Relevant bibliographies by topics / FEM discretization

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'FEM discretization'

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Published: 1 March 2025

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Journal articles on the topic "FEM discretization"

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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 with respect to the substructures for the first discretization and by piecewise constant functions for the second discretization. It has been established that the condition number of the preconditioned systems does not depend on the jumps of the coefficients across the substructure boundaries and outside of a thin layer along the substructure boundaries. The algorithms are very well suited for parallel computations.
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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 (January 29, 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 the category of vector spaces. Moreover, we discuss parallel decomposability of discretization, and through examples, connect it to different FEM formulations and choices of basis functions.
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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 (January 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 variation processes is proposed, allowing in particular a stable DG discretization of hypersingular integral operators. Robustness of the stabilized discretization with respect to various degeneracies in the characteristic triple of the stochastic process is proved. We provide in particular an hp-error analysis of the DG-FEM. Numerical experiments for model equations confirm the theoretical results.
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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 (February 25, 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 compute it. To alleviate this problem, we propose regularization of given functional by error estimate of the FEM discretization. This regularization provides robustness of solutions and improves obtained functional values as well. While the idea is broadly applicable, in this paper we apply our method to the heat conduction optimization. Problems of this type are of practical importance in design of heat conduction channels, heat sinks and other types of heat guides.
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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 (January 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 algorithm for the new discretization. These are also demonstrated in numerical experiments. Furthermore, this paper focuses on extensions of this new scheme to quadrilateral meshes, mixed FEMs, and three space dimensions.
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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 (October 16, 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 functions given in terms of Hilbert transforms of the corresponding trial functions; inf-sup constants are independent of temporal order and the time-step sequences, allowing quasi-optimal, high-order discretizations on graded time-step sequences, and also $hp$-time discretizations. For solutions exhibiting Gevrey regularity in time and taking values in certain weighted Bochner spaces, we establish novel exponential convergence estimates in terms of $N_t$, the number of (elliptic) spatial problems to be solved. The space-time variational setting allows general space discretizations and, in particular, for spatial $hp$-FEM discretizations. We report numerical tests of the method for model problems in one space dimension with typical singular solutions in the spatial and temporal variable. $hp$-discretizations in both spatial and temporal variables are used without any loss of stability, resulting in overall exponential convergence of the space-time discretization.
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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 (October 12, 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 the integration points and discretization error is derived in detail, and the optimized location of the integration points is found through the optimization procedure, and then the OGIR–FEM is finally proposed to solve the acoustic problem. It also can be directly used to solve the optional acoustic problem, including the damped problems. Numerical example involving distorted meshes indicates that present OGIR–FEM has a superior error reducing performance in comparison with the other error reducing finite elements. These researches indicate that the proposed method can be more widely applied to solving practical acoustic problems with more accurate solutions.
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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 main conclusions.
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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 (November 17, 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 analysis. The advantages and limitations of using these methods are discussed, and a comparison between FVM and FDM is provided. Advanced discretization techniques, such as the Finite Element Method (FEM), and coupled thermal-electromagnetic analyses are also examined. The paper highlights studies that have utilized FVM or FDM in developing optimized designs and effective thermal management strategies for AFPM machines. Lastly, potential future research directions are identified, including the development of more efficient discretization methods, the incorporation of advanced materials, and the investigation of novel cooling techniques. This review offers valuable insights into the current state of research and potential future directions in the thermal analysis of AFPM machines using discretization methods.
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Dissertations / Theses on the topic "FEM discretization"

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Rücker, Carsten. "Advanced Electrical Resistivity Modelling and Inversion using Unstructured Discretization." Doctoral thesis, Universitätsbibliothek Leipzig, 2011. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-69066.

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In this dissertation an approach is presented for the three-dimensional electrical resistivity tomography (ERT) using unstructured discretizations. The geoelectrical forward problem is solved by the finite element method using tetrahedral meshes with linear and quadratic shape functions. Unstructured meshes are suitable for modelling domains of arbitrary geometry (e.g., complicated topography). Furthermore, the best trade-off between accuracy and numerical effort can be achieved due to the capability of problem-adapted mesh refinement. Unstructured discretizations also allow the consideration of spatial extended finite electrodes. Due to a corresponding extension of the forward operator using the complete electrode model, known from medical impedance tomography, a study about the influence of such electrodes to geoelectrical measurements is given. Based on the forward operator, the so-called triple-grid-technique is developed to solve the geoelectrical inverse problem. Due to unstructured discretization, the ERT can be applied by using a resolution dependent parametrization on arbitrarily shaped two-dimensional and three-dimensional domains. A~Gauss-Newton method is used with inexact line search to fit the data within error bounds. A global regularization scheme is applied using special smoothness constraints. Furthermore, an advanced regularization scheme for the ERT is presented based on unstructured meshes, which is able to include a-priori information into the inversion and significantly improves the resulting ERT images. Structural information such as material interfaces known from other geophysical techniques are incorporated as allowed sharp resistivity contrasts. Model weighting functions can define individually the allowed deviation of the final resistivity model from given start or reference values. As a consequent further development the region concept is presented where the parameter domain is subdivided into lithological or geological regions with individual inversion and regularization parameters. All used techniques and concepts are part of the open source C++ library GIMLi, which has been developed during this thesis as an advanced tool for the method-independent solution of the inverse problem.
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Rückert, Jens. "Kirchhoff Plates and Large Deformations - Modelling and C^1-continuous Discretization." Doctoral thesis, Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-121275.

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In this thesis a theory for large deformation of plates is presented. Herein aspects of the common 3D-theory for large deformation with the Kirchhoff hypothesis for reducing the dimension from 3D to 2D is combined. Even though the Kirchhoff assumption was developed for small strain and linear material laws, the deformation of thin plates made of isotropic non-linear material was investigated in a numerical experiment. Finally a heavily deformed shell without any change in thickness arises. This way of modeling leads to a two-dimensional strain tensor essentially depending on the first two fundamental forms of the deformed mid surface. Minimizing the resulting deformation energy one ends up with a nonlinear equation system defining the unknown displacement vector U. The aim of this thesis was to apply the incremental Newton technique with a conformal, C^1-continuous finite element discretization. For this the computation of the second derivative of the energy functional is the key difficulty and the most time consuming part of the algorithm. The practicability and fast convergence are demonstrated by different numerical experiments.
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Ponce, Cristobal. "Port-Hamiltonian modeling, discretization and shape control of multidimensional flexible mechanical systems." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://www.theses.fr/2024UBFCD061.

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Cette thèse traite de la modélisation, de la discrétisation et du contrôle de forme des systèmes mécaniques flexibles dans le cadre des systèmes Port-Hamiltoniens (PHS). Les contributions sont triples. Tout d'abord, nous proposons des méthodologies généralisées pour la modélisation des systèmes mécaniques multidimensionnels, linéaires et non linéaires, en utilisant le principe de Hamilton généralisé et étendu, fournissant des représentations explicites et implicites des PHS. Ensuite, nous développons des techniques de discrétisation préservant la structure à travers des méthodes d'éléments finis mixtes (FEM), incluant des approches à deux, trois et quatre champs adaptées aux systèmes PHS et PH-DAE linéaires et non linéaires. Enfin, nous introduisons un contrôleur en dimension finie basé sur des approximations d'ordre faible de systèmes PHS linéaires discrétisés à grande échelle. Ce contrôleur garantit la convergence vers les formes optimales, offrant la meilleure approximation des configurations désirées, tout en assurant la stabilité asymptotique du système discrétisé à grande échelle
This thesis addresses the modeling, discretization, and shape control of flexible mechanical systems within the Port-Hamiltonian Systems (PHS) framework. The contributions are threefold. First, we propose generalized methodologies for modeling both linear and nonlinear multidimensional mechanical systems using the generalized extended Hamilton's principle, providing explicit and implicit PHS representations. Second, we develop structure-preserving discretization techniques via mixed Finite Element Methods (FEM), including two, three, and four-field approaches tailored to linear and nonlinear PHS and PH-DAE systems. Finally, we introduce a finite-dimensional controller based on low-order approximations of large-scale discretized linear PHS. This controller ensures convergence to the optimal shapes, offering the best approximation to the desired configurations, while guaranteeing asymptotic stability of the large-scale discretized system
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He, Bo. "Compatible discretizations for Maxwell equations." The Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=osu1143171299.

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Palionytė, Agnė. "Kontinualių struktūrų diskretizavimas vaizdų algebros metodais." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2011. http://vddb.laba.lt/obj/LT-eLABa-0001:E.02~2011~D_20110616_163839-19284.

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Baigiamajame magistro darbe nagrinėjami struktūrų modeliavimo, diskretizavimo ir optimizavimo uždaviniai, jų sprendimo būdai ir algoritmai. Pasiūlyta originali strypinių struktūrų optimizavimo ir diskretizavimo technika, kurioje naudojami vaizdų algebros metodai ir baigtinių elementų metodo (toliau – BEM) programiniai paketai. Atlikta BEM programinių paketų apžvalga, parinkti tinkamiausi paketai darbo tikslams realizuoti ir rezultatams verifikuoti. Išanalizuoti skaitmeninių vaizdų skeletų išgavimo metodai. Pasiūlytas originalus vaizdo skeleto apdorojimo algoritmas skerspjūvio charakteristikoms nustatyti. Sudarytas ir programiškai realizuotas strypinių struktūrų optimizavimo-diskretizavimo algoritmas. Realizuota programinė sistema susideda iš vaizdų apdorojimo ir duomenų paruošimo dalies (MATLAB kalba) bei BEM skaičiavimų dalies (ANSYS vidine programavimo kalba APDL). Skaičiavimo rezultatai atvaizduojami ir verifikuojami STAAD.Pro paketu. Diskretizavimo metu strypinės struktūros mazgų vieta randama vaizdo skeleto segmentų sankirtos taškuose, o segmentų skerspjūvių plotai randami atkarpų, jungiančių šiuos mazgus, vidurio taškuose. Kai struktūros mazgų padėtis fiksuota arba mazgai yra per arti vienas kito atliekamas mazgų padėties koregavimas. Darbe atlikti testiniai skaičiavimai, rezultatų analizė ir verifikavimas, suformuluotos išvados.
In the master thesis the problems of structure modeling, discretization-optimization and their solution methods and algorithms are analyzed. The original technique for optimization and discretization of beam structures has been suggested; The packages of image algebra methods and of the finite element methods were employed for that. Several packages of finite element method have been reviewed and the most suitable packages for the current problems were identified. The methods for obtaining skeletons of digital images were explored. The algorithms for optimization and discretization of beam structures has been suggested and coded. The program created consents of the part for image processing and input data preparing, and the part for image the finite element via method. The results obtained are represented and verified by STAAD.Pro package. During the discretization, the positions of structure nodes are obtained in the intersection of skeleton segments. The segments' cross-section areas are obtained in the middle-points between two adjacent nodes. The positions of nodes may be corrected if the nodes close to each other. The test-calculation, analysis of results and verification are presented and conclusions are drawn.
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Bachini, Elena. "Numerical methods for Shallow Water Equations on regular surfaces." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3422699.

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Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this thesis we derive an intrinsic shallow water model starting from the Navier-Stokes equations defined on a local reference frame anchored on the bottom surface. The resulting equations are characterized by non-autonomous flux functions and source terms embodying only geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier-Stokes equations with respect to a geometry-based order parameter. We then derive numerical discretization schemes compatibles with the intrinsic setting of the formulation, starting from studying a first order upwind Godunov Finite Volume scheme intrinsically defined on the bottom surface. We analyze convergence properties of the resulting scheme both theoretically and numerically. Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures. The low-order discretization method is subsequently extended to the Discontinuous Galerkin framework. We implement a linear version of the DG scheme defined intrinsically on the surface and we start from the resolution of the scalar transport equation. We test the scheme for convergence and then we move towards the intrinsic shallow water model. Simulations on synthetic test cases are reported and the improvement with respect to the first order finite volume discretization is clearly visible. Finally, we consider a finite element method for advection-diffusion-reaction equations on surfaces. Unlike many previous techniques, this approach is based on the geometrically intrinsic formulation and the resulting finite element method is fully intrinsic to the surface. In the last part of this work, we lay out in detail the formulation and compare it to a well-established finite element scheme for surface PDEs. We then evaluate the method for several steady and transient problems involving both diffusion and advection-dominated regime. The experimental results show the theoretically expected convergence rates and good performance of the established finite element methods.
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Gibert, Gaël. "Propagation de fissures en fatigue par une approche X-FEM avec raffinement automatique de maillage." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSEI088.

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Dans cette thèse, une nouvelle approche est présentée, combinant la méthode des éléments finis étendus (X-FEM) et un raffinement adaptatif et automatique de maillage (AMR). La méthode X-FEM, développée durant les deux dernières par une importante communauté, a prouvé son efficacité pour gérer l'évolution de discontinuités dans de nombreux problèmes de mécanique de la rupture. Comme cette méthode permet de décrire la fissure indépendamment du maillage de la structure, un raffinement hiérarchique relativement simple peut être appliqué sur ce dernier pour adapter localement l'échelle de discrétisation à celle des phénomènes physiques mis en jeux. Cela permet d'obtenir une description précise de quantités physiques d'intérêt dans une zone limitée autour du front de fissure et réduire considérablement le coût numérique, particulièrement lorsque le trajet de propagation n'est pas connu a priori. Dans ce travail, on propose une stratégie pour combiner X-FEM et AMR : les relations de compatibilité cinématique et les méthodes de projection nécessaires pour les matériaux dépendant de l'histoire de chargement doivent inclure correctement le modèle d'enrichissement. L'implémentation de cette approche combinant X-FEM et AMR, dans le code éléments finis industriel Cast3M, est présentée en détails. En particulier, une nouvelle méthode de projection spécifique à ce contexte est proposée. Des applications numériques et une étude expérimentale de propagation par fatigue en plasticité confinée ont été réalisées pour démontrer la précision, la robustesse et l'efficacité de cette méthode
To guarantee the high level of safety of industrial components under fatigue cycles it is essential to be able to predict the initiation and growth of cracks during their entire lifetime. However the numerical cost of a propagation simulation on engineer-sized problems with non-linear behavior may be prohibitive, with the classical techniques. Here, a new approach combining the eXtended Finite Element Method (X-FEM) and automatic Adaptive Mesh Refinement (AMR) is presented taking advantage of both methods. The X-FEM, developed over the past two decades by a large community, have proven its efficiency to handle evolving discontinuities in a variety of fracture analysis. Since this method enables to describe the crack and its propagation independently of the mesh of the structure, a simple hierarchical mesh refinement procedure can be applied. Automatic adaptive re-meshing is a valuable method for elastic-plastic crack propagation analysis since it permits a locally fine mesh and then an accurate description of physical quantities in a limited area around the crack front. This is particularly important when local fracture criteria are concerned. Moreover local refinement saves computational effort, particularly when the propagation path is not a priori known. In the present work, it is shown that both methods combine with minimal effort: the kinematic continuity relations and the field transfer process, needed for history-dependent material, must include in a proper way the enrichment of the model. If this requirement is not fulfilled, numerical error may be introduced. Implementation of this combined X-FEM/AMR approach in the finit elements code Cast3M is presented in detail. In particular, an innovative field transfer strategy is proposed in 2D and 3D. Numerical applications of crack propagation in elastic-plastic media demonstrate accuracy, robustness and efficiency of the technique. Moreover, an experimental study has been conducted on a example propagation with notable impact of confined plasticity. This study provides experimental data to compare with the numerical results obtained with the developed method. This validates our modelization choices. It also is the opportunity to test the developed method robustness on a realistic case of utilization. This study showed the interest of the proposed modelization taking into account plasticity induced crack closure during the fatigue propagation
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Moreno, Navarro Pablo. "Multiphysics formulation and multiscale finite element discretizations of thermo-electro-magneto-mechanic coupling for smart materials design." Thesis, Compiègne, 2019. http://www.theses.fr/2019COMP2525.

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Les algorithmes numériques basés sur la méthode des éléments finis seront spécialisés dans l’analyse, la conception et l’optimisation de capteurs et d’actionneurs (S-A), ainsi que dans leur application aux structures intelligentes. Les S-A basés sur des actifs tangibles peuvent coupler plusieurs domaines, tels que les domaines mécanique, électrique, magnétique et thermique. Ils sont utilisés dans de nombreuses applications, notamment dans les structures intelligentes, la surveillance des dommages ou l’aérodynamique. Malgré l’expérience considérable de ces études, les étapes abordées consistent d’abord à développer une formulation thermodynamiquement cohérente à l’échelle macro pour introduire des modèles de plasticité; deuxièmement, fournir les outils permettant de prendre en compte les hétérogénéités des modèles multi-échelles pour les matériaux intelligents. L’objectif principal est la mise au point d’un code informatique de recherche permettant de simuler et d’étudier les performances, non seulement des S-A eux-mêmes, mais également des structures intelligentes dans lesquelles ces S-A seront montés
Numerical algorithms based on the Finite Element Method will be specialized for Analysis, Design, and Optimization of Sensors and Actuators (S-A) and their Application to Smart Structures. The S-A based on tangible assets can couple several fields, such as mechanical, electrical, magnetic, and thermal. They are used in many applications, particularly in smart structures, damage monitoring, or aerodynamics. Despite the considerable experience in these studies, the steps addressed are first to develop a thermodynamically consistent formulation for macro-scale to introduce plasticity models; second, to provide the tools to take into account the heterogeneities of multi-scale models for smart materials. The main objective is the development of a research computer code to simulate and study the performance, not only of the S-A themselves but also of the smart structures in which these S-A will be mounted
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Lang, Rostislav. "Návrh a výpočet membránové konstrukce zastřešení stadionu." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2013. http://www.nusl.cz/ntk/nusl-226463.

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This diploma thesis deals with problem of design and calculation of membrane structure of stadium roof. This is a complex engineering problem, which includes many partial problems: finding of initial form of membrane, statically and architecturally suitable arrangement of catenaries, economical solution of boundary conditions (foundations). All components affect each other and cannot be dealt without mutual coordination. It always greatly depends on the experience and intuition of engineer who design such structure. Task which cannot be resolved according to the theory of the first order. Equilibrium forces on the deformed structure, which in many projected structures gives satisfactory results, did not correspond to reality. It is therefore necessary to consider equilibrium of forces on the deformed structure according to the theory of large deformations. Diploma thesis was entered with regard to the intention of the companies Ing. Software Dlubal s.r.o. and FEM consulting s.r.o., working together to develop software RFEM. These companies plan to complement this program system with a module MEMBRANE for searching of initial shapes of membrane structures. This work is a contribution to the creation of this module.
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Beckstein, Pascal. "Methodenentwicklung zur Simulation von Strömungen mit freier Oberfläche unter dem Einfluss elektromagnetischer Wechselfelder." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-232474.

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Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.
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Book chapters on the topic "FEM discretization"

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Schnack, E., I. Becker, and N. Karaosmanoglu. "Three-dimensional Coupling of FEM and BEM in Elasticity." In Discretization Methods in Structural Mechanics, 415–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-49373-7_39.

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Yagawa, G., T. Yamada, and T. Furukawa. "Parallel Computing with Free Mesh Method: Virtually Meshless FEM." In IUTAM Symposium on Discretization Methods in Structural Mechanics, 165–72. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4589-3_19.

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Combescure, A., A. Gravouil, H. Maigre, J. Réthore, and D. Grégoire. "2D X-FEM Simulation of Dynamic Brittle Crack Propagation." In IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 185–98. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6530-9_11.

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Pavlatos, G. D., and D. E. Beskos. "Dynamic Inelastic Soil-Structure Interaction using a Hybrid BEM/FEM Scheme." In IUTAM Symposium on Discretization Methods in Structural Mechanics, 233–40. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4589-3_27.

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Menouillard, T., N. Moës, and A. Combescure. "An optimal explicit time stepping scheme for cracks modeled with X-FEM." In IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 267–81. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6530-9_16.

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Banichuk, N. V., and V. V. Saurin. "Some Aspects of Fem Application for Sensitivity Analysis of Quasi-Brittle Fracture Conditions." In IUTAM Symposium on Discretization Methods in Structural Mechanics, 217–24. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4589-3_25.

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Gravouil, A., A. Combescure, T. Elguedj, E. Ferrié, J. Y. Buffière, and W. Ludwig. "Application of X-FEM to 3D Real Cracks and Elastic-Plastic Fatigue Crack Growth." In IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 213–31. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6530-9_13.

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Ventura, Giulio. "Single Domain Quadrature Techniques for Discontinuous and Non-Linear Enrichments in Local Partion of Unity FEM." In IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 343–61. Dordrecht: Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-6530-9_20.

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Dedner, Andreas, Robert Klöfkorn, Martin Nolte, and Mario Ohlberger. "Dune-Fem: A General Purpose Discretization Toolbox for Parallel and Adaptive Scientific Computing." In Advances in DUNE, 17–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-28589-9_2.

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Ding, Jianxin, and Qingzhou Yang. "Superposed Element Method for the Temperature Field Simulation in Mass Concrete Structures Containing Cooling Pipes." In Lecture Notes in Civil Engineering, 129–39. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-4090-1_12.

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AbstractPipe cooling is an important measure for controlling the temperature in mass concrete structures, so it is one of the key problems to specifically simulate the effect of the cooling pipes in temperature field analysis. Because the size of cooling pipe is quite small from that of mass concrete structure, its exact simulation is the focus of simulation calculation. In this paper, a new method called SEM (superposed element method) is proposed to analyze the temperature field of mass concrete with cooling pipes in it. First, the structure is divided into two independent meshes. One is the global mesh without cooling pipes, and the other is the local mesh of the cooling pipes together with its adjacent region. Then the elements within the local mesh is treated based on FEM, and the two independent meshes are coupled together through the coupling surface by the coordination of heat conduction. Finally, using the SEM proposed in this paper, the numerical model with a single pipe was analyzed and the calculation precision was validated. The convenient process of grid discretization and good performance in both precision and efficiency show the feasibility of the new method in engineering application.
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Conference papers on the topic "FEM discretization"

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Aravinda Priyadrashini, K., and B. N. Rao. "Coupled Finite Element-Moving Least Squares Technique for Stochastic Structural Response of Cracked Structures." In ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93756.

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In recent years, a class of Galerkin-based meshfree or meshless methods have been developed that do not require a structured mesh to discretize the problem, such as the element-free Galerkin method, and the reproducing kernel particle method. These methods employ a moving least-squares (MLS) approximation method that allows resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. These methods employ a moving least-squares approximation method that allows resultant shape functions to be constructed entirely in terms of arbitrarily placed nodes. Meshless discretization presents significant advantages for modeling fracture propagation. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. Since no element connectivity data are needed, the burdensome remeshing required by the FEM is avoided. A growing crack can be modeled by simply extending the free surfaces, which correspond to the crack. In addition, stochastic meshless method (SMM) facilitates to have different discretizations for capturing the spatial variability of the material properties and the structural response, without much difficulty in mapping between the two discretizations. However, the computational cost of a SMM typically exceeds the cost of a SFEM. Hence, it is advantageous to adopt MLS approximation for material property discretization and FEM for structural response computation. This paper presents a new coupled finite element-moving least squares technique for predicting probabilistic structural response and reliability of cracked structures.
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Shivanna, Kiran H., Srinivas C. Tadepalli, Vincent A. Magnotta, and Nicole M. Grosland. "A Framework for Finite Element Mesh Quality Improvement and Visualization in Orthopaedic Biomechanics." In ASME 2009 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2009. http://dx.doi.org/10.1115/sbc2009-205622.

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The finite element method (FEM) is an invaluable tool in the numerical simulation of biological processes. FEM entails discretization of the structure of interest into elements. This discretization process is termed finite element meshing. The validity of the solution obtained is highly dependent on the quality of the mesh used. Mesh quality can decrease with increased complexity of the structure of interest, as is often evident when meshing biologic structures. This necessitated the development/implementation of generalized mesh quality improvement algorithms.
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Chen, Chang-New. "Extended GDQ and Related Discrete Element Analysis Methods for Transient Analyses of Continuum Mechanics Problems." In ASME 2002 Pressure Vessels and Piping Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/pvp2002-1286.

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The extended GDQ proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of continuum mechanics problems. It is a direct integration approach. Two integration methods are developed. They are time-element by time-element method and stages by stages method. These two time integration algorithms can be used to solve generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of continuum mechanics problems by using a certain discretization technique such as the DQEM, FEM, FDM,…, etc.
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Chen, Chang-New. "Extended GDQ and Related Discrete Element Analysis Methods for Transient Offshore Mechanics and Engineering Problems." In ASME 2002 21st International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2002. http://dx.doi.org/10.1115/omae2002-28484.

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The extended GDQ proposed by the author is used to develop solution algorithms for solving the discrete transient equation system of an offshore mechanics or arctic engineering problem. It is a direct integration approach. Two integration methods are developed. They are time-element by time-element method and stages by stages method. These two time integration algorithms can be used to solve generic discrete transient equation system of an originally discrete system or a discrete system resulting from the discretization of a transient system of offshore mechanics and arctic problems by using a certain discretization technique such as the DQEM, FEM, FDM,…, etc.
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Kondratyev, Nikolay V., Yuri G. Soloveichik, Denis V. Vagin, and Ilya I. Patrushev. "GPU implementation of iterative solver for linear systems obtained by FEM discretization." In 2016 13th International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE). IEEE, 2016. http://dx.doi.org/10.1109/apeie.2016.7806466.

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Kondratyev, Nikolay V., Yuri G. Soloveichik, Denis V. Vagin, and Ilya I. Patrushev. "GPU implementation of iterative solver for linear systems obtained by FEM discretization." In 2016 13th International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE). IEEE, 2016. http://dx.doi.org/10.1109/apeie.2016.7806929.

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Dennis, Brian H., and George S. Dulikravich. "Simultaneous Determination of Steady Temperatures and Heat Fluxes on Surfaces of Three Dimensional Objects Using FEM." In ASME 2001 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/imece2001/htd-24310.

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Abstract A finite element method (FEM) formulation is presented for the prediction of unknown steady boundary conditions in heat conduction on multiply connected three-dimensional solid objects. The present FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-specified on other boundaries. Details of the discretization, linear system solution techniques, regularization, and sample results for 3-D problems are presented.
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Dennis, Brian H., and George S. Dulikravich. "Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries." In ASME 1998 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/imece1998-0215.

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Abstract A finite element method (FEM) formulation for the detection of unknown steady boundary conditions in heat conduction and linear elasticity and thermoelasticity continuum problems is presented. The present FEM formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-specified on other boundaries. Details of the discretization, linear system solution techniques, and sample results for 2-D problems are presented.
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Kondratyev, Nikolay v., Marina G. Persova, Yuri G. Soloveichik, and Dmitry S. Kiselev. "Using HYB Sparse Matrix Storage Format for Solving Linear Systems Obtained by FEM Discretization on GPU." In 2018 XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE). IEEE, 2018. http://dx.doi.org/10.1109/apeie.2018.8546266.

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Fatu, Aurelian, Mohamed Hajjam, and Dominique Bonneau. "A New Model of Thermoelastohydrodynamic Lubrication in Dynamically Loaded Journal Bearings." In World Tribology Congress III. ASMEDC, 2005. http://dx.doi.org/10.1115/wtc2005-63291.

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A comprehensive method of thermoelastohydrodynamic (TEHD) lubrication analysis for dynamically loaded journal bearings is presented. The Reynolds equation in the film is solved using the Finite Element (FEM) discretization. Thermal distortions as well as the elastic deformation of the bearing surfaces are computed using FEM method. The lubrication film temperature is treated as a time-dependent three-dimensional variable with a parabolic variation with respect to the film thickness. In order to compute the film and solid temperature, a new heat flux conservation algorithm is proposed. Fourier series approximate the instantaneous temperature fields in the solid boundary layers. Solving the complex problem of big end connecting rod bearing TEHD lubrication proves the algorithm efficiency.
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