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Journal articles on the topic 'FEM discretization'

Author: Grafiati

Published: 1 March 2025

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1

Dryja, M., and M. Sarkis. "Additive Average Schwarz Methods for Discretization of Elliptic Problems with Highly Discontinuous Coefficients." Computational Methods in Applied Mathematics 10, no. 2 (2010): 164–76. http://dx.doi.org/10.2478/cmam-2010-0009.

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AbstractA second order elliptic problem with highly discontinuous coefficients has been considered. The problem is discretized by two methods: 1) continuous finite element method (FEM) and 2) composite discretization given by a continuous FEM inside the substructures and a discontinuous Galerkin method (DG) across the boundaries of these substructures. The main goal of this paper is to design and analyze parallel algorithms for the resulting discretizations. These algorithms are additive Schwarz methods (ASMs) with special coarse spaces spanned by functions that are almost piecewise constant w

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2

Martello, Giulia. "Discretization Analysis in FEM Models." MATEC Web of Conferences 53 (2016): 01063. http://dx.doi.org/10.1051/matecconf/20165301063.

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Lahtinen, Valtteri, and Antti Stenvall. "A category theoretical interpretation of discretization in Galerkin finite element method." Mathematische Zeitschrift 296, no. 3-4 (2020): 1271–85. http://dx.doi.org/10.1007/s00209-020-02456-1.

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Abstract The Galerkin finite element method (FEM) is used widely in finding approximative solutions to field problems in engineering and natural sciences. When utilizing FEM, the field problem is said to be discretized. In this paper, we interpret discretization in FEM through category theory, unifying the concept of discreteness in FEM with that of discreteness in other fields of mathematics, such as topology. This reveals structural properties encoded in this concept: we propose that discretization is a dagger mono with a discrete domain in the category of Hilbert spaces made concrete over t

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4

MARAZZINA, DANIELE, OLEG REICHMANN, and CHRISTOPH SCHWAB. "hp-DGFEM FOR KOLMOGOROV–FOKKER–PLANCK EQUATIONS OF MULTIVARIATE LÉVY PROCESSES." Mathematical Models and Methods in Applied Sciences 22, no. 01 (2012): 1150005. http://dx.doi.org/10.1142/s0218202512005897.

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We analyze the discretization of nonlocal degenerate integrodifferential equations arising as so-called forward equations for jump-diffusion processes. Such equations arise in option pricing problems when the stochastic dynamics of the markets is modeled by Lévy driven stochastic volatility models. Well-posedness of the arising equations is addressed. We develop and analyze stable discretization schemes, in particular the discontinuous Galerkin Finite Element Methods (DG-FEM). In the DG-FEM, a new regularization of hypersingular integrals in the Dirichlet form of the pure jump part of infinite

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Ovchinnikov, George V., Denis Zorin, and Ivan V. Oseledets. "Robust regularization of topology optimization problems with a posteriori error estimators." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 1 (2019): 57–69. http://dx.doi.org/10.1515/rnam-2019-0005.

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Abstract Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material). Using a finite elements discretization (FEM) of the PDE and functional we obtain an integer programming problem. Due to approximation error of the FEM discretization, optimization problem becomes mesh-depended and possess false, physically inadequate optimums, while functional value heavily depends on the fineness of discretization scheme used to compu

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Schedensack, Mira. "A New Generalization of the P1 Non-Conforming FEM to Higher Polynomial Degrees." Computational Methods in Applied Mathematics 17, no. 1 (2017): 161–85. http://dx.doi.org/10.1515/cmam-2016-0031.

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AbstractThis paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz spaces of arbitrary polynomial degree and its discretization coincides with the mentioned non-conforming FEM for the lowest polynomial degree. The discretization directly approximates the gradient of the solution instead of the solution itself. Besides the a priori and medius analysis, this paper proves optimal convergence rates for an adaptive algori

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Devaud, Denis. "Petrov–Galerkin space-time hp-approximation of parabolic equations in H1/2." IMA Journal of Numerical Analysis 40, no. 4 (2019): 2717–45. http://dx.doi.org/10.1093/imanum/drz036.

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Abstract We analyse a class of variational space-time discretizations for a broad class of initial boundary value problems for linear, parabolic evolution equations. The space-time variational formulation is based on fractional Sobolev spaces of order $1/2$ and the Riemann–Liouville derivative of order $1/2$ with respect to the temporal variable. It accommodates general, conforming space discretizations and naturally accommodates discretization of infinite horizon evolution problems. We prove an inf-sup condition for $hp$-time semidiscretizations with an explicit expression of stable test func

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Yao, Lingyun, Wanyi Tian, and Fei Wu. "An Optimized Generalized Integration Rules for Error Reduction of Acoustic Finite Element Model." International Journal of Computational Methods 15, no. 07 (2018): 1850062. http://dx.doi.org/10.1142/s0219876218500627.

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In the finite element method (FEM), the accuracy in acoustic problems will deteriorate with the increasing frequency due to the “dispersion effect”. In order to minimize discretization error, a novel optimized generalized integration rules (OGIR) is introduced into FEM for the reduction of discretization error. In the present work, the adaptive genetic algorithm (AGA) is implemented to sight the optimized location of integration points. Firstly, the generalized integration rules (GIR) is used to parameterize the Gauss point location, then the relationship between the location parameterize of t

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9

Zhao, Jingjun, Jingyu Xiao, and Yang Xu. "Stability and Convergence of an Effective Finite Element Method for Multiterm Fractional Partial Differential Equations." Abstract and Applied Analysis 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/857205.

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A finite element method (FEM) for multiterm fractional partial differential equations (MT-FPDEs) is studied for obtaining a numerical solution effectively. The weak formulation for MT-FPDEs and the existence and uniqueness of the weak solutions are obtained by the well-known Lax-Milgram theorem. The Diethelm fractional backward difference method (DFBDM), based on quadrature for the time discretization, and FEM for the spatial discretization have been applied to MT-FPDEs. The stability and convergence for numerical methods are discussed. The numerical examples are given to match well with the m

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10

Xu, Haochen. "Analyzing heat transfer in Axial Flux Permanent Magnet electrical machines: A literature review on the discretization methods-FVM and FDM." Theoretical and Natural Science 11, no. 1 (2023): 223–30. http://dx.doi.org/10.54254/2753-8818/11/20230412.

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Axial Flux Permanent Magnet (AFPM) machines have gained significant attention due to their high power density, efficiency, and compact design. However, effective heat transfer analysis is critical for optimizing their performance and reliability. This paper presents a comprehensive literature review on the application of discretization methods, specifically the Finite Volume Method (FVM) and Finite Difference Method (FDM), in the thermal analysis of AFPM machines. The fundamentals of FVM and FDM are briefly explained, followed by an exploration of their applications in AFPM machine thermal ana

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11

Li, Long-yuan, and Peter Bettess. "Adaptive Finite Element Methods: A Review." Applied Mechanics Reviews 50, no. 10 (1997): 581–91. http://dx.doi.org/10.1115/1.3101670.

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The adaptive finite element method (FEM) was developed in the early 1980s. The basic concept of adaptivity developed in the FEM is that, when a physical problem is analyzed using finite elements, there exist some discretization errors caused owing to the use of the finite element model. These errors are calculated in order to assess the accuracy of the solution obtained. If the errors are large, then the finite element model is refined through reducing the size of elements or increasing the order of interpolation functions. The new model is re-analyzed and the errors in the new model are recal

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Zhao, Jingjun, Jingyu Xiao, and Yang Xu. "A Finite Element Method for the Multiterm Time-Space Riesz Fractional Advection-Diffusion Equations in Finite Domain." Abstract and Applied Analysis 2013 (2013): 1–15. http://dx.doi.org/10.1155/2013/868035.

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We present an effective finite element method (FEM) for the multiterm time-space Riesz fractional advection-diffusion equations (MT-TS-RFADEs). We obtain the weak formulation of MT-TS-RFADEs and prove the existence and uniqueness of weak solution by the Lax-Milgram theorem. For multiterm time discretization, we use the Diethelm fractional backward finite difference method based on quadrature. For spatial discretization, we show the details of an FEM for such MT-TS-RFADEs. Then, stability and convergence of such numerical method are proved, and some numerical examples are given to match well wi

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Pal, Mahendra Kumar, M. L. L. Wijerathne, and Muneo Hori. "Numerical Modeling of Brittle Cracks Using Higher Order Particle Discretization Scheme–FEM." International Journal of Computational Methods 16, no. 04 (2019): 1843006. http://dx.doi.org/10.1142/s0219876218430065.

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Higher order extension of Particle Discretization Scheme (HO-PDS), its implementation in FEM framework (HO-PDS-FEM) and applications in efficiently simulating cracks are presented in this paper. PDS is an approximation scheme which uses a conjugate domain tessellation pair like Voronoi and Delaunay in approximating a function and its derivatives. In approximating a function (or derivatives), HO-PDS first produces local polynomial approximations for the target function (or derivatives) within each element of respective tessellation. The approximations over the whole domain are then obtained by

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Korga, Sylwester, Anna Makarewicz, and Klaudiusz Lenik. "METHODS OF DISCRETIZATION OBJECTS CONTINUUM IMPLEMENTED IN FEM PREPROCESSORS." Advances in Science and Technology Research Journal 9, no. 28 (2015): 130–33. http://dx.doi.org/10.12913/22998624/60800.

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15

El Moutea, Omar, Nadia Nakbi, Abdeslam El Akkad, et al. "A Mixed Finite Element Approximation for Time-Dependent Navier–Stokes Equations with a General Boundary Condition." Symmetry 15, no. 11 (2023): 2031. http://dx.doi.org/10.3390/sym15112031.

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In this paper, we present a numerical scheme for addressing the unsteady asymmetric flows governed by the incompressible Navier–Stokes equations under a general boundary condition. We utilized the Finite Element Method (FEM) for spatial discretization and the fully implicit Euler scheme for time discretization. In addition to the theoretical analysis of the error in our numerical scheme, we introduced two types of a posteriori error indicators: one for time discretization and another for spatial discretization, aimed at effectively controlling the error. We established the equivalence between

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16

Liu, Xiang, Guo-ping Cai, Fu-jun Peng, Hua Zhang, and Liang-liang Lv. "Nonlinear vibration analysis of a membrane based on large deflection theory." Journal of Vibration and Control 24, no. 12 (2017): 2418–29. http://dx.doi.org/10.1177/1077546316687924.

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This paper investigates nonlinear vibration of a simply supported rectangular membrane based on large deflection theory. Dynamic stress caused by transverse displacement of the membrane is considered in modeling the membrane. The assumed mode method and the nonlinear finite element method (FEM) are both used as discretization methods for the membrane. In the assumed mode method, an approximate analytical formula of the natural frequency is derived. In the nonlinear FEM, a three-node triangular membrane element is proposed. The difference between the membrane’s dynamical characteristics obtaine

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Klochkov, Yuriy V., Valeria A. Pshenichkina, Anatoliy P. Nikolaev, Olga V. Vakhnina, and Mikhail Yu Klochkov. "Quadrilateral element in mixed FEM for analysis of thin shells of revolution." Structural Mechanics of Engineering Constructions and Buildings 19, no. 1 (2023): 64–72. http://dx.doi.org/10.22363/1815-5235-2023-19-1-64-72.

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The purpose of study is to develop an algorithm for the analysis of thin shells of revolution based on the hybrid formulation of finite element method in two dimensions using a quadrilateral fragment of the middle surface as a discretization element. Nodal axial forces and moments, as well as components of the nodal displacement vector were selected as unknown variables. The number of unknowns in each node of the four-node discretization element reaches nine: six force variables and three kinematic variables. To obtain the flexibility matrix and the nodal forces vector, a modified Reissner fun

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Mariano, Valeria, Jorge A. Tobon Vasquez, and Francesca Vipiana. "A Novel Discretization Procedure in the CSI-FEM Algorithm for Brain Stroke Microwave Imaging." Sensors 23, no. 1 (2022): 11. http://dx.doi.org/10.3390/s23010011.

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In this work, the contrast source inversion method is combined with a finite element method to solve microwave imaging problems. The paper’s major contribution is the development of a novel contrast source variable discretization that leads to simplify the algorithm implementation and, at the same time, to improve the accuracy of the discretized quantities. Moreover, the imaging problem is recreated in a synthetic environment, where the antennas, and their corresponding coaxial port, are modeled. The implemented algorithm is applied to reconstruct the tissues’ dielectric properties inside the

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19

Beuchler, Sven, and Martin Purrucker. "Schwarz Type Solvers for -FEM Discretizations of Mixed Problems." Computational Methods in Applied Mathematics 12, no. 4 (2012): 369–90. http://dx.doi.org/10.2478/cmam-2012-0030.

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AbstractThis paper investigates the discretization of mixed variational formulation as, e.g., the Stokes problem by means of the hp-version of the finite element method. The system of linear algebraic equations is solved by the preconditioned Bramble-Pasciak conjugate gradient method. The development of an efficient preconditioner requires three ingredients, a preconditioner related to the components of the velocity modes, a preconditioner for the Schur complement related to the components of the pressure modes and a discrezation by a stable finite element pair which satisfies the discrete inf

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20

Huszty, Csaba, and Ferenc Izsák. "Symplectic time-domain finite element method (STD-FEM) for room acoustic modeling." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 268, no. 5 (2023): 3089–99. http://dx.doi.org/10.3397/in_2023_0447.

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A new, extended symplectic time-domain finite element method (STD-FEM) is proposed for room acoustic modeling. As a mathematical model for sound propagation and reflection, the classical time-domain wave equations are used, which can be extended with air absorption. Frequency-dependent locally reactive boundary conditions are also introduced to the model. Spatially, a third-order tensor product type spectral element discretization is applied, which allows us to use explicit time steps. For this purpose, a partitioned Runge-Kutta method is employed, which is an extension of a third-order symple

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21

Koleva, Miglena. "FINITE ELEMENT SOLUTION OF BOUNDARY VALUE PROBLEMS WITH NONLOCAL JUMP CONDITIONS." Mathematical Modelling and Analysis 13, no. 3 (2008): 383–400. http://dx.doi.org/10.3846/1392-6292.2008.13.383-400.

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We consider stationary linear problems on non‐connected layers with distinct material properties. Well posedness and the maximum principle (MP) for the differential problems are proved. A version of the finite element method (FEM) is used for discretization of the continuous problems. Also, the MP and convergence for the discrete solutions are established. An efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments for linear and nonlinear problems are discussed.

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22

Liu, G. R. "On Partitions of Unity Property of Nodal Shape Functions: Rigid-Body-Movement Reproduction and Mass Conservation." International Journal of Computational Methods 13, no. 02 (2016): 1640003. http://dx.doi.org/10.1142/s021987621640003x.

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This paper discusses the Partitions of Unity (PU) property that is one of the most important properties of nodal shape functions used in various numerical methods via discretization, including element-based and/or meshfree methods, such as FEM, S-FEM, S-PIM, EFG, XFEM, etc. The significance of the PU property and the possible consequences of using shape functions that do not possess the PU property in a numerical method are examined in theory. It proves that the PU property is a necessary (not sufficient in general) condition to enable the basic feature of rigid-body-movement production for st

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23

Gungor, Arif Can, Marzena Olszewska-Placha, Malgorzata Celuch, Jasmin Smajic, and Juerg Leuthold. "Advanced Modelling Techniques for Resonator Based Dielectric and Semiconductor Materials Characterization." Applied Sciences 10, no. 23 (2020): 8533. http://dx.doi.org/10.3390/app10238533.

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This article reports recent developments in modelling based on Finite Difference Time Domain (FDTD) and Finite Element Method (FEM) for dielectric resonator material measurement setups. In contrast to the methods of the dielectric resonator design, where analytical expansion into Bessel functions is used to solve the Maxwell equations, here the analytical information is used only to ensure the fixed angular variation of the fields, while in the longitudinal and radial direction space discretization is applied, that reduced the problem to 2D. Moreover, when the discretization is performed in ti

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Chukwuyem, Nwankwo Jude, Njoseh Ignatius Nkonyeasua, and Joshua Sarduana Apanapudor. "Runge-Kutta Finite Element Method for the Fractional Stochastic Wave Equation." Journal of Advances in Mathematics and Computer Science 39, no. 12 (2024): 70–83. https://doi.org/10.9734/jamcs/2024/v39i121950.

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This paper presents the development and application of the Runge-Kutta Finite Element Method (RK-FEM) to solve fractional stochastic wave equations. Fractional differential equations (FDEs) play a significant role in modelling complex systems with memory and hereditary properties, while the inclusion of stochastic components accounts for randomness inherent in physical systems. The fractional stochastic wave equation represents a natural extension of classical wave equations, incorporating both fractional time derivatives and stochastic processes to model phenomena such as anomalous diffusion

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Yang, Yidu. "Two-grid Discretization Schemes of the Nonconforming FEM for Eigenvalue Problems." Journal of Computational Mathematics 27, no. 6 (2009): 748–63. http://dx.doi.org/10.4208//jcm.2009.09-m2876.

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Solin, P., J. Cerveny, L. Dubcova, and D. Andrs. "Monolithic discretization of linear thermoelasticity problems via adaptive multimesh hp-FEM." Journal of Computational and Applied Mathematics 234, no. 7 (2010): 2350–57. http://dx.doi.org/10.1016/j.cam.2009.08.092.

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Zdechlik, Robert, and Agnieszka Kałuża. "The FEM model of groundwater circulation in the vicinity of the Świniarsko intake, near Nowy Sącz (Poland)." Geologos 25, no. 3 (2019): 255–62. http://dx.doi.org/10.2478/logos-2019-0028.

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Abstract Modern hydrogeological research uses numerical modelling, which is most often based on the finite difference method (FDM) or finite element method (FEM). The present paper discusses an example of application of the less frequently used FEM for simulating groundwater circulation in the vicinity of the intake at Świniarsko near Nowy Sącz. The research area is bordered by rivers and watersheds, and within it, two well-connected aquifers occur (Quaternary gravelly-sandy sediments and Paleogene cracked flysch rocks). The area was discretized using a Triangle generator, taking into account

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Kahla, Nabil Ben, Saeed AlQadhi, and Mohd Ahmed. "Radial Point Interpolation-Based Error Recovery Estimates for Finite Element Solutions of Incompressible Elastic Problems." Applied Sciences 13, no. 4 (2023): 2366. http://dx.doi.org/10.3390/app13042366.

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Error estimation and adaptive applications help to control the discretization errors in finite element analysis. The study implements the radial point interpolation (RPI)-based error-recovery approaches in finite element analysis. The displacement/pressure-based mixed approach is used in finite element formulation. The RPI approach considers the radial basis functions (RBF) and polynomials basis functions together to interpolate the finite element solutions, i.e., displacement over influence zones to recover the solution errors. The energy norm is used to represent global and local errors. The

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Chen, Hao, and Li Li Xie. "Extension to Elasto-Plastic Version of a Fracture Mechanics Method." Applied Mechanics and Materials 703 (December 2014): 376–80. http://dx.doi.org/10.4028/www.scientific.net/amm.703.376.

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This paper develops a three dimensional elastic fracture analysis method, PDS-FEM (Particle Discretization Scheme Finite Element Method), to its elasto-plastic version. The Newton-Raphson iteration method is adopted for solving material nonlinearity, and the conjugate gradient method is applied to solve the linear equations of FEM. In order to apply the fracture analysis method to the engineering scale analysis, CPU based parallel computing technology is applied, and the computation speed is highly advanced. In this trial test, a simple stress based failure criterion is employed for the failur

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Nadal, E., J. J. Ródenas, J. Albelda, M. Tur, J. E. Tarancón, and F. J. Fuenmayor. "Efficient Finite Element Methodology Based on Cartesian Grids: Application to Structural Shape Optimization." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/953786.

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This work presents an analysis methodology based on the use of the Finite Element Method (FEM) nowadays considered one of the main numerical tools for solving Boundary Value Problems (BVPs). The proposed methodology, so-called cg-FEM (Cartesian grid FEM), has been implemented for fast and accurate numerical analysis of 2D linear elasticity problems. The traditional FEM uses geometry-conforming meshes; however, in cg-FEM the analysis mesh is not conformal to the geometry. This allows for defining very efficient mesh generation techniques and using a robust integration procedure, to accurately i

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Reddy, Gujji Murali Mohan, Alan B. Seitenfuss, Débora de Oliveira Medeiros, Luca Meacci, Milton Assunção, and Michael Vynnycky. "A Compact FEM Implementation for Parabolic Integro-Differential Equations in 2D." Algorithms 13, no. 10 (2020): 242. http://dx.doi.org/10.3390/a13100242.

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Although two-dimensional (2D) parabolic integro-differential equations (PIDEs) arise in many physical contexts, there is no generally available software that is able to solve them numerically. To remedy this situation, in this article, we provide a compact implementation for solving 2D PIDEs using the finite element method (FEM) on unstructured grids. Piecewise linear finite element spaces on triangles are used for the space discretization, whereas the time discretization is based on the backward-Euler and the Crank–Nicolson methods. The quadrature rules for discretizing the Volterra integral

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Liu, Chao, and Robert G. Kelly. "A Review of the Application of Finite Element Method (FEM) to Localized Corrosion Modeling." CORROSION 75, no. 11 (2019): 1285–99. http://dx.doi.org/10.5006/3282.

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The modeling of localized corrosion has usually focused on calculating the spatial and/or temporal distributions of chemical species, potential, and current. These are affected by the reactions considered, the geometry, and the modes of mass transport of importance. Finite element method (FEM) is a numerical technique to obtain approximate solutions to the differential equations based on different types of discretization in which the domain of interest is divided into different types of elements. The introduction of the FEM opened a variety of opportunities for increasing the complexity, and t

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Yoshida, Takumi, Takeshi Okuzono, and Kimihiro Sakagami. "Time Domain Room Acoustic Solver with Fourth-Order Explicit FEM Using Modified Time Integration." Applied Sciences 10, no. 11 (2020): 3750. http://dx.doi.org/10.3390/app10113750.

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This paper presents a proposal of a time domain room acoustic solver using novel fourth-order accurate explicit time domain finite element method (TD-FEM), with demonstration of its applicability for practical room acoustic problems. Although time domain wave acoustic methods have been extremely attractive in recent years as room acoustic design tools, a computationally efficient solver is demanded to reduce their overly large computational costs for practical applications. Earlier, the authors proposed an efficient room acoustic solver using explicit TD-FEM having fourth-order accuracy in bot

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Kololikiye, Gilang Ramadan, Yulvi Zaika, and Harimurti Harimurti. "Prefabricatred Vertical Drain Improved Soft Soil Using Three-Dimensional Finite Element Method." Rekayasa Sipil 15, no. 2 (2021): 150–56. http://dx.doi.org/10.21776/ub.rekayasasipil.2021.015.02.10.

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The subgrade layer of freeway construction in East Java contains high compressibility of soft soil with 24.5 m depth and 10.2 m height of the embankment. It is necessary to stabilize using PVD by accelerating the process of consolidation to increase its bearing capacity. In this study, 3D FEM programming is used to analyze the consolidation in pursuing to compare with the analytical results. 3D FEM shows the settlement without PVD is 0.834 m with excess pore water -4 kN/m2, while using PVD the settlement 0.819 m with excess pore pressure -8 kN/m2. For the analytical results, both variations in

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35

Elleithy, W. "FEM-BEM coupling for elasto-plastic analysis: automatic adaptive generation of the FEM and BEM zones of discretization." PAMM 7, no. 1 (2007): 2020053–54. http://dx.doi.org/10.1002/pamm.200700335.

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Hori, Muneo, Kenji Oguni, and Hide Sakaguchi. "Proposal of FEM implemented with particle discretization for analysis of failure phenomena." Journal of the Mechanics and Physics of Solids 53, no. 3 (2005): 681–703. http://dx.doi.org/10.1016/j.jmps.2004.08.005.

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Bui-Thanh, Tan, and Quoc P. Nguyen. "FEM-based discretization-invariant MCMC methods for PDE-constrained Bayesian inverse problems." Inverse Problems and Imaging 10, no. 4 (2016): 943–75. http://dx.doi.org/10.3934/ipi.2016028.

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38

Bauer, Andrew C., and Abani K. Patra. "Performance of parallel preconditioners for adaptive hp FEM discretization of incompressible flows." Communications in Numerical Methods in Engineering 18, no. 5 (2002): 305–13. http://dx.doi.org/10.1002/cnm.465.

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39

Liu, Guirong, Meng Chen, and Ming Li. "Lower Bound of Vibration Modes Using the Node-Based Smoothed Finite Element Method (NS-FEM)." International Journal of Computational Methods 14, no. 04 (2017): 1750036. http://dx.doi.org/10.1142/s0219876217500360.

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The smoothed finite element method (S-FEM) has been recently developed as an effective solver for solid mechanics problems. This paper represents an effective approach to compute the lower bounds of vibration modes or eigenvalues of elasto-dynamic problems, by making use of the important softening effects of node-based S-FEM (NS-FEM). We first use NS-FEM, FEM and the analytic approach to compute the eigenvalues of transverse free vibration in strings and membranes. It is found that eigenvalues by NS-FEM are always smaller than those by FEM and the analytic method. However, NS-FEM produces spur

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Führer, Thomas, Norbert Heuer, Michael Karkulik, and Rodolfo Rodríguez. "Combining the DPG Method with Finite Elements." Computational Methods in Applied Mathematics 18, no. 4 (2018): 639–52. http://dx.doi.org/10.1515/cmam-2017-0041.

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AbstractWe propose and analyze a discretization scheme that combines the discontinuous Petrov–Galerkin and finite element methods. The underlying model problem is of general diffusion-advection-reaction type on bounded domains, with decomposition into two sub-domains. We propose a heterogeneous variational formulation that is of the ultra-weak (Petrov–Galerkin) form with broken test space in one part, and of Bubnov–Galerkin form in the other. A standard discretization with conforming approximation spaces and appropriate test spaces (optimal test functions for the ultra-weak part and standard t

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Sawicki, Dominik, and Eugeniusz Zieniuk. "Parametric Integral Equations Systems Method In Solving Unsteady Heat Transfer Problems For Laser Heated Materials." Acta Mechanica et Automatica 9, no. 3 (2015): 167–72. http://dx.doi.org/10.1515/ama-2015-0028.

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Abstract One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods allow an easy and fast way to simulate the heating process inside of the material. The most popular numerical methods FEM and BEM, used to simulate this kind of processes have one fundamental defect, which is the necessity of discretization of the boundary or the domain. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES), which do not require classical discretization of the boundary and

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Kielhorn, Lars, Thomas Rüberg, and Jürgen Zechner. "Simulation of electrical machines: a FEM-BEM coupling scheme." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 36, no. 5 (2017): 1540–51. http://dx.doi.org/10.1108/compel-02-2017-0061.

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Purpose Electrical machines commonly consist of moving and stationary parts. The field simulation of such devices can be demanding if the underlying numerical scheme is solely based on a domain discretization, such as in the case of the finite element method (FEM). This paper aims to present a coupling scheme based on FEM together with boundary element methods (BEMs) that neither hinges on re-meshing techniques nor deals with a special treatment of sliding interfaces. While the numerics are certainly more involved, the reward is obvious: the modeling costs decrease and the application engineer

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Rastegari, Shafagh, Seyed Majid Hosseini, Mojtaba Hasani, and Abdolreza Jamilian. "An Overview of Basic Concepts of Finite Element Analysis and Its Applications in Orthodontics." Journal of Dentists 11 (July 5, 2023): 23–30. http://dx.doi.org/10.12974/2311-8695.2023.11.04.

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Purpose: The aim of this article is to acquaint the readers with the aims and goals of the finite element method and how to use it in dentistry and especially in orthodontics. Methods: The finite element method (FEM) has shown to be a beneficial research tool that has assisted scientists in various analyses such as stress-strain, heat transfer, dynamic, collision, and deformation analyses. The FEM is responsible for predicting the behavior of objects under different working conditions. It is a computational procedure to measure the stress in an element, which performs a model solution to

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Li, Mingxia, Jingzhi Li, and Shipeng Mao. "Numerical Analysis of an Adaptive FEM for Distributed Flux Reconstruction." Communications in Computational Physics 15, no. 4 (2014): 1068–90. http://dx.doi.org/10.4208/cicp.050313.210613s.

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AbstractThis paper studies convergence analysis of an adaptive finite element algorithm for numerical estimation of some unknown distributed flux in a stationary heat conduction system, namely recovering the unknown Neumann data on interior inaccessible boundary using Dirichlet measurement data on outer accessible boundary. Besides global upper and lower bounds established in [23], a posteriori local upper bounds and quasi-orthogonality results concerning the discretization errors of the state and adjoint variables are derived. Convergence and quasi-optimality of the proposed adaptive algorith

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Löschner, Fabian, José Antonio Fernández-Fernández, Stefan Rhys Jeske, Andreas Longva, and Jan Bender. "Micropolar Elasticity in Physically-Based Animation." Proceedings of the ACM on Computer Graphics and Interactive Techniques 6, no. 3 (2023): 1–24. http://dx.doi.org/10.1145/3606922.

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We explore micropolar materials for the simulation of volumetric deformable solids. In graphics, micropolar models have only been used in the form of one-dimensional Cosserat rods, where a rotating frame is attached to each material point on the one-dimensional centerline. By carrying this idea over to volumetric solids, every material point is associated with a microrotation, an independent degree of freedom that can be coupled to the displacement through a material's strain energy density. The additional degrees of freedom give us more control over bending and torsion modes of a material. We

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Skordaris, Georgios, Konstantinos Bouzakis, and Paschalis Charalampous. "A critical review of FEM models to simulate the nano-impact test on PVD coatings." MATEC Web of Conferences 188 (2018): 04017. http://dx.doi.org/10.1051/matecconf/201818804017.

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Nano-impact test is a reliable method for assessing the brittleness of PVD coatings with mono- or multi-layer structures. For the analytical description of this test, a 3D-FEM Finite Element Method (FEM) model and an axis-symmetrical one were developed using the ANSYS LS-DYNA software. The axis-symmetrical FEM simulation of the nano-impact test can lead to a significantly reduced computational time compared to a 3D-FEM model and increased result's accuracy due to the denser finite element discretization network. In order to create an axissymmetrical model, it was necessary to replace the cube

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Williams, F. W., and D. Kennedy. "Derivation of New Transcendental Member Stiffness Determinant for Vibrating Frames." International Journal of Structural Stability and Dynamics 03, no. 02 (2003): 299–305. http://dx.doi.org/10.1142/s0219455403000835.

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Transcendental dynamic member stiffness matrices for vibration problems arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretization errors. Assembling them into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or their squares) are found with certainty using the Wittrick–Williams algorithm. This paper gives equations for the recently discovered transcendental member stiffness determinant, which equals the appropriately normalized FEM dynamic stiffness matr

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Mavrič, Boštjan, and Božidar Šarler. "Application of the RBF collocation method to transient coupled thermoelasticity." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 5 (2017): 1064–77. http://dx.doi.org/10.1108/hff-03-2016-0110.

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Purpose In this study, the authors aim to upgrade their previous developments of the local radial basis function collocation method (LRBFCM) for heat transfer, fluid flow, electromagnetic problems and linear thermoelasticity to dynamic-coupled thermoelasticity problems. Design/methodology/approach The authors solve a thermoelastic benchmark by considering a linear thermoelastic plate under thermal and pressure shock. Spatial discretization is performed by a local collocation with multi-quadrics augmented by monomials. The implicit Euler formula is used to perform the time stepping. The system

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Erath, Christoph, and Robert Schorr. "Stable Non-symmetric Coupling of the Finite Volume Method and the Boundary Element Method for Convection-Dominated Parabolic-Elliptic Interface Problems." Computational Methods in Applied Mathematics 20, no. 2 (2020): 251–72. http://dx.doi.org/10.1515/cmam-2018-0253.

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AbstractMany problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems numerically is the non-symmetric coupling of finite elements (FEM) and boundary elements (BEM) analyzed in [H. Egger, C. Erath and R. Schorr, On the nonsymmetric coupling method for parabolic-elliptic interface problems, SIAM J. Numer. Anal. 56 2018, 6, 3510–3533]. If, for example, the interior problem represents a fluid, this method is not appropriate sinc

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Цуканова, Екатерина, and Ekaterina Tsukanova. "Analysis of forced vibrations of frameworks by finite element method using dynamic finite element." Bulletin of Bryansk state technical university 2015, no. 2 (2015): 93–103. http://dx.doi.org/10.12737/22911.

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The analysis of forced vibrations of frameworks using finite element method is considered. The dynamic finite element, the base functions of which represent exact dynamic shapes of structural elements, is used for system discretization. The assessment of errors as a result of classic FEM application is given. The efficiency of application of dynamic finite element for analysis of forced vibrations and dynamic stress-deformed state of structures is shown.

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