Journal articles: 'Boundary element methods. Time-domain analysis'

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Gimperlein, Heiko, and David Stark. "Algorithmic aspects of enriched time domain boundary element methods." Engineering Analysis with Boundary Elements 100 (March 2019): 118–24. http://dx.doi.org/10.1016/j.enganabound.2018.02.010.

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Bai, Xiaoyong, and Ronald Y. S. Pak. "On the stability of direct time-domain boundary element methods for elastodynamics." Engineering Analysis with Boundary Elements 96 (November 2018): 138–49. http://dx.doi.org/10.1016/j.enganabound.2018.08.001.

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Nintcheu Fata, S. "Treatment of domain integrals in boundary element methods." Applied Numerical Mathematics 62, no. 6 (June 2012): 720–35. http://dx.doi.org/10.1016/j.apnum.2010.07.003.

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Ingber, Marc S., John A. Tanski, and Paul Alsing. "A domain decomposition tool for boundary element methods." Engineering Analysis with Boundary Elements 31, no. 11 (November 2007): 890–96. http://dx.doi.org/10.1016/j.enganabound.2007.03.002.

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Sarkis, Marcus, and Xuemin Tu. "Singular Function Mortar Finite Element Methods." Computational Methods in Applied Mathematics 3, no. 1 (2003): 202–18. http://dx.doi.org/10.2478/cmam-2003-0014.

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AbstractWe consider the Poisson equation with Dirichlet boundary conditions on a polygonal domain with one reentrant corner. We introduce new nonconforming finite element discretizations based on mortar techniques and singular functions. The main idea introduced in this paper is the replacement of cut-off functions by mortar element techniques on the boundary of the domain. As advantages, the new discretizations do not require costly numerical integrations and have smaller a priori error estimates and condition numbers. Based on such an approach, we prove optimal accuracy error bounds for the discrete solution. Based on such techniques, we also derive new extraction formulas for the stress intensive factor. We establish optimal accuracy for the computed stress intensive factor. Numerical examples are presented to support our theory.

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Providakis, Costas P., and Dimitri E. Beskos. "Dynamic Analysis of Plates by Boundary Elements." Applied Mechanics Reviews 52, no. 7 (July 1, 1999): 213–36. http://dx.doi.org/10.1115/1.3098936.

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A review of boundary element methods for the numerical treatment of free and forced vibrations of flexural plates is presented. The integral formulation and the corresponding numerical solution from the direct boundary element method viewpoint are described for elastic or inelastic flexural plates experiencing small deformations. When the material is elastic the formulation can be either in the frequency or the time domain in conjunction with the elastodynamic or the elastostatic fundamental solution of the corresponding flexural plate problem. When use is made of the elastodynamic fundamental solution, the discretization is essentially restricted to the perimeter of the plate, while an interior discretization in addition to the boundary one is needed when the elastostatic fundamental solution is employed in the formulation. However, the great simplicity of the elastostatic fundamental solution leads eventually to more efficient schemes. Besides, through dual reciprocity techniques one can again restrict the discretization to the plate perimeter. Free vibrations are solved by the determinant method when use is made of the elastodynamic fundamental solution, or by generalized eigenvalue analysis when use is made of the elastostatic fundamental solution. Forced vibrations are solved either in the frequency domain in conjunction with Fourier or Laplace transform or the time domain in conjunction with a step-by-step time integration. When the material is inelastic the problem is formulated incrementally in the time domain in conjunction with the elastostatic fundamental solution and the plate response is obtained through step-by-step time integration. Special formulations such as indirect, Green’s function, symmetric, dual and multiple reciprocity, or boundary collocation ones are also reviewed. Effects such as those of corners, viscoelasticity, anisotropy, inhomogeneity, in-plane forces, shear deformation and rotatory inertia, variable thickness, internal supports, elastic foundation and large defections are discussed as well. Representative numerical examples serve to illustrate boundary element methods and demonstrate their advantages over other numerical methods. This review article includes 150 references.

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Beskos, Dimitri E. "Boundary Element Methods in Dynamic Analysis." Applied Mechanics Reviews 40, no. 1 (January 1, 1987): 1–23. http://dx.doi.org/10.1115/1.3149529.

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A review of boundary element methods for the numerical solution of dynamic problems of linear elasticity is presented. The integral formulation and the corresponding numerical solution of three- and two-dimensional elastodynamics from the direct boundary element method viewpoint and in both the frequency and time domains are described. The special case of the anti-plane motion governed by the scalar wave equation is also considered. In all the cases both harmonic and transient dynamic disturbances are taken into account. Special features of material behavior such as viscoelasticity, inhomogeneity, anisotropy, and poroelasticity are briefly discussed. Some other nonconventional boundary element methods as well as the hybrid scheme that results from the combination of boundary and finite elements are also reviewed. All these boundary element methodologies are applied to: soil-structure interaction problems that include the dynamic analysis of underground and above-ground structures, foundations, piles, and vibration isolation devices; problems of crack propagation and wave diffraction by cracks; and problems dealing with the dynamics of beams, plates, and shells. Finally, a brief assessment of the progress achieved so far in dynamic analysis is made and areas where further research is needed are identified.

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Fukuhara, Mio, Ryota Misawa, Kazuki Niino, and Naoshi Nishimura. "Stability of boundary element methods for the two dimensional wave equation in time domain revisited." Engineering Analysis with Boundary Elements 108 (November 2019): 321–38. http://dx.doi.org/10.1016/j.enganabound.2019.08.015.

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Mei, Tian-Long, Teng Zhang, Maxim Candries, Evert Lataire, and Zao-Jian Zou. "Comparative study on ship motions in waves based on two time domain boundary element methods." Engineering Analysis with Boundary Elements 111 (February 2020): 9–21. http://dx.doi.org/10.1016/j.enganabound.2019.10.013.

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Ingber, Marc S., Andrea A. Mammoli, and Mary J. Brown. "A comparison of domain integral evaluation techniques for boundary element methods." International Journal for Numerical Methods in Engineering 52, no. 4 (October 10, 2001): 417–32. http://dx.doi.org/10.1002/nme.217.

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Steinbach, Olaf, and Marco Zank. "Coercive space-time finite element methods for initial boundary value problems." ETNA - Electronic Transactions on Numerical Analysis 52 (2020): 154–94. http://dx.doi.org/10.1553/etna_vol52s154.

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Newman, J. N., and C. H. Lee. "Boundary-Element Methods In Offshore Structure Analysis." Journal of Offshore Mechanics and Arctic Engineering 124, no. 2 (April 11, 2002): 81–89. http://dx.doi.org/10.1115/1.1464561.

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Boundary-element methods, also known as panel methods, have been widely used for computations of wave loads and other hydrodynamic characteristics associated with the interactions of offshore structures with waves. In the conventional approach, based on the low-order panel method, the submerged surface of the structure is represented by a large number of small quadrilateral plane elements, and the solution for the velocity potential or source strength is approximated by a constant value on each element. In this paper, we describe two recent developments of the panel method. One is a higher-order method where the submerged surface can be represented exactly, or approximated to a high degree of accuracy by B-splines, and the velocity potential is also approximated by B-splines. This technique, which was first used in the research code HIPAN, has now been extended and implemented in WAMIT. In many cases of practical importance, it is now possible to represent the geometry exactly to avoid the extra work required previously to develop panel input files for each structure. It is also possible to combine the same or different structures which are represented in this manner, to analyze multiple-body hydrodynamic interactions. Also described is the pre-corrected Fast Fourier Transform method (pFFT) which can reduce the computational time and required memory of the low-order method by an order of magnitude. In addition to descriptions of the two methods, several different applications are presented.

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Pinsky, P. M., and N. N. Abboud. "Transient Finite Element Analysis of the Exterior Structural Acoustics Problem." Journal of Vibration and Acoustics 112, no. 2 (April 1, 1990): 245–56. http://dx.doi.org/10.1115/1.2930119.

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Considerable progress has been made in the development of numerical methods for the time-harmonic exterior structural acoustics problem involving solution of the coupled Helmholtz equation. In contrast, numerical solution procedures for the transient case have not been studied so extensively. In this paper a finite element formulation is proposed for solution of the time-dependent coupled wave equation over an infinite fluid domain. The formulation is based on a finite computational fluid domain surrounding the structure and incorporates a sequence of boundary operators on the fluid truncation boundary. These operators are designed to minimize reflection of outgoing waves and are based on an asymptotic expansion of the exact solution for the time-dependent problem. In the fluid domain, a mixed two-field finite element approximation, based on a specialization of the Hu-Washizu principle for elasticity, is proposed and employs pressure and displacement potential as independent fields. Since radiation dissipation renders the coupled system nonconservative, a variational formalism based on the Morse and Feshbach concept of a “mirror-image” adjoint system is used. The variational formalism also accommodates viscoelastic dissipation in the structure (or its coatings) and this is considered in the paper. Very accurate results for model problems involving a single layer of fluid elements have been obtained and are discussed in detail.

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Xia, Chen, Chengzhi Qi, and Xiaozhao Li. "Viscoelastic Boundary Conditions for Multiple Excitation Sources in the Time Domain." Mathematical Problems in Engineering 2018 (October 10, 2018): 1–11. http://dx.doi.org/10.1155/2018/7982342.

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Transmitting boundaries are important for modeling the wave propagation in the finite element analysis of dynamic foundation problems. In this study, viscoelastic boundaries for multiple seismic waves or excitations sources were derived for two-dimensional and three-dimensional conditions in the time domain, which were proved to be solid by finite element models. Then, the method for equivalent forces’ input of seismic waves was also described when the proposed artificial boundaries were applied. Comparisons between numerical calculations and analytical results validate this seismic excitation input method. The seismic response of subway station under different seismic loads input methods indicates that asymmetric input seismic loads would cause different deformations from the symmetric input seismic loads, and whether it would increase or decrease the seismic response depends on the parameters of the specific structure and surrounding soil.

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Bonnet, Marc, Giulio Maier, and Castrenze Polizzotto. "Symmetric Galerkin Boundary Element Methods." Applied Mechanics Reviews 51, no. 11 (November 1, 1998): 669–704. http://dx.doi.org/10.1115/1.3098983.

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This review article concerns a methodology for solving numerically, for engineering purposes, boundary and initial-boundary value problems by a peculiar approach characterized by the following features: the continuous formulation is centered on integral equations based on the combined use of single-layer and double-layer sources, so that the integral operator turns out to be symmetric with respect to a suitable bilinear form. The discretization is performed either on a variational basis or by a Galerkin weighted residual procedure, the interpolation and weight functions being chosen so that the variables in the approximate formulation are generalized variables in Prager’s sense. As main consequences of the above provisions, symmetry is exhibited by matrices with a key role in the algebraized versions; some quadratic forms have a clear energy meaning; variational properties characterize the solutions and other results, invalid in traditional boundary element methods enrich the theory underlying the computational applications. The present survey outlines recent theoretical and computational developments of the title methodology with particular reference to linear elasticity, elastoplasticity, fracture mechanics, time-dependent problems, variational approaches, singular integrals, approximation issues, sensitivity analysis, coupling of boundary and finite elements, and computer implementations. Areas and aspects which at present require further research are identified, and comparative assessments are attempted with respect to traditional boundary integral-elements. This article includes 176 references.

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Kalis, H., and I. Kangro. "SIMPLE METHODS OF ENGINEERING CALCULATION FOR SOLVING HEAT TRANSFER PROBLEMS." Mathematical Modelling and Analysis 8, no. 1 (March 31, 2003): 33–42. http://dx.doi.org/10.3846/13926292.2003.9637208.

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There are well-known numerical methods for solving the initial‐boundary value problems for partial differential equations. We mention only some of them: finite difference method (FDM), finite element method (FEM), boundary element method (BEM), Galerkin type methods and others. In the given work FDM and BEM are considered for determination a distribution of heat in the multilayer media. These methods were used for the reduction of the 1D heat transfer problem described by a partial differential equation to an initial‐value problem for a system of ordinary differential equations (ODEs). Such a procedure allows us to obtain a simple engineering algorithm for solving heat transfer equation in multilayered domain. In a stationary case the exact finite difference scheme is obtained. An inverse problem is also solved. The heat transfer coefficients are found and temperatures in the interior layers depending on the given temperatures inside and outside of a domain are obtained.

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Beskos, Dimitri E. "Boundary Element Methods in Dynamic Analysis: Part II (1986-1996)." Applied Mechanics Reviews 50, no. 3 (March 1, 1997): 149–97. http://dx.doi.org/10.1115/1.3101695.

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A review of boundary element methods for the numerical solution of elastodynamic problems covering the period 1986-1996 is presented. It is a continuation of a review article on the same subject by the same author which appeared previously in Applied Mechanics Reviews (AMR 40(1) 1-23 (Jan 1987) Reprint No AMR015). Integral formulations and their advanced numerical treatment in both frequency and time domains from the direct boundary element method viewpoint are described. They cover two - and three - dimensional cases as well as the anti-plane case of linear elastodynamics under harmonic or transient disturbances. Indirect formulations, boundary methods, T-matrix methods, symmetric formulations, dual reciprocity boundary element methods and hybrid schemes combining boundary with finite elements are also described. All these boundary element methodologies are applied to: i) wave propagation analysis including wave propagation due to external loads, wave diffraction by surface or subsurface irregularities and cracks and crack propagation; ii) dynamic analysis of structures including beams, membranes, plates and shells as well as two - and three - dimensional structures; iii) soil-structure interaction including foundation analysis, piles and underground structures; iv) fluid-structure interaction including structures inside fluids or containing fluids and dam-reservoir systems; and v) the special subjects of viscoelasticity, inhomogeneity, anisotropy, poroelasticity-thermoelasticity, large deformations, contact analysis, inverse scattering and optimum design and control. Finally, areas where further research is needed are identified. There are 1333 references.

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Antes, Heinz, and Otto Von Estorff. "On causality in dynamic response analysis by time-dependent boundary element methods." Earthquake Engineering & Structural Dynamics 15, no. 7 (October 1987): 865–70. http://dx.doi.org/10.1002/eqe.4290150707.

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Wang, Haitao, Zhenhan Yao, and Pengbo Wang. "On the preconditioners for fast multipole boundary element methods for 2D multi-domain elastostatics." Engineering Analysis with Boundary Elements 29, no. 7 (July 2005): 673–88. http://dx.doi.org/10.1016/j.enganabound.2005.03.002.

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Park, Ilwook, Usik Lee, and Donghyun Park. "Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis." Mathematical Problems in Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/541276.

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It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

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Antonopoulou, Dimitra, and Michael Plexousakis. "A posteriori analysis for space-time, discontinuous in time Galerkin approximations for parabolic equations in a variable domain." ESAIM: Mathematical Modelling and Numerical Analysis 53, no. 2 (March 2019): 523–49. http://dx.doi.org/10.1051/m2an/2018059.

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This paper presents an a posteriori error analysis for the discontinuous in time space–time scheme proposed by Jamet for the heat equation in multi-dimensional, non-cylindrical domains Jamet (SIAM J. Numer. Anal. 15 (1978) 913–928). Using a Clément-type interpolant, we prove abstract a posteriori error bounds for the numerical error. Furthermore, in the case of two-dimensional spatial domains we transform the problem into an equivalent one, of parabolic type, with space-time dependent coefficients but posed on a cylindrical domain. We formulate a discontinuous in time space–time scheme and prove a posteriori error bounds of optimal order. The a priori estimates of Evans (American Mathematical Society (1998)) for general parabolic initial and boundary value problems are used in the derivation of the upper bound. Our lower bound coincides with that of Picasso (Comput. Meth. Appl. Mech. Eng. 167 (1998) 223–237), proposed for adaptive, Runge-Kutta finite element methods for linear parabolic problems. Our theoretical results are verified by numerical experiments.

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Elleithy, Wael. "Multi-Domain Analysis by FEM-BEM Coupling and BEM-DD Part I: Formulation and Implementation." Applied Mechanics and Materials 353-356 (August 2013): 3263–68. http://dx.doi.org/10.4028/www.scientific.net/amm.353-356.3263.

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Several existing interface relaxation methods for finite element–boundary element coupling (FEM–BEM) and for boundary element–domain decomposition (BEM–DD) are reviewed. Furthermore, an interface relaxation method for BEM–DD is presented. This is Part I of two papers. In Part II, the convergence conditions of the interface relaxation FEM-BEM coupling and BEM-DD method are established. Example application is given for elaboration

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Harari, Isaac, and Thomas J. R. Hughes. "Design and Analysis of Finite Element Methods for the Helmholtz Equation in Exterior Domains." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S366—S373. http://dx.doi.org/10.1115/1.3120842.

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Finite element methods for the reduced wave equation in unbounded domains are presented. A computational problem over a finite domain is formulated by imposing an exact impedance relation at an artificial exterior boundary. Method design is based on a detailed examination of discrete errors in simplified settings, leading to a thorough analytical understanding of method performance. For this purpose, model problems of radiation with inhomogeneous Neumann boundary conditions, including the effects of a moving acoustic medium, are considered for the entire range of propagation and decay. A Galerkin/least-squares method is shown to exhibit superior behavior for this class of problems.

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Li, Shang Ming. "Transient Analysis of Dam-Reservoir Interaction Based on Dynamic Stiffness of SBFEM." Advanced Materials Research 378-379 (October 2011): 213–17. http://dx.doi.org/10.4028/www.scientific.net/amr.378-379.213.

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The scaled boundary finite element method (SBFEM) was extended to solve dam-reservoir interaction problems in the time domain and a dynamic stiffness used in the SBFEM of semi-infinite reservoir in the time domain was proposed, which was evaluated by the Bessel function. Based on the dynamic stiffness, transient responses subjected to horizontal ground motions were analyzed through coupling the SBFEM and finite element method (FEM). A dam was modeled by FEM, while the whole fluid in reservoir was modeled by the SBFEM alone or a combination of FEM and SBFEM. Two benchmark examples were considered to check the accuracy of the dynamic stiffness. Results were compared with those from analytical or substructure methods and good agreements were found.

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Mousavi, Hamed, Mojtaba Azhari, Mohammad Mehdi Saadatpour, and Saeid Sarrami-Foroushani. "A Coupled Improved Element Free Galerkin-Finite Strip (IEFG-FS) Method for Free Vibration Analysis of Plate." International Journal of Applied Mechanics 11, no. 10 (December 2019): 1950103. http://dx.doi.org/10.1142/s1758825119501035.

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In this paper, a coupling of improved element-free Galerkin (IEFG) method and semi-analytical finite strip (FS) method is presented for free vibration analysis of thin plates. This method is very easy to implement and has advantages of both IEFG and FS methods, so that IEFG method is used in sub-domain with complex geometry, and FS method is used for the remaining domains. The use of the FS method considerably reduces the analysis time, and the essential boundary conditions are easily enforced in FS sub-domain. In the IEFG method, the shape function does not have the Kronecker delta function property. Therefore, Lagrange multipliers method is used to satisfy the boundary conditions. Finally, five examples are presented to show the effectiveness of this work.

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Sellitto, Andrea, R. Borrelli, Francesco Caputo, T. Ludwig, Aniello Riccio, and Francesco Scaramuzzino. "3D Global-Local Analysis Using Mesh Superposition Method." Key Engineering Materials 577-578 (September 2013): 505–8. http://dx.doi.org/10.4028/www.scientific.net/kem.577-578.505.

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One of the main issue in a FEM analysis is to determine and minimizing discretization errors. This kind of errors assume a critical importance especially where the solution, in terms of displacement and stress, quickly changes inside the finite element. This issue can be overcame adopting a very refined element discretization in those regions.Hence, for this kind of simulations, it is common practice to use global-local methods rather than adopt a refined discretization over the entire domain. Indeed, global-local methods allow to define very refined elements distributions in some regions of interest, which can be coupled with coarser element distributions in the rest of the domain.A global-local approach based on the superposition technique is presented in this work. This approach allows the coupling of two different meshed domain by superimposing the refined local mesh on the global mesh for the region of interest. The coupling takes place without introducing multi-point constraints or transition regions; the mesh continuity and the well-conditioning of the stiffness matrix are satisfied by appropriate boundary conditions. This approach allows to obtain accurate solutions in the areas of interest while keeping the computational time within satisfactory limits. Several numerical applications are presented which allow to assess the effectiveness of the proposed approach for 3D linear static simulations.

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Rong, Yao, Yang Sun, LiQing Zhu, and Xiao Xiao. "Analysis of the Three-Dimensional Dynamic Problems by Using a New Numerical Method." Advances in Civil Engineering 2021 (May 4, 2021): 1–12. http://dx.doi.org/10.1155/2021/5555575.

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The problems of the consolidation of saturated soil under dynamic loading are very complex. At present, numerical methods are widely used in the research. However, some traditional methods, such as the finite element method, involve more degrees of freedom, resulting in low computational efficiency. In this paper, the scaled boundary element method (SBFEM) is used to analyze the displacement and pore pressure response of saturated soil due to consolidation under dynamic load. The partial differential equations of linear problems are transformed into ordinary differential equations and solved along the radial direction. The coefficients in the equations are determined by approximate finite elements on the circumference. As a semianalytical method, the application of scaled boundary element method in soil-structure interaction is extended. Dealing with complex structures and structural nonlinearity, it can simulate two-phase saturated soil-structure dynamic interaction in infinite and finite domain, which has an important engineering practical value. Through the research, some conclusions are obtained. The dimension of the analytical problem can be reduced by one dimension if only the boundary surface is discretized. The SBFEM can automatically satisfy the radiation conditions at infinite distances. The 3D scaled boundary finite element equation for dynamic consolidation of saturated soils is not only accurate in finite element sense but also convenient in mathematical processing.

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Dello Russo, Anahí, and Ana E. Alonso. "Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains." Computational Methods in Applied Mathematics 14, no. 1 (January 1, 2014): 1–33. http://dx.doi.org/10.1515/cmam-2013-0014.

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Abstract. In this paper we present a theoretical framework for the analysis of the numerical approximations of a particular class of eigenvalue problems by mixed/hybrid methods. More precisely, we are interested in eigenproblems which are defined over curved domains or have internal curved boundaries and which may be associated with non-compact inverse operators. To do this, we consider external domain approximations $\Omega _{h}$ of the original domain $\Omega $, i.e., $\Omega _{h} \lnot \subset \Omega $. Sufficient conditions to ensure good convergence properties and optimal error bounds for the external approximations of the eigenfunction/eigenvalue pairs are established. Then, these results are applied to the study of the Stokes eigenvalue problem with slip boundary condition defined on a curved non-convex two-dimensional domain.

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Mammoli, A. A., and M. S. Ingber. "Stokes flow around cylinders in a bounded two-dimensional domain using multipole-accelerated boundary element methods." International Journal for Numerical Methods in Engineering 44, no. 7 (March 10, 1999): 897–917. http://dx.doi.org/10.1002/(sici)1097-0207(19990310)44:7<897::aid-nme530>3.0.co;2-s.

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Kim, Taehyun, and Usik Lee. "Vibration Analysis of Thin Plate Structures Subjected to a Moving Force Using Frequency-Domain Spectral Element Method." Shock and Vibration 2018 (September 24, 2018): 1–27. http://dx.doi.org/10.1155/2018/1908508.

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A frequency-domain spectral element method (SEM) is proposed for the vibration analysis of thin plate structures subjected to a moving point force. The thin plate structures may consist of multiple rectangular thin plates with arbitrary boundary conditions that form multispan thin plate structures, such as bridges. The time-domain point force moving on a thin rectangular plate with arbitrary trajectory is transformed into a series of stationary point forces in the frequency domain. The vibration responses induced by the moving point force are then obtained by superposing all vibration responses excited by each stationary point force. For the vibration response of a specific stationary point force, the plate subjected to the specific stationary point force is represented by four spectral finite plate elements, which were developed in the authors’ previous work. The SEM-based vibration analysis technique is first presented for single-span thin plate structures and then extended to the multispan thin plate structures. The high accuracy and computational efficiency of the proposed SEM-based vibration analysis technique are verified by comparison with other well-known solution methods, such as the exact theory, integral transform method, finite element method, and the commercial finite element analysis package ANSYS.

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CERROLAZA, M., F. NIETO, and Y. GONZÁLEZ. "COMPUTATION OF THE DYNAMIC COMPRESSION EFFECTS IN SPINE DISCS USING INTEGRAL METHODS." Journal of Mechanics in Medicine and Biology 18, no. 05 (August 2018): 1750103. http://dx.doi.org/10.1142/s0219519417501032.

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The computational modeling using integral methods of dynamic loading and its effects on the nutrients transport in spine discs is addressed in this work. The numerical simulation and analysis was carried out using the Boundary Element Method (BEM) and a 3D model (axisymmetric) of the disc. The boundary model was discretized using linear interpolated elements and a multi-region approach. Concentration and production of three nutrients as lactate, oxygen and glucose were obtained. The maximum lactate concentration was observed very close to the interface between the nucleus and the inner annulus. A relatively simple model discretized with 130 boundary elements yielded very similar results to these coming from more complex FEM-based models. The numerical efforts in the domain and boundary discretizations were optimized using the BEM. Our results are in good agreement with those obtained using with finite element-based models. As expected, the dynamic loading increased the oxygen–glucose consumption and the lactate production, thus leading to a poor oxygen–glucose concentration at the nucleus of the disc. All of that is a favorable environment for a disc degeneration mechanism to be developed.

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Shekarbeigi, Mehdi, and Hasan Sharafi. "The Structural Dynamic Analysis of Embankment Dams Using Finite Difference and Finite Element Methods." Current World Environment 10, Special-Issue1 (June 28, 2015): 796–805. http://dx.doi.org/10.12944/cwe.10.special-issue1.96.

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This study is aimed to provide a structural dynamic analysis of embankment dams using numerical methods. The dynamic analyses are performed based on the time histories by applying accelerogram of several real earthquakes. For a dynamic analysis, it is initially performed a comprehensive study of the characteristics and coordinates of the earthquake accelerograms. The numerical analysis method is established on the comparison of the results of the numerical finite difference (FDM) and finite element (FEM) methods. This paper constitutes two-dimensional numerical plane-strain dynamic analyses in time domain. The focus of this research is to examine the amplified impacts of accelerations and the lateral (horizontal) and vertical (settlement) displacements due to earthquake loading. All the models are undergone the static analysis, followed by dynamic analysis, and after the initial static equilibrium, they are placed under dynamic loading. It is presented a case study on Jamishan Embankment Dam in Kermanshah Province, Iran. The analytical results indicate that there is a good agreement between both numerical methods; however, there are some rare cases with contradictory results, majorly due to the slight differences of fundamental calculations or the definitions of damping ratio and boundary conditions in both numerical methods. Nevertheless, the results illustrate that the free board height of the Jamishan Dam determined by the consultant engineer is responsive to the most critical conditions and prevents the water overflow from the dam in case of strong vibrations.

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Langer, Ulrich, and Andreas Schafelner. "Adaptive Space-Time Finite Element Methods for Non-autonomous Parabolic Problems with Distributional Sources." Computational Methods in Applied Mathematics 20, no. 4 (October 1, 2020): 677–93. http://dx.doi.org/10.1515/cmam-2020-0042.

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AbstractWe consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable coefficients that are possibly discontinuous in space and time. Distributional sources are also admitted. Discontinuous coefficients, non-smooth boundaries, changing boundary conditions, non-smooth or incompatible initial conditions, and non-smooth right-hand sides can lead to non-smooth solutions. We present new a priori and a posteriori error estimates for low-regularity solutions. In order to avoid reduced rates of convergence that appear when performing uniform mesh refinement, we also consider adaptive refinement procedures based on residual a posteriori error indicators and functional a posteriori error estimators. The huge system of space-time finite element equations is then solved by means of GMRES preconditioned by space-time algebraic multigrid. In particular, in the 4d space-time case, simultaneous space-time parallelization can considerably reduce the computational time. We present and discuss numerical results for several examples possessing different regularity features.

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Rungamornrat, Jaroon, and Sakravee Sripirom. "Stress Analysis of Three-Dimensional Media Containing Localized Zone by FEM-SGBEM Coupling." Mathematical Problems in Engineering 2011 (2011): 1–27. http://dx.doi.org/10.1155/2011/702082.

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This paper presents an efficient numerical technique for stress analysis of three-dimensional infinite media containing cracks and localized complex regions. To enhance the computational efficiency of the boundary element methods generally found inefficient to treat nonlinearities and non-homogeneous data present within a domain and the finite element method (FEM) potentially demanding substantial computational cost in the modeling of an unbounded medium containing cracks, a coupling procedure exploiting positive features of both the FEM and a symmetric Galerkin boundary element method (SGBEM) is proposed. The former is utilized to model a finite, small part of the domain containing a complex region whereas the latter is employed to treat the remaining unbounded part possibly containing cracks. Use of boundary integral equations to form the key governing equation for the unbounded region offers essential benefits including the reduction of the spatial dimension and the corresponding discretization effort without the domain truncation. In addition, all involved boundary integral equations contain only weakly singular kernels thus allowing continuous interpolation functions to be utilized in the approximation and also easing the numerical integration. Nonlinearities and other complex behaviors within the localized regions are efficiently modeled by utilizing vast features of the FEM. A selected set of results is then reported to demonstrate the accuracy and capability of the technique.

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35

Wang, Shige, Zhongwang Wang, Leilei Chen, Haojie Lian, Xuan Peng, and Haibo Chen. "Resolving Domain Integral Issues in Isogeometric Boundary Element Methods via Radial Integration: A Study of Thermoelastic Analysis." Computer Modeling in Engineering & Sciences 124, no. 2 (2020): 585–604. http://dx.doi.org/10.32604/cmes.2020.09904.

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Chatzipantelidis, Panagiotis, Zoltan Horváth, and Vidar Thomée. "On Preservation of Positivity in Some Finite Element Methods for the Heat Equation." Computational Methods in Applied Mathematics 15, no. 4 (October 1, 2015): 417–37. http://dx.doi.org/10.1515/cmam-2015-0018.

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AbstractWe consider the initial boundary value problem for the homogeneous heat equation, with homogeneous Dirichlet boundary conditions. By the maximum principle the solution is nonnegative for positive time if the initial data are nonnegative. We complement in a number of ways earlier studies of the possible extension of this fact to spatially semidiscrete and fully discrete piecewise linear finite element discretizations, based on the standard Galerkin method, the lumped mass method, and the finite volume element method. We also provide numerical examples that illustrate our findings.

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Soares, Delfim. "Coupled Numerical Methods to Analyze Interacting Acoustic-Dynamic Models by Multidomain Decomposition Techniques." Mathematical Problems in Engineering 2011 (2011): 1–28. http://dx.doi.org/10.1155/2011/245170.

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In this work, coupled numerical analysis of interacting acoustic and dynamic models is focused. In this context, several numerical methods, such as the finite difference method, the finite element method, the boundary element method, meshless methods, and so forth, are considered to model each subdomain of the coupled model, and multidomain decomposition techniques are applied to deal with the coupling relations. Two basic coupling algorithms are discussed here, namely the explicit direct coupling approach and the implicit iterative coupling approach, which are formulated based on explicit/implicit time-marching techniques. Completely independent spatial and temporal discretizations among the interacting subdomains are permitted, allowing optimal discretization for each sub-domain of the model to be considered. At the end of the paper, numerical results are presented, illustrating the performance and potentialities of the discussed methodologies.

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Laitinen, E., A. Lapin, and S. Lapin. "On the Iterative Solution Methods for Finite-Dimensional Inclusions with Applications to Optimal Control Problems." Computational Methods in Applied Mathematics 10, no. 3 (2010): 283–301. http://dx.doi.org/10.2478/cmam-2010-0016.

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AbstractIterative methods for finite-dimensional inclusions which arise in applying a finite-element or a finite-difference method to approximate state-constrained optimal control problems have been investigated. Specifically, problems of control on the right- hand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergence for the iterative algorithms based on the finding of the control function or Lagrange multipliers are proved.

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Boateng, Francis Ohene, Joseph Ackora-Prah, Benedict Barnes, and John Amoah-Mensah. "A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem." European Journal of Pure and Applied Mathematics 14, no. 3 (August 5, 2021): 706–22. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3893.

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In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear ellipticÂ partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. The method reduces the 2D PDE into a 1D system of ordinary differential equations and applies a compactly supported wavelet to approximate the solution. The problem is embedded in a fictitious domain to aid the enforcement of the Dirichlet boundary conditions. We present numerical analysis and show that our method yields better approximation to the solution of the Dirichlet problem than traditional methods like the finite element and finite difference methods.

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Zhao, Ya Nan, Li Quan Wang, and Hong Wang Du. "The Wave-Load Analysis of the Offshore Wind Power Installation Vessel Based on Frequency-Domain Methods." Advanced Materials Research 189-193 (February 2011): 1804–8. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.1804.

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The wave force spectrum expressed in terms of Morison's equation was deduced by ocean wave theory and spectral analysis theory, and the spectral analysis of wave force were analyzed with the finite element method which was applied to the leg of the offshore wind power installation vessel, the natural frequencies and the vibration model were accomplished with boundary conditions. The dynamic response of the leg were studied in different conditions, it can be concluded that the wave force of the leg is only related with geometric shape and working depth of truss legs.

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Zlotnik, Alexander. "On Superconvergence of a Gradient for Finite Element Methods for an Elliptic Equation with the Nonsmooth Right–hand Side." Computational Methods in Applied Mathematics 2, no. 3 (2002): 295–321. http://dx.doi.org/10.2478/cmam-2002-0018.

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AbstractThe elliptic equation under the nonhomogeneous Dirichlet boundary condition in 2D and 3D cases is solved. A rectangular nonuniform partition of a domain and polylinear finite elements are taken. For the interpolant of the exact solution u, a priori error estimates are proved provided that u possesses a weakened smoothness. Next error estimates are in terms of data. An estimate is established for the right–hand side f of the equation having a generalized smoothness. Error estimates are derived in the case of f which is not compatible with the boundary function. The proofs are based on some propositions from the theory of functions. The corresponding lower error estimates are also included; they justify the sharpness of the estimates without the logarithmic multipliers. Finally, we prove similar results in the case of 2D linear finite elements and a uniform partition.

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Şimon-Marinică, Adrian Bogdan, Nicolae-Ioan Vlasin, Florin Manea, and Gheorghe-Daniel Florea. "Finite element method to solve engineering problems using ansys." MATEC Web of Conferences 342 (2021): 01015. http://dx.doi.org/10.1051/matecconf/202134201015.

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The Finite Element Analysis method, is a powerful computational technique for approximate solutions to a variety of real – world engineering problems having complex domains subjected to general boundary conditions. The method itself has become an essential step in the design or modelling of a physical phenomenon in various engineering disciplines. A physical phenomenon usually occurs in a continuum of matter (solid, liquid or gas) involving several field variables. The field variables vary from point to point, thus possessing an infinite number of solutions in the domain. The basis of finite volume method relies on the decomposition of the domain into a finite number of subdomains (elements) for which the systematic approximate solution is constructed by applying the variational or weighted residual methods. In effect, finite volume method reduces the problem to that of a finite number of unknowns by dividing the domain into elements and by expressing the unknown field variable in term of the assumed approximating functions within each element.

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Sun, L., G. H. Dong, Y. P. Zhao, and C. F. Liu. "Numerical analysis of the effects on a floating structure induced by ship waves." Journal of Ship Research 55, no. 02 (June 1, 2011): 124–34. http://dx.doi.org/10.5957/jsr.2011.55.2.124.

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Ship-generated waves can make bad effects on offshore structures. A numerical model is presented for evaluating the forces exerted on a nearby floating structure by ship generated waves. The ship waves were modeled using Michell thin-ship theory (Wigley waves), the forces were computed using a boundary element method in the time domain, and the motions of the offshore structures were evaluated using the equation of motion of the floating body, and predicted using the fourth-order Runge-Kutta method. The numerical method was validated by comparing its results to those of frequency-domain methods reported in the literature. It was then applied to calculate the force of ship waves on a floating box. The ship's speed, dimensions, and distance were varied. The numerical results indicate some useful rules for varying these factors.

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Kim, D. J., and M. H. Kim. "Wave-Current Interaction with a Large Three-Dimensional Body by THOBEM." Journal of Ship Research 41, no. 04 (December 1, 1997): 273–85. http://dx.doi.org/10.5957/jsr.1997.41.4.273.

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The effects of uniform steady currents (or small forward velocity) on the interaction of a large three-dimensional body with waves are investigated by a time-domain higher-order boundary element method (THOBEM). The current speed is assumed to be small so that the viscous effects and the steady wave system generated by currents are insignificant. Using regular perturbation with two small parameters є and δ associated with wave slope and current velocity, respectively, the boundary value problem is decomposed into the zeroth-order steady double-body-flow problem at 0(δ) with a rigid-wall free-surface condition and the first-order unsteady wave problem with the modified free-surface and body-boundary conditions expanded up to O(eδ). Higher-order boundary integral equation methods are then used to solve the respective problems with the Rankine sources distributed over the entire boundary. The free surface is integrated at each time step by Adams-Bashforth-Moulton method. The Sommerfeld/Orlanski radiation condition is numerically implemented to absorb all the wave energy at the open boundary. To solve the so-called corner problem, discontinuous elements are used at the intersection of free-surface and radiation boundaries Using the developed numerical method, wave forces, wave field and run-up, mean drift forces and wave drift damping are calculated.

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Prinn, A. G. "On Computing Impulse Responses from Frequency-Domain Finite Element Solutions." Journal of Theoretical and Computational Acoustics 29, no. 01 (March 2021): 2050024. http://dx.doi.org/10.1142/s2591728520500243.

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In acoustics, knowledge of the impulse response of a system is often important. While impulse responses may be measured, they may also be predicted using numerical methods. This work considers the generation of impulse responses from frequency-domain finite element solutions. It is shown that these impulse responses, obtained by inverse Fourier transformation, are noncausal. Through error analysis, it is demonstrated that the noncausality can be reduced by increasing the duration of a source signal used to excite a simulated system. It is found that increasing the source signal duration increases the dispersion-related phase error present in the simulated impulse responses. The findings of this study are used to simulate an impulse response for a system with a nonuniform, frequency-dependent, complex impedance boundary condition.

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Gao, Yichao, Feng Jin, Xiang Wang, and Jinting Wang. "Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary." Mathematical Problems in Engineering 2011 (2011): 1–23. http://dx.doi.org/10.1155/2011/210624.

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The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB). Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.

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Tadeu, António, and Igor Castro. "Coupling the BEM/TBEM and the MFS for the Numerical Simulation of Wave Propagation in Heterogeneous Fluid-Solid Media." Mathematical Problems in Engineering 2011 (2011): 1–26. http://dx.doi.org/10.1155/2011/159389.

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This paper simulates wave propagation in an elastic medium containing elastic, fluid, rigid, and empty heterogeneities, which may be thin. It uses a coupling formulation between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS). The full domain is divided into subdomains, which are handled separately by the BEM/TBEM or the MFS, to overcome the specific limitations of each of these methods. The coupling is enforced by applying the prescribed boundary conditions at all medium interfaces. The accuracy, efficiency, and stability of the proposed algorithms are verified by comparing the results with reference solutions. The paper illustrates the computational efficiency of the proposed coupling formulation by computing the CPU time and the error. The transient analysis of wave propagation in the presence of a borehole driven in a cracked medium is used to illustrate the potential of the proposed coupling formulation.

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Lin, Ray-Qing, Weijia Kuang, and Arthur M. Reed. "Numerical Modeling of Nonlinear Interactions Between Ships and Surface Gravity Waves, Part 1: Ship Waves in Calm Water." Journal of Ship Research 49, no. 01 (March 1, 2005): 1–11. http://dx.doi.org/10.5957/jsr.2005.49.1.1.

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This paper presents a pseudo-spectral model for nonlinear ship-surface wave interactions. The algorithm used in the model is a combination of spectral and boundary element methods: the boundary element method is used to translate physical quantities between the nonuniform ship surface and the regular grid of the spectral representation; the spectral method is used throughout the remainder of the fluid domain. All possible wave-wave interactions are included in the model (up to N-wave interactions for the truncation order N of the spectral expansions). This paper focuses on the mathematical theory and numerical method of the model and presents some numerical results for steady Kelvin waves in calm water. The nonlinear bow waves at high Froude numbers from the pseudo-spectral model are much closer to the experimental results than those from linear ship wave models. Our results demonstrate that the pseudo-spectral model is significantly faster than previous ship wave models: with the same resolution, the CPU time of the pseudo-spectral model is orders of magnitude less than those of previous models. Convergence speed of this model is ANLogN instead of BN2, where N is the number of unknown (note that the N for the traditional boundary element method may be significantly larger than the N for the pseudo-spectral method for the same quality solution). A and B are CPU time requirements in each time step for our model and others, respectively.

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MAKRIDAKIS, CH, F. IHLENBURG, and I. BABUŠKA. "ANALYSIS AND FINITE ELEMENT METHODS FOR A FLUID-SOLID INTERACTION PROBLEM IN ONE DIMENSION." Mathematical Models and Methods in Applied Sciences 06, no. 08 (December 1996): 1119–41. http://dx.doi.org/10.1142/s0218202596000468.

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In this paper we study a time-harmonic fluid-solid interaction model problem in one dimension. This is a Helmholtz-type system equipped with boundary and transmission conditions. We show the existence of a unique solution to this problem and study its stability and regularity properties. We analyze the convergence of finite element methods with respect to appropriate energy norms. Computational results are also presented.

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Shankar Badry, Ravi, Maruthi Kotti, and Pradeep Kumar Ramancharla. "A Comparative Study of Absorbing Layer Methods to Model Radiating Boundary Conditions for the Wave Propagation in Infinite Medium." International Journal of Engineering & Technology 7, no. 3.35 (September 2, 2018): 25. http://dx.doi.org/10.14419/ijet.v7i3.35.29141.

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Radiating boundary condition is an important consideration in the finite element modelling of unbounded media. Absorbing layer techniquessuch as Perfectly Matched Layers (PML) and Absorbing Layers by Increasing Damping (ALID) becoming popular as they are efficient in absorbing outward propagating waves energy. In this study, a comparative analysis has been carried out between PML and ALID+VABC (Absorbing Boundary conditions for Viscoelastic materials) methods. The methods are analyzedusing LS-DYNAexplicit solver and the efficiency is compared with standard solutions.The study concluded that PML requires less number of elements to model the boundary conditions when compared with ALID+VABC. But PMLrequires a smaller element length which increases overall computational time. Both the methods are efficient in absorbing the wave energy. However, PML requires additional implementation cost to solve the complex equations.

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Journal articles on the topic 'Boundary element methods. Time-domain analysis'

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