Relevant bibliographies by topics / Enriched polynomial space

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

Academic literature on the topic 'Enriched polynomial space'

Author: Grafiati
Published: 7 September 2024
Last updated: 31 July 2025

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Journal articles on the topic "Enriched polynomial space"

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Du, Xunbai, Sina Dang, Yuzheng Yang, and Yingbin Chai. "The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis." Mathematics 10, no. 23 (2022): 4595. http://dx.doi.org/10.3390/math10234595.

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Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases
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Chai, Yingbin, Kangye Huang, Shangpan Wang, Zhichao Xiang, and Guanjun Zhang. "The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation." Mathematics 11, no. 7 (2023): 1664. http://dx.doi.org/10.3390/math11071664.

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The traditional finite element method (FEM) could only provide acceptable numerical solutions for the Helmholtz equation in the relatively small wave number range due to numerical dispersion errors. For the relatively large wave numbers, the corresponding FE solutions are never adequately reliable. With the aim to enhance the numerical performance of the FEM in tackling the Helmholtz equation, in this work an extrinsic enriched FEM (EFEM) is proposed to reduce the inherent numerical dispersion errors in the standard FEM solutions. In this extrinsic EFEM, the standard linear approximation space
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Liu, Yan Xin, Han Xiang Wang, Qian Qian Fu, Xiang Xiang Yang, and Guo Dong Ding. "The Construction of the SGW-Based Bar-Beam Elements." Applied Mechanics and Materials 423-426 (September 2013): 1202–6. http://dx.doi.org/10.4028/www.scientific.net/amm.423-426.1202.

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PsdVoigt2 function was used to fit SGW function and a series of bar beam elements based on the theory of SGW and wavelet finite element were constructed. Traditional finite element polynomial interpolation was replaced by the SGW scaling function and transformation matrix was utilized to transform wavelet interpolation coefficients to physical space. Thereby the shape function and element were constructed. The precision of a series of bar beam elements constructed with the SGW scale function as the interpolation function were verified by the calculation cases. The calculation results showed th
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Choi, Hyung-Gyu, Young Il Byun, Chul Ki Song, Martin B. G. Jun, Chaemin Lee, and San Kim. "A Solution Procedure to Improve 3D Solid Finite Element Analysis with an Enrichment Scheme." Applied Sciences 13, no. 12 (2023): 7114. http://dx.doi.org/10.3390/app13127114.

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This paper presents a novel and efficient solution procedure to improve 3D solid finite element analysis with an enrichment scheme. To this end, we employ finite elements enriched by polynomial cover functions, which can expand their solution space without requiring mesh refinement or additional nodes. To facilitate this solution procedure, an error estimation method and cover function selection scheme for 3D solid finite element analysis are developed. This enables the identification of nodes with suboptimal solution accuracy, allowing for the adaptive application of cover functions in a syst
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Xu, Xiaorui, and Yu-Xin Ren. "Resolving turbulent boundary layer on coarse grid using function enrichment based on variational reconstructions." Physics of Fluids 34, no. 12 (2022): 125106. http://dx.doi.org/10.1063/5.0124478.

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An improved finite volume scheme based on variational reconstruction and function enrichment has been proposed in this paper. By incorporating the law-of-the-wall into the variational reconstruction, the proposed method can resolve turbulent flow accurately on grids much coarser than those needed by traditional methods. The usual reconstruction in a finite volume scheme assumes that the solution is belonging to a polynomial function space, which is inaccurate to resolve the velocity profile within the turbulent boundary layer unless the grid in wall-normal direction is fine enough. In the pres
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Chandler-wilde, Simon, Stephen Langdon, and Oliver Phillips. "Towards high frequency boundary element methods for multiple scattering." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 2 (2023): 5319–25. http://dx.doi.org/10.3397/in_2022_0775.

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Standard Boundary Element Methods (BEM) for time-harmonic acoustics, using piecewise polynomial finite-element type approximation spaces, have a computational cost that grows rapidly with frequency, to ensure at least a fixed number of degrees of freedom per wavelength. Hybrid Numerical-Asymptotic (HNA) BEMs, based on enriched approximation spaces consisting of the products of piecewise polynomials with carefully chosen oscillatory functions, have a computational cost that is almost frequency-independent for some problem classes (e.g. Chandler-Wilde, Graham, Langdon, Spence, Acta Numerica 2012
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Torii, André Jacomel, Roberto Dalledone Machado, and Marcos Arndt. "GFEM for modal analysis of 2D wave equation." Engineering Computations 32, no. 6 (2015): 1779–801. http://dx.doi.org/10.1108/ec-07-2014-0144.

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Purpose – The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation. Design/methodology/approach – The GFEM can be viewed as an extension of the standard Finite Element Method (FEM) that allows non-polynomial enrichment of the approximation space. In this paper the authors enrich the approximation space with sine e cosine functions, since these functions frequently appear in the analytical solution of the problem under study. The results are compared with the ones obtained with the polynomial FEM using higher o
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Albeladi, Ghadah, Mohamed Gamal та Youssri Hassan Youssri. "G-Metric Spaces via Fixed Point Techniques for Ψ-Contraction with Applications". Fractal and Fractional 9, № 3 (2025): 196. https://doi.org/10.3390/fractalfract9030196.

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The primary aim of this manuscript is to establish unique fixed point results for a class of Ψ-contraction operators in complete G-metric spaces. By combining and extending various fixed point theorems in the context of Ψ-contraction operators, we introduce a novel function, denoted as ψ, and explore its properties. Our work presents new theoretical results, supported by examples and applications, that enrich the study of G-metric spaces. These results not only generalize and unify a broad range of existing findings in the literature but also expand their use to boundary value problems, Fredho
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Hu, Jun, та Shangyou Zhang. "Finite element approximations of symmetric tensors on simplicial grids in ℝn: The lower order case". Mathematical Models and Methods in Applied Sciences 26, № 09 (2016): 1649–69. http://dx.doi.org/10.1142/s0218202516500408.

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In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric tensor finite element spaces of order [Formula: see text] from [Finite element approximations of symmetric tensors on simplicial grids in [Formula: see text]: The higher order case, J. Comput. Math. 33 (2015) 283–296], enriched, for each [Formula: see text]-dimensional simplex, by [Formula: see text] face bubble functions in the symmetric tensor finite element space of
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Wang, Yifeng. "Symmetry and symmetric transformations in mathematical imaging." Theoretical and Natural Science 31, no. 1 (2024): 320–23. http://dx.doi.org/10.54254/2753-8818/31/20241037.

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The article delves into the intricate relationship between symmetry and mathematical imaging, spanning various mathematical disciplines. Symmetry, a concept deeply ingrained in mathematics, manifests in art, nature, and physics, providing a powerful tool for understanding complex structures. The paper explores three types of symmetriesreflection, rotational, and translationalexemplified through concrete mathematical expressions. Evariste Galoiss Group Theory emerges as a pivotal tool, providing a formal framework to understand and classify symmetric operations, particularly in the roots of pol
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Dissertations / Theses on the topic "Enriched polynomial space"

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Nudo, Frederico. "Approximations polynomiales et méthode des éléments finis enrichis, avec applications." Electronic Thesis or Diss., Pau, 2024. http://www.theses.fr/2024PAUU3067.

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Un problème très courant en science computationnelle est la détermination d'une approximation, dans un intervalle fixe, d'une fonction dont les évaluations ne sont connues que sur un ensemble fini de points. Une approche courante pour résoudre ce problème repose sur l'interpolation polynomiale. Un cas d'un grand intérêt pratique est celui où ces points suivent une distribution équidistante dans l'intervalle considéré. Dans ces hypothèses, un problème lié à l'interpolation polynomiale est le phénomène de Runge, caractérisé par une augmentation de l'erreur d'interpolation près des extrémités de
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Nora, Pedro Miguel Teixeira Olhero Pessoa. "Kleisli dualities and Vietoris coalgebras." Doctoral thesis, 2019. http://hdl.handle.net/10773/29882.

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In this thesis we aim for a systematic way of extending Stone-Halmos duality theorems to categories including all compact Hausdorff spaces. To achieve this goal, we combine duality theory and quantale-enriched category theory. Our main idea is that, when passing from the two-element discrete space to a cogenerator of the category of compact Hausdorff spaces, all other involved structures should be substituted by corresponding enriched versions. Accordingly, we work with the unit interval [0, 1] and present duality theory for ordered compact spaces and (suitably defined) finitely cocomplet
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Book chapters on the topic "Enriched polynomial space"

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Boules, Adel N. "Banach Spaces." In Fundamentals of Mathematical Analysis. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198868781.003.0006.

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The first four sections of this chapter form its core and include classical topics such as bounded linear transformations, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and the Hahn-Banach theorem. The chapter includes a good number of applications of the four fundamental theorems of functional analysis. Sections 6.5 and 6.6 provide a good account of the properties of the spectrum and adjoint operators on Banach spaces. They may be largely bypassed, since the treatment of the corresponding topics for operators on Hilbert spaces in chapter 7 is self-cont
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Brezzi, F., L. P. Franca, T. J. R. Hughest, and A. Russo. "Stabilization Techniques and Subgrid Scales Capturing." In The State of the Art in Numerical Analysis. Oxford University PressOxford, 1997. http://dx.doi.org/10.1093/oso/9780198500148.003.0015.

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Abstract We present an overview of stabilized finite element methods and of the standard Galerkin method enriched with residual-free bubble functions. The inadequacy of the standard Galerkin method using piecewise polynomials is discussed for different applications; the treatment using stabilized methods in their different versions is reviewed; and the connection to the standard Galerkin method with richer subspaces follows using the subgrid method or the residual-free-bubbles viewpoint. We close with a discussion on how to approximate the exact problem suggested by residual-free bubbles. The
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Conference papers on the topic "Enriched polynomial space"

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Ghanem, Roger, and Debraj Ghosh. "An Enrichment Scheme for Polynomial Chaos Expansion Applied to Random Eigenvalue Problem." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-85450.

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For a system with the parameters modeled as uncertain, polynomial approximations such as polynomial chaos expansion provide an effective way to estimate the statistical behavior of the eigenvalues and eigenvectors, provided the eigenvalues are widely spaced. For a system with a set of clustered eigenvalues, the corresponding eigenvalues and eigenvectors are very sensitive to perturbation of the system parameters. An enrichment scheme to the polynomial chaos expansion is proposed here in order to capture the behavior of such eigenvalues and eigenvectors. It is observed that for judiciously chos
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Le Bozec-Chiffoleau, Sulian, Charles Prud'homme, and Gilles Simonin. "Polynomial Time Presolve Algorithms for Rotation-Based Models Solving the Robust Stable Matching Problem." In Thirty-Third International Joint Conference on Artificial Intelligence {IJCAI-24}. International Joint Conferences on Artificial Intelligence Organization, 2024. http://dx.doi.org/10.24963/ijcai.2024/317.

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The Robust Stable Matching (RSM) problem involves finding a stable matching that allows getting another stable matching within a minimum number of changes when a pair becomes forbidden. It has been shown that such a problem is NP-Hard. In this paper, we enrich the mathematical model for the RSM problem based on new theoretical properties. We derive from these properties new polynomial time pre-solving algorithms which both reduce the search space and speed up the exploration. We also extend our results to the instances of the Many-to-Many problem and give its corresponding constraint programmi
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Reports on the topic "Enriched polynomial space"

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Horrocks, Ian, Ulrike Sattler, and Stephan Tobies. A Description Logic with Transitive and Converse Roles, Role Hierarchies and Qualifying Number Restrictions. Aachen University of Technology, 1999. http://dx.doi.org/10.25368/2022.94.

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As widely argued [HG97; Sat96], transitive roles play an important role in the adequate representation of aggregated objects: they allow these objects to be described by referring to their parts without specifying a level of decomposition. In [HG97], the Description Logic (DL) ALCHR+ is presented, which extends ALC with transitive roles and a role hierarchy. It is argued in [Sat98] that ALCHR+ is well-suited to the representation of aggregated objects in applications that require various part-whole relations to be distinguished, some of which are transitive. However, ALCHR+ allows neither the
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