlights • We derive that Cahn–Hilliard equation possesses a local energy dissipation law (LEDL). • Based on the observation, three LEDL schemes for the CH equation are derived. • Three schemes are independent of boundary conditions. • Such schemes are proven to conserve the LEDL in any local region. • Our schemes hold the total energy stable laws and the mass laws. Abstract In this paper, we show that the Cahn–Hilliard equation possesses a local energy dissipation law, which is independent of boundary conditions and produces much more information of the original problem. To inherit the intrinsic property, we derive three novel local structure-preserving algorithms for the 2D Cahn–Hilliard equation by the concatenating method. In particular, when the nonlinear bulk potential f (ϕ) in the equation is chosen as the Ginzburg–Landau double-well potential, the method discussed by Zhang and Qiao (2012) [50] is a special case of our scheme II. Thanks to the Leibnitz rules and properties of operators, the three schemes are rigorously proven to conserve the discrete local energy dissipation law in any local time–space region. Under periodic boundary conditions, the schemes are proven to possess the discrete mass conservation and total energy dissipation laws. Numerical experiments are conducted to show the performance of the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper presents a new approach, referred to here as the two-dimensional spectral-Tchebychev (2D-ST) technique, to predict the dynamics of thick plates having arbitrary geometries under different boundary conditions. The integral boundary value problem governing the dynamics of plate-like structures is obtained using the Mindlin plate theory and following an energy-based approach. To solve the boundary value problem numerically, a spectral-Tchebychev based solution technique is developed. To simplify the calculation of integral and derivative operations and thus to increase the numerical efficiency of the solution approach, a one-to-one coordinate mapping technique is used to map the arbitrary geometry onto an equivalent rectangular in-plane shape of the plate. The proposed solution technique is applied to various different plate problems to assess the accuracy and show the applicability of the technique. In each case, the convergence of the solution is analyzed, and the predicted (non-dimensional) natural frequencies are compared to those found in the literature or to those found using finite element modeling. It is shown that the calculated natural frequencies converge exponentially with increasing number of Tchebychev polynomials used and are in excellent agreement with those found in the literature and found form a finite elements solution. Therefore, it is concluded that the presented spectral-Tchebychev solution technique can accurately and efficiently capture the dynamics of thick plates having arbitrary geometries. Furthermore, the utility of the 2D-ST is demonstrated by comparing the results obtained using a three-dimensional solution approach. [ABSTRACT FROM AUTHOR]

A hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P , promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2 . An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy. Significant accuracy gains in manufactured solution error norms are noted even with modest promotion of the underlying polynomial order. The paper also demonstrates the CVFEM/DG methodology on two production-like simulation cases that include an inner block subjected to solid rotation, i.e., each of the simulations include a sliding mesh, non-conformal interface. The first production case presented is a turbulent flow past a high-rate-of-rotation cube ( Re , 4000; RPM, 3600) on like and mixed-order polynomial interfaces. The final simulation case is a full-scale Vestas V27 225 kW wind turbine (tower and nacelle omitted) in which a hybrid topology, low-order mesh is used. Both production simulations provide confidence in the underlying capability and demonstrate the viability of this hybrid method for deployment towards high-fidelity wind energy validation and analysis. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis for the stick-slip vibration of a transversely moving beam, considering both stick-slip transition and friction force discontinuity. The dynamic state of the beam was separated into the stick state and the slip state, and boundary conditions were defined for both. By applying the finite element method, two matrix-vector equations were derived: one for stick state and the other for slip state. However, the equations have different degrees of freedom depending on whether the end of a beam sticks or slips, so we encountered difficulties in time integration. To overcome the difficulties, we proposed a new numerical technique to alternatively use the matrix-vector equations with different matrix sizes. In addition, to eliminate spurious high-frequency responses, we applied the generalized- α time integration method with appropriate value of high-frequency numerical dissipation. Finally, the dynamic responses of stick-slip vibration were analyzed in time and frequency domains: the dynamic behavior of the beam was explained to facilitate understanding of the stick-slip motion, and frequency characteristics of the stick-slip vibration were investigated in relation to the natural frequencies of the beam. The effects of the axial load and the moving speed upon the dynamic response were also examined. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid Wave Based Method – Finite Element unit cell method to predict the absorption, reflection and transmission properties of arbitrary, two-dimensional periodic structures. The planar periodic structure, represented by its unit cell combined with Bloch–Floquet periodicity boundary conditions, is modelled within the Finite Element Method, allowing to represent complex geometries and to include any type of physics. The planar periodic structure is coupled to semi-infinite acoustic domains above and/or below, in which the dynamic pressure field is modelled with the Wave Based Method, applying a wave function set that fulfills the Helmholtz equation and satisfies the Sommerfeld radiation condition and the Bloch–Floquet periodicity conditions inherently. The dynamic fields described within both frameworks are coupled using a direct coupling strategy, accounting for the mutual dynamic interactions via a weighted residual formulation. The method explicitly accounts for the interaction between the unit cell and the surrounding acoustic domain, also accounting for higher order periodic waves. The convergence of the method is analysed and its applicability is shown for a variety of problems, proving it to be a useful tool combining the strengths of two methods. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive finite element method is proposed for solving Kohn–Sham equation with the multilevel correction technique. In the method, the Kohn–Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn–Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn–Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments. [ABSTRACT FROM AUTHOR]

Local multiscale methods often construct multiscale basis functions in the offline stage without taking into account input parameters, such as source terms, boundary conditions, and so on. These basis functions are then used in the online stage with a specific input parameter to solve the global problem at a reduced computational cost. Recently, online approaches have been introduced, where multiscale basis functions are adaptively constructed in some regions to reduce the error significantly. In multiscale methods, it is desired to have only 1–2 iterations to reduce the error to a desired threshold. Using Generalized Multiscale Finite Element Framework [10] , it was shown that by choosing sufficient number of offline basis functions, the error reduction can be made independent of physical parameters, such as scales and contrast. In this paper, our goal is to improve this. Using our recently proposed approach [4] and special online basis construction in oversampled regions, we show that the error reduction can be made sufficiently large by appropriately selecting oversampling regions. Our numerical results show that one can achieve a three order of magnitude error reduction, which is better than our previous methods. We also develop an adaptive algorithm and enrich in selected regions with large residuals. In our adaptive method, we show that the convergence rate can be determined by a user-defined parameter and we confirm this by numerical simulations. The analysis of the method is presented. [ABSTRACT FROM AUTHOR]

This paper presents the application of the spectral-Tchebychev (ST) technique for solution of three-dimensional dynamics of curved beams/structures having variable and arbitrary cross-section under mixed boundary conditions. To accurately capture the vibrational behavior of curved structures, a three-dimensional (3D) solution approach is required since these structures generally exhibit coupled motions. In this study, the integral boundary value problem (IBVP) governing the dynamics of the curved structures is found using extended Hamilton's principle where the strain energy is expressed using 3D linear elasticity equation. To solve the IBVP numerically, the 3D spectral Tchebychev (3D-ST) approach is used. To evaluate the integral and derivative operations defined by the IBVP and to render the complex geometry into an equivalent straight beam with rectangular cross-section, a series of coordinate transformations are applied. To validate and assess the performance of the presented solution approach, two case studies are performed: (i) curved beam with rectangular cross-section, (ii) curved and pretwisted beam with airfoil cross-section. In both cases, the results (natural frequencies and mode shapes) are also found using a finite element (FE) solution approach. It is shown that the difference in predicted natural frequencies are less than 1%, and the mode shapes are in excellent agreement based on the modal assurance criteria (MAC) analyses; however, the presented spectral-Tchebychev solution approach significantly reduces the computational burden. Therefore, it can be concluded that the presented solution approach can capture the 3D vibrational behavior of curved beams as accurately as an FE solution, but for a fraction of the computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we develop an efficient lattice Boltzmann model for the two-phase moving contact line problem with variable density. The Navier–Stokes and Cahn–Hilliard equations are recovered from the lattice Boltzmann model proposed by Fakhari and Rahimian [5] . To improve numerical stability, we present a semi-implicit lattice Boltzmann method together with a mixed finite difference scheme. In order to describe the behavior of the contact line motion on the boundary, we incorporate the generalized Navier boundary condition [25] by the nonequilibrium extrapolation method [8] . The proposed method is easy to implement and retains the advantage of the standard lattice Boltzmann method. Numerical tests are carried out to verify the proposed method. Our numerical results show that the present approach is able to model two-phase flows with variable density and moving contact line. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new extrapolation cascadic multigrid method, which makes it possible to solve three dimensional elliptic boundary value problems with over 100 million unknowns on a desktop computer in half a minute. First, by combining Richardson extrapolation and quadratic finite element (FE) interpolation for the numerical solutions on two-level of grids (current and previous grids), we provide a quite good initial guess for the iterative solution on the next finer grid, which is a third-order approximation to the FE solution. And the resulting large linear system from the FE discretization is then solved by the Jacobi-preconditioned conjugate gradient (JCG) method with the obtained initial guess. Additionally, instead of performing a fixed number of iterations as used in existing cascadic multigrid methods, a relative residual tolerance is introduced in the JCG solver, which enables us to obtain conveniently the numerical solution with the desired accuracy. Moreover, a simple method based on the midpoint extrapolation formula is proposed to achieve higher-order accuracy on the finest grid cheaply and directly. Test results from four examples including two smooth problems with both constant and variable coefficients, an H 3 -regular problem as well as an anisotropic problem are reported to show that the proposed method has much better efficiency compared to the classical V-cycle and W-cycle multigrid methods. Finally, we present the reason why our method is highly efficient for solving these elliptic problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents computational models employing special transformation-based media—which we call software metamaterials—for the purpose of enhancing the ability of numerical modeling methods for solving multi-scale electromagnetic boundary value problems involving features with multiple length or frequency scales or both. The multi-scale problems, in general, suffer from difficulties in mesh generation and the number of unknowns due to certain meshing requirements dictated by the fine features of the problem. The underlying idea in this study is to introduce transformation media into the computational domain of the finite element method (or finite difference methods) in order to allow uniform and easy-to-generate meshes by avoiding mesh refinement, and therefore, to develop efficient and simple computer-aided simulation tools. In other words, a virtual equivalent problem is created, which acts like the original problem. The techniques proposed in this paper are validated via several finite element simulations in the context of TMz electromagnetic scattering problems. [Copyright &y& Elsevier]

Abstract: This paper proposes the identification of vibration excitations by an inverse method. The use of the local operator of a structure, for which the vibration field is obtained by measurements, is investigated. This method has already been developed on analytically known structures, but there are as yet few applications. The goal of this paper is to adapt the same technique by using an operator obtained with the Finite Element Method rather than a discretised differential motion equation. The first difficulty is the measurement of rotational degrees of freedom. A concept analogous to an observation matrix enabling only the measurement of displacements is then proposed. The method of extracting the operator on a part of the structure is also discussed. Two variants are proposed: an operator with free boundary conditions and a truncated operator without boundary conditions. The first permits identifying internal forces at the boundaries of the subdomain, whereas the second ignores them. In order to regularise the inverse method, a Tikhonov approach is used. An important point of this paper is the discussion of the effect of this regularisation which implies ambiguities between reconstructed forces and moments in the results. The possibility of an a priori “force only” assumption is then demonstrated and recommended. After illustrations obtained from numerical simulations on beams, an experimental validation is provided for a beam excited by a shaker where several signals are used, giving several signal to noise ratios. The results are discussed and compared to the force measured directly by a piezoelectric sensor. [Copyright &y& Elsevier]

This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing. [ABSTRACT FROM AUTHOR]

An acceleration frequency response function (FRF) based model updating method is presented in this paper, which introduces Kriging model as metamodel into the optimization process instead of iterating the finite element analysis directly. The Kriging model is taken as a fast running model that can reduce solving time and facilitate the application of intelligent algorithms in model updating. The training samples for Kriging model are generated by the design of experiment (DOE), whose response corresponds to the difference between experimental acceleration FRFs and its counterpart of finite element model (FEM) at selected frequency points. The boundary condition is taken into account, and a two-step DOE method is proposed for reducing the number of training samples. The first step is to select the design variables from the boundary condition, and the selected variables will be passed to the second step for generating the training samples. The optimization results of the design variables are taken as the updated values of the design variables to calibrate the FEM, and then the analytical FRFs tend to coincide with the experimental FRFs. The proposed method is performed successfully on a composite structure of honeycomb sandwich beam, after model updating, the analytical acceleration FRFs have a significant improvement to match the experimental data especially when the damping ratios are adjusted. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the local ultraconvergence of k -degree ( k ≥ 3 ) finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular/triangular meshes T h on a bounded rectangular domain D . The k -degree finite element estimates are developed for the Green's function and its derivatives. They are employed to explore the relationship among d i s t ( x , ∂ D ) , d i s t ( x , M ) and the ultraconvergence of k -degree finite element methods at vertex x , where M is the set of corners of D . Numerical examples are conducted to demonstrate our theoretical results. [ABSTRACT FROM AUTHOR]

Based on the numerical method proposed in Hu et al. (2018) [22] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the strategy of separately handling the nonlinear Hartree potential and exchange-correlation potential, and ii). parallelizing the algorithm in an eigenpairwise approach. The feasibility of two approaches is analyzed in detail, and the new algorithm is described completely. Compared with previous results, a significant improvement of numerical efficiency can be observed from plenty of numerical experiments, which make the new method more suitable for the practical problems. • An accelerating multilevel correction AFEM is designed to solve Kohn-Sham equation. • Solving large-scale nonlinear eigenvalue problem is avoided. • A small-scale Kohn-Sham equation and large-scale boundary value problem are required. • Hartree potential and exchange-correlation potential are handling in a nested scheme. • The novel algorithm can be performed in an eigenpairwise approach. [ABSTRACT FROM AUTHOR]

In this paper we study the dynamics of parabolic semilinear differential equations with homogeneous Dirichlet boundary conditions via the discretization of finite element method. We provide an appropriate functional setting to treat this problem and, as a first step, we show the continuity of the set of equilibria and of its linear unstable manifolds. [ABSTRACT FROM AUTHOR]

In this paper, a full (nested) multigrid scheme is proposed to solve eigenvalue problems. The idea here is to use a correction method to transform the eigenvalue problem solving to a series of corresponding boundary value problem solving and eigenvalue problems defined on a very low-dimensional finite element space. The boundary value problems which are defined on a sequence of multilevel finite element spaces can be solved by some multigrid iteration steps. The computational work of this new scheme can reach the same optimal order as solving the corresponding boundary value problem by the full multigrid method. Therefore, this type of full multigrid method improves the overfull efficiency of the eigenvalue problem solving. [ABSTRACT FROM AUTHOR]

Motivated by the need to handle complex boundary conditions efficiently and accurately in particle-in-cell (PIC) simulations, this paper presents a three-dimensional (3D) linear immersed finite element (IFE) method with non-homogeneous flux jump conditions for solving electrostatic field involving complex boundary conditions using structured meshes independent of the interface. This method treats an object boundary as part of the simulation domain and solves the electric field at the boundary as an interface problem. In order to resolve charging on a dielectric surface, a new 3D linear IFE basis function is designed for each interface element to capture the electric field jump on the interface. Numerical experiments are provided to demonstrate the optimal convergence rates in L 2 and H 1 norms of the IFE solution. This new IFE method is integrated into a PIC method for simulations involving charging of a complex dielectric surface in a plasma. A numerical study of plasma–surface interactions at the lunar terminator is presented to demonstrate the applicability of the new method. [ABSTRACT FROM AUTHOR]

This paper quantitatively investigates groundwater-seawater interactions and explores the annual variations and spatial distributions in submarine groundwater discharge (SGD) and seawater intrusion (SWI) in the Bohai Sea coastal zone in Tianjin, China. A three-dimensional finite element model, FEMWATER in the GMS environment, is developed to simulate density-dependent flow and transport in coastal groundwater aquifers. A sensitivity analysis is used to explore how the model output varies with the hydrogeological parameters and boundary conditions. The results suggest that both SGD and SWI occur across the sea-aquifer interface. Along the modeled 45 km stretch of coastline, the annual SGD and SWI rates are 4.23 × 10 7 m 3 /yr and 0.86 × 10 7 m 3 /yr, respectively. The results also indicate that SGD is highest in the winter and lowest in the summer, and SWI exhibits the opposite trend. This change in flow direction across the sea-aquifer interface corresponds to seasonal changes in sea level. SGD mainly occurs in the southern and northern parts of the study area, and SWI primarily occurs in the central part. The results of the sensitivity analysis suggest that the SGD and SWI model outputs are most sensitive to sea level and the hydraulic conductivity in the top layer. [ABSTRACT FROM AUTHOR]

• Present a nonuniform size modified Poisson-Boltzmann ion channel model (nuSMPBIC). • Partition nuSMPBIC into three-submodels to overcome singularity difficulties. • Propose efficient iterative methods for solving a nuSMPBIC finite element system. • Develop a nuSMPBIC finite element package for a 3D ion channel molecular structure. • Report numerical tests for voltage-dependent anion channel and four ionic species. In this paper, a nonuniform size modified Poisson-Boltzmann ion channel (nuSMPBIC) model is presented as a nonlinear system of an electrostatic potential and multiple ionic concentrations. It mixes nonlinear algebraic equations with a Poisson boundary value problem involving Dirichlet-Neumann mixed boundary value conditions and a membrane surface charge density to reflect the effects of ion sizes and membrane charges on electrostatics and ionic concentrations. To overcome the difficulties of strong singularities and exponential nonlinearities, it is split into three submodels with a solution of Model 1 collecting all the singular points and Models 2 and 3 much easier to solve numerically than the original nuSMPBIC model. A damped two-block iterative method is then presented to solve Model 3, along with a novel modified Newton iterative scheme for solving each related nonlinear algebraic system. To this end, an effective nuSMPBIC finite element solver is derived and then implemented as a program package that works for an ion channel protein with a three-dimensional molecular structure and a mixture of multiple ionic species. Numerical results for a voltage-dependent anion channel (VDAC) in a mixture of four ionic species demonstrate a fast convergence rate of the damped two-block iterative method, the high performance of the software package, and the importance of considering nonuniform ion sizes. Moreover, the nuSMPBIC model is validated by the anion selectivity property of VDAC. [ABSTRACT FROM AUTHOR]

Abstract: The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. [Copyright &y& Elsevier]

Abstract: This paper extends the analysis of the self-excitated vibrations of a drilling structure presented in an earlier paper [T. Richard, C. Germay, E. Detournay, A simplified model to explore the root cause of stick-slip vibrations in drilling systems with drag bits, Journal of Sound and Vibration 305 (3) (2007) 432–456] by basing the formulation of the model on a continuum representation of the drillstring rather than on a characterization of the drilling structure by a 2 degree of freedom system. The particular boundary conditions at the bit–rock interface, which according to this model are responsible for the self-excited vibrations, account for both cutting and frictional contact processes. The cutting process combined with the quasi-helical motion of the bit leads to a regenerative effect that introduces a coupling between the axial and torsional modes of vibrations and a state-dependent delay in the governing equations, while the frictional contact process is associated with discontinuities in the boundary conditions when the bit sticks in its axial and angular motion. The dynamic response of the drilling structure is computed using the finite element method. While the general tendencies of the system response predicted by the discrete model are confirmed by this computational model (for example that the occurrence of stick-slip vibrations as well as the risk of bit bouncing are enhanced with an increase of the weight-on-bit or a decrease of the rotational speed), new features in the self-excited response of the drillstring can be detected. In particular, stick-slip vibrations are predicted to occur at natural frequencies of the drillstring different from the fundamental one (as sometimes observed in field operations), depending on the operating parameters. [Copyright &y& Elsevier]

Abstract: This paper proposes a hybrid method for the prediction of vibrational and acoustic responses of low-damping system in the medium-to-high frequency ranges by using the power flow analysis (PFA) algorithm and statistical energy analysis (SEA) coupling concepts. The main part of this method is the application of the coupling loss factor (CLF) of SEA to the boundary condition of PFA in reverberant system. First, for hybrid PFA, the hybrid boundary conditions on 1-D and 2-D cases were derived in the general form. To verify the derived boundary conditions, numerical analyses for each case were performed. The hybrid PFA solutions using derived boundary conditions were compared with the classical PFA solutions with various reverberance factors including the effects of the characteristic length, excitation frequency and group velocity besides damping loss factor of the subsystem. Additionally, the hybrid PFA on 3-D case and the hybrid power flow finite element method (PFFEM) for hybrid PFA of built-up structures are described in the other companion paper. [Copyright &y& Elsevier]

Abstract: In this paper, the first nine frequency parameters of circular and annular plates with variable thickness and combined boundary conditions are computed for different thickness to radius ratios. Several combined boundary conditions are considered for inner and outer edges. These are free, soft and hard simply supported, and clamped boundary conditions. Three-dimensional elasticity theory is used. Results of this paper are compared with works of other authors and the results of finite element method analysis which are in agreement. Data for thick circular and annular plates with linear and parabolic thickness variation and different combinations are presented for the first time. [Copyright &y& Elsevier]

In order to apply model reduction technique to improve the computational efficiency for the large-scale FEM model of a vehicle, this paper presents the handling approaches for three widely-used boundary conditions, namely fixed boundary condition (FBC), prescribed motion (PSM) and coupling (COUP), respectively. It is found that iterated improved reduction system (IIRS) reduction method tends to generate better reduction approximation. Guyan method is not sensitive to the sequence of reduction and constraint under FBC, and can thus provide flexibility in handling different boundary conditions for the same system. As for PSM, ‘constraint first’ is recommended no matter which reduction method is used, and then separate reduction models can be coupled to form a new model with relative small dofs. By selecting appropriate master dofs for model reduction, the coupled model based on reduced models could produce same results as the original full one. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe a procedure for computing the dynamic stiffness matrix relative to the in-plane effect for an orthotropic rectangular plate. The dynamic stiffness matrix is calculated for free edge boundary conditions. The formulation is based on strong solutions for the equations of motion for an orthotropic plate obtained with the Levy series and a Gorman decomposition of the free boundary conditions. The results obtained for the in-plane harmonic response are validated by the Finite Element Method. [ABSTRACT FROM AUTHOR]

This paper deals with the dynamic response of pump-turbine impellers. A pump-turbine impeller is a complex structure attached to a rotor and rotating inside a casing full of water with very small clearances between the rotating and the stationary parts. The dynamic response of this type of structures is very complex and it is very much affected by the connection to the rotor as well as by the added mass and boundary conditions. As a consequence its calculation presents several uncertainties. First, the dynamic response of pump-turbine impellers is introduced. Second an experimental investigation in a real impeller attached to the rotor and inside the machine was carried out. For this investigation, the impeller of an existing pump-turbine unit with an installed power of 110 MW and a diameter of 2.87 m was studied. For a better analysis of the experimental results a numerical model using FEM was also built-up. Frequencies and mode-shapes were identified numerically and experimentally and the characteristics of the structural response analyzed. To determine the influence of the rotor and supporting structures on the impeller response the results were compared with the ones obtained with the same impeller but suspended (non-connected to the rotor). Experimental and numerical simulation were also used for this case. The changes in the dynamic response due to the rotor connection were determined. Finally the results obtained are compared with the results from other pump-turbine impellers of different designs and general conclusions about the dynamics of this type of structures are given. [ABSTRACT FROM AUTHOR]

The finite element vibration analysis of plates has become one of the classical problems over the past several decades. Different finite element plate models based on classical, standard and improved shear deformable plate theories, three-dimensional elasticity equations or their combinations have been developed. The ability and accuracy of each such model can be established by validating it against analytical models, if it is possible, or other numerical models. In this paper, a comparative study of different plate finite element models used for the free vibration analysis of homogeneous isotropic and anisotropic, composite laminated and sandwich thin and thick plates with different boundary conditions is presented. The aim of the study is to find out the weaknesses and strengths of each model used and to pick out their interchangeability for the finite element calculations. For comparisons, the plate models based on classical and first-order shear deformation theories within the framework of both single-layer and layer-wise concept and three-dimensional theory of elasticity are used. The models are created using the finite element package ABAQUS TM . Natural frequencies obtained by the authors are compared with results known in the literature from different analytical or approximate solutions and, then, the correlation between them is discussed in detail. At the end, conclusions are drawn concerning the utility of each model considered for vibration predictions of plates. [ABSTRACT FROM AUTHOR]

An alternative vector potential formulation is used to solve the Navier–Stokes (N–S) equations in 3D incompressible viscous flow problems with and without through-flow boundaries. Difficulties of the vector potential formulation include the implementation of boundary conditions for through-flow boundaries and the numerical treatment of fourth-order partial differential equations. The advantages on the other hand are the automatic satisfaction of the continuity equation; and pressure is decoupled from the velocity. The objective of this paper is to introduce the appropriate gauge and boundary conditions on the vector potential formulation by a localized meshless method. To handle the divergence-free property, a Coulomb gauge condition is enforced on the vector potential to ensure its existence and uniqueness mathematically. We further improve the algorithm to through-flow problems for the boundary conditions of vector potential by introducing the concept of Stokes' theorem. Based on this innovation, there is no need to include an additional variable to tackle the through-flow fields. This process will greatly simplify the imposition of boundary conditions by the vector potential approach. Under certain conditions, the coupled fourth-order partial differential equations can be easily solved by using this meshless local differential quadrature (LDQ) method. Due to the LDQ capability to deal with the high order differential equations, this algorithm is very attractive to solve this fourth-order vector potential formulation for the N–S equations as comparing to the conventional numerical schemes such as finite element or finite difference methods. The proposed vector potential formulation is simpler and has improved accuracy and efficiency compared to other pressure-free or pressure-coupled algorithms. This investigation can be regarded as the first complete study to obtain the N–S solutions by vector potential formulation through a LDQ method. Two classic 3D benchmark problems, lid-driven cavity and backward-facing step flows, are numerically solved to examine the feasibility of the improved algorithm. Results show the flexibility of the proposed vector potential formulation for the 3D Navier–Stokes equations. [ABSTRACT FROM AUTHOR]

In this paper, we construct second- and third-order hyperbolic residual-distribution schemes for general advection–diffusion problems on arbitrary triangular grids. We demonstrate that the accuracy of the second-order hyperbolic schemes in [J. Comput. Phys. 227 (2007) 315–352] and [J. Comput. Phys. 229 (2010) 3989–4016] can be greatly improved by requiring the scheme to preserve exact quadratic solutions. The improved second-order scheme can be easily extended to a third-order scheme by further requiring the exactness for cubic solutions. These schemes are constructed based on the SUPG methodology formulated in the framework of the residual-distribution method, and thus can be considered as economical and powerful alternatives to high-order finite-element methods. For both second- and third-order schemes, we construct a fully implicit solver by the exact residual Jacobian of the proposed second-order scheme, and demonstrate rapid convergence, typically with no more than 10–15 Newton iterations (and about 200–800 linear relaxations per Newton iteration), to reduce the residuals by ten orders of magnitude. We also demonstrate that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier–Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids even for a curved boundary problem, without introducing curved elements. A quadratic reconstruction of the curved boundary normals and a high-order integration technique on curved boundaries are also provided in details. [ABSTRACT FROM AUTHOR]

In this paper, an approach is presented to model the propagation of elastic waves and their interaction with defects in plate structures. The formulation is based on the Scaled Boundary Finite Element Method (SBFEM), a general semi-analytical method requiring the discretization of boundaries only. For a homogeneous finite or infinite plate section, only the through-thickness direction of the plate is discretized. To describe a defect, the full boundary of a short plate section of irregular shape is discretized. High-order spectral elements are employed for the discretization. The formulation for infinite plates can model the transmission into an unbounded domain exactly. Results are compared with conventional Finite Element Analyses in both time domain and frequency domain. The presented approach allows for the simulation of complex reflection and scattering phenomena using a very small number of degrees of freedom while the mesh consists of one-dimensional elements only. [ABSTRACT FROM AUTHOR]

The inclusion of rib-stiffened plates within the framework of Statistical Energy Analysis (SEA) is a challenge in the field of engineering noise control for the low- and mid-frequency ranges. This paper focuses on periodic ribbed plates with symmetric ribs and assesses different approaches using SEA to model bending wave transmission when one or both of the rectangular plates that form an L-junction are a periodic ribbed plate. SEA is compared with measurements and Finite Element Methods (FEM) with all plate boundaries pinned to give boundary conditions that are representative of engineering structures typically used for noise control. When one or both plates are ribbed, and the ribs are parallel to the junction, the closest agreement between measurements and FEM is with SEA models that use a combination of Bloch theory and wave theory to determine the coupling loss factors. However, when both plates are ribbed plates, one with ribs orientated perpendicular to the junction and the other with ribs parallel to the junction, the available SEA models which assume an effective isotropic plate, or an equivalent isotropic plate or angle-dependent bending stiffness all underestimate the energy level difference. [ABSTRACT FROM AUTHOR]

The accurate and detailed knowledge of the local flexibility which is introduced by a crack into a structure may be used in damage diagnosis. This paper investigates the variation of the local flexibility of cracked shafts under harmonic type of loadings causing tensional as well as compressional stresses around the crack faces in a periodic manner which inevitably lead to the opening and closure of the crack, i.e. the breathing mechanism. Time-dependent nonlinear finite element method (FEM) is adopted to analyze various crack sizes as well as time-dependent axial, bending and torsional types of loading. Special boundary conditions are adopted between crack faces to avoid penetration along the contact area and simultaneously permit the existence of stick or slip contact zones according to Coulomb׳s law. Deflection differences at the loaded edge between uncracked and cracked shaft are used for the computation of the local flexibilities. Apart from the computation of the diagonal terms of local flexibility matrix intensive emphasis is given to its off-diagonal coefficients which cause the coupling of motion between different degrees of freedom and thus may affect considerably the overall vibrational behavior of the shaft. [ABSTRACT FROM AUTHOR]

This paper presents an extension of the Pipe-in-Pipe (PiP) model for calculating vibrations from underground railways that allows for the incorporation of a multi-layered half-space geometry. The model is based on the assumption that the tunnel displacement is not influenced by the existence of a free surface or ground layers. The displacement at the tunnel–soil interface is calculated using a model of a tunnel embedded in a full space with soil properties corresponding to the soil in contact with the tunnel. Next, a full space model is used to determine the equivalent loads that produce the same displacements at the tunnel–soil interface. The soil displacements are calculated by multiplying these equivalent loads by Green׳s functions for a layered half-space. The results and the computation time of the proposed model are compared with those of an alternative coupled finite element–boundary element model that accounts for a tunnel embedded in a multi-layered half-space. While the overall response of the multi-layered half-space is well predicted, spatial shifts in the interference patterns are observed that result from the superposition of direct waves and waves reflected on the free surface and layer interfaces. The proposed model is much faster and can be run on a personal computer with much less use of memory. Therefore, it is a promising design tool to predict vibration from underground tunnels and to assess the performance of vibration countermeasures in an early design stage. [ABSTRACT FROM AUTHOR]

Parallel finite element nonlinear Stokes models have been successfully used for three-dimensional ice-sheet and glacier simulations due to their accuracy and efficiency, and their capability for easily handling highly irregular domains and different types of boundary conditions. In particular, the well-known Taylor-Hood element pair (continuous piecewise quadratic elements for velocity and continuous piecewise linear elements for pressure) results in highly accuracy velocity and pressure approximations. However, the Taylor-Hood element suffers from poor mass conservation which can lead to significant numerical mass balance errors for long-time simulations. In this paper, we develop and investigate a new finite element Stokes ice sheet dynamics model that enforces local element-wise mass conservation by enriching the pressure finite element space by adding the discontinuous piecewise constant pressure space to the Taylor-Hood pressure space. Through various numerical tests based on manufactured solutions, benchmark test problems, and the realistic Greenland ice-sheet, we demonstrate that, for ice-sheet modeling, the enriched Taylor-Hood finite element model remains highly accurate and efficient, and is physically more reliable and robust compared to the classic Taylor-Hood finite element model. [ABSTRACT FROM AUTHOR]

This paper is concerned with the P1 finite element approximation of the eigenvalue problem of second-order elliptic operators subject to the Dirichlet boundary condition. The focus is on the preservation of the basic properties of the principal eigenvalue and eigenfunctions of the continuous problem. It is shown that when the stiffness matrix is an irreducible M-matrix, the discrete eigenvalue problem maintains almost all of the basic properties such as the smallest eigenvalue being real and simple and the corresponding eigenfunctions being either positive or negative inside the physical domain. Mesh conditions leading to such a stiffness matrix are also studied. A sufficient condition is that the mesh is simplicial, interiorly connected, and acute when measured in the metric specified by the inverse of the diffusion matrix. The acute requirement can be replaced by the Delaunay condition in two dimensions. Numerical results show that when the stiffness matrix is not an M-matrix, a finite element approximation can be structurally different from the continuous eigenvalue problem: the eigenfunctions corresponding to the smallest eigenvalue can change sign over the physical domain and the smallest eigenvalue (in modulus) can even be complex for the case with nonsymmetric operators. [ABSTRACT FROM AUTHOR]

Abstract: We establish the boundary smoothing properties for the linear Kawahara equation: in this paper. Firstly, by Laplacian transformation, we give the explicit formula of the solution of (0.1): Then, by the fine estimates on ( ), we establish the boundary smoothing effect: for any , if the boundary data , then the solution and possesses the sharp trace regularity [Copyright &y& Elsevier]

Abstract: An exact expression of steady discrete shocks was recently obtained by the author in [9] for a class of residual-based compact schemes (RBC) applied to the inviscid Bürgers equation in a finite domain. Following the same lines, the analysis is extended to an infinite domain for a scalar conservation law with a general convex flux. For the dissipative high-order schemes considered, discrete shocks in infinite domain or with boundary conditions at short distance (Rankine–Hugoniot relations) are found to be very close. Besides, the present analytical description of shock capturing in infinite domain is explicit and so simple that it could lead to a new approach for correcting parasitic oscillations of high order RBC schemes. In a second part of the paper, exact solutions are also derived for equivalent differential equations (EDE) approximating schemes (subscript denotes the accuracy order) at orders 2p and . Although EDE involves Taylor expansions around steep structures, agreement between the exact EDE shock-profiles and the discrete shocks is remarkably good for and schemes. In addition, a strong similarity is demonstrated between the analytical expressions of discrete shocks and EDE shock profiles. [Copyright &y& Elsevier]

Abstract: The characteristics of beam-mode stability of fluid-conveying shell systems are investigated in this paper for shells with clamped-free (cantilevered) boundary conditions. An FEM algorithm is developed to conduct the investigation. A periodic shell structure of functionally graded material (FGM), termed as PFGM shell here, is designed so as to enhance the stability for the shell system, and to eliminate the stress concentration problems that exist in periodic structures. Results show that by the introduction of periodic design the critical velocities can be raised over several desired ranges of the dimensionless fluid density β, and the stress concentration is effectively reduced in the PFGM shell. Finally, the effects of the geometric shape, material parameters and spring supports on the dynamical stability are probed. [Copyright &y& Elsevier]

Abstract: In this paper, the dispersion properties of elastic waves in helical waveguides are investigated. The formulation is based on the Scaled Boundary Finite Element method (SBEFM). With a set of orthogonal unit basis introduced as the contravariant basis, the helical coordinate is firstly considered, where components of tensor retain the dimension of original quantity. Based on the strain–displacement relation, the eigenvalue matrix is obtained about wavenumbers and frequencies. The cross section of the waveguides is discretized by using high-order spectral elements. Moreover, the formulated linear matrix is utilized to design efficient and accurate algorithms to compute the eigenvalues of helical waveguides. Compared with the Pochhammer–Chree curves, the convergence and accuracy of the SBFEM are discussed. Finally, we give some dispersion curves for a wide range of lay angles and analyze in detail properties of cut-off frequency, mode separation and mode transition for elastic wave propagation in the helical waveguides. [Copyright &y& Elsevier]

Abstract: In this paper, an exact dynamic stiffness formulation using one-dimensional (1D) higher-order theories is presented and subsequently used to investigate the free vibration characteristics of solid and thin-walled structures. Higher-order kinematic fields are developed using the Carrera Unified Formulation, which allows for straightforward implementation of any-order theory without the need for ad hoc formulations. Classical beam theories (Euler–Bernoulli and Timoshenko) are also captured from the formulation as degenerate cases. The Principle of Virtual Displacements is used to derive the governing differential equations and the associated natural boundary conditions. An exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses. The explicit terms of the dynamic stiffness matrices are also presented. The resulting dynamic stiffness matrix is used with particular reference to the Wittrick–Williams algorithm to carry out the free vibration analysis of solid and thin-walled structures. The accuracy of the theory is confirmed both by published literature and by extensive finite element solutions using the commercial code . [Copyright &y& Elsevier]

Abstract: Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried out to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both and norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order to for the solution itself in norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order to in the norm for or Lipschitz continuous interfaces associated with a or continuous solution. [Copyright &y& Elsevier]

Abstract: Free vibration of stepped thickness rectangular plates is investigated in this paper using the spectral finite element method (SFEM). It is impossible to obtain closed-form solutions for a uniform rectangular plate with arbitrary boundary conditions except the Levy-type plates, i.e., at least simply-supported at two opposite edges. Moreover, the variation of plate thickness adds complexity to the problem. The Kantorovich method is employed to obtain an analytical approximation solution form. Then, a plate spectral finite element is developed accordingly in the frequency domain. Similar to the conventional finite element method (CFEM), after assembling elements and applying boundary conditions, each modal frequency and associated mode shape function can be determined by iteratively solving corresponding equations in plate x and y directions. Available literature results along with NASTRAN simulations are used to validate our SFEM predictions of stepped thickness plates with various boundary conditions. Compared to the CFEM, only a fraction of the mesh is needed to achieve comparable accuracy in each mode. Substantial computation cost can then be saved. Mode shape functions are extracted and presented in a semi-analytical form. Physical insights of wave propagation characteristics in a stepped thickness rectangular plate can be collected from these results. In summary, an efficient and accurate SFEM is developed to conduct free vibration analysis of stepped thickness rectangular plates with various boundary conditions. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the analysis of dynamic behavior of elastic cylindrical shells of rotation subjected to an annular flow of compressible fluid (gas) having both the axial and tangential velocity components. The behavior of the rotating and flowing fluid is described in the framework of the potential theory. The elastic shell is considered based on the model of the classical shell theory. Numerical simulation is done using a semi-analytical variant of the finite element method. The results of numerical experiments made to analyze the stability of shells with different boundary conditions, geometrical dimensions and widths of the annular gap are discussed. The influence of the fluid rotation on the critical flow velocities and the influence of the axial flow on the critical angular velocities of fluid rotation are estimated with reference to the variants, in which one of the velocity components is not taken into account. The effect of elasticity of the outer shell on the boundary of hydroelastic stability is analyzed. [Copyright &y& Elsevier]

Abstract: This paper presents a displacement reconstruction scheme using acceleration measured at a high sampling rate and displacement measured at a considerably low sampling rate. The governing equation and the boundary conditions for the reconstruction are derived using the variational statement of an inverse problem to minimize the errors between measured and reconstructed responses. The transfer function of the governing equation is identically 1 over whole frequency domain, and the proposed scheme would not result in any reconstruction error. A finite impulse response filter (FIR filter) is formulated through the finite element discretization of the governing equation. The Hermitian shape function is adopted to interpolate the displacement in a finite element. The transfer functions of the FIR filter are derived, and their characteristics are thoroughly discussed. It is recommended that the displacement sampling rate should be higher than the Nyquist rate of the target frequency, which is the lowest physically meaningful frequency in measured acceleration. In case the displacement sampling rate is lower than the recommended rate, the use of a higher target accuracy, which is the predefined accuracy at the target frequency, is required. The reconstruction of velocity with the proposed scheme is also presented. The validity of the proposed scheme is demonstrated with a numerical simulation study and a field test on a simply-supported railway bridge. [Copyright &y& Elsevier]