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Journal articles on the topic 'Enriched polynomial space'

Author: Grafiati

Published: 7 September 2024

Last updated: 31 July 2025

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Zhang, Zhiwen, Xin Hu, Thomas Y. Hou, Guang Lin, and Mike Yan. "An Adaptive ANOVA-Based Data-Driven Stochastic Method for Elliptic PDEs with Random Coefficient." Communications in Computational Physics 16, no. 2 (2014): 571–98. http://dx.doi.org/10.4208/cicp.270913.020414a.

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AbstractIn this paper, we present an adaptive, analysis of variance (ANOVA)-based data-driven stochastic method (ANOVA-DSM) to study the stochastic partial differential equations (SPDEs) in the multi-query setting. Our new method integrates the advantages of both the adaptive ANOVA decomposition technique and the data-driven stochastic method. To handle high-dimensional stochastic problems, we investigate the use of adaptive ANOVA decomposition in the stochastic space as an effective dimension-reduction technique. To improve the slow convergence of the generalized polynomial chaos (gPC) method

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12

Khaleel, Mustafa Ibrahim, Mejdl Safran, Sultan Alfarhood, and Michelle Zhu. "A Hybrid Many-Objective Optimization Algorithm for Job Scheduling in Cloud Computing Based on Merge-and-Split Theory." Mathematics 11, no. 16 (2023): 3563. http://dx.doi.org/10.3390/math11163563.

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Scheduling jobs within a cloud environment is a critical area of research that necessitates meticulous analysis. It entails the challenge of optimally assigning jobs to various cloud servers, each with different capabilities, and is classified as a non-deterministic polynomial (NP) problem. Many conventional methods have been suggested to tackle this difficulty, but they often struggle to find nearly perfect solutions within a reasonable timeframe. As a result, researchers have turned to evolutionary algorithms to tackle this problem. However, relying on a single metaheuristic approach can be

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13

Herrmann, Christian. "On the complexity of equational decision problems for finite height complemented and orthocomplemented modular lattices." Algebra universalis 83, no. 1 (2021). http://dx.doi.org/10.1007/s00012-021-00760-3.

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AbstractWe study the computational complexity of the satisfiability problem and the complement of the equivalence problem for complemented (orthocomplemented) modular lattices L and classes thereof. Concerning a simple L of finite height, $$\mathcal {NP}$$ NP -hardness is shown for both problems. Moreover, both problems are shown to be polynomial-time equivalent to the same feasibility problem over the division ring D whenever L is the subspace lattice of a D-vector space of finite dimension at least 3. Considering the class of all finite dimensional Hilbert spaces, the equivalence problem for

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14

Solyaev, Yury, and Vasiliy Dobryanskiy. "Enriched C1 Finite Elements for Crack Problems in Simplified Strain Gradient Elasticity." International Journal for Numerical Methods in Engineering 126, no. 13 (2025). https://doi.org/10.1002/nme.70081.

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ABSTRACTWe present a new type of triangular finite element developed for plane strain crack problems within the framework of simplified strain gradient elasticity (SGE). The finite element space incorporates a conventional fifth‐degree polynomial interpolation originally developed for plate bending problems and later adopted for SGE. Enrichment is performed by adding near‐field analytic SGE solutions for crack problems, preserving continuity of interpolation at the mesh nodes. This allows us an accurate representation of strain and stress fields near the crack tip and enables direct calculatio

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15

Sherman, Alexander. "Ghost Distributions on Supersymmetric Spaces I: Koszul Induced Superspaces, Branching, and the Full Ghost Centre." Transformation Groups, October 7, 2024. http://dx.doi.org/10.1007/s00031-024-09878-9.

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AbstractGiven a Lie superalgebra $$\mathfrak {g}$$ g , Gorelik defined the anticentre $$\mathcal {A}$$ A of its enveloping algebra, which consists of certain elements that square to the center. We seek to generalize and enrich the anticentre to the context of supersymmetric pairs $$(\mathfrak {g},\mathfrak {k})$$ ( g , k ) , or more generally supersymmetric spaces G/K. We define certain invariant distributions on G/K, which we call ghost distributions, and which in some sense are induced from invariant distributions on $$G_0/K_0$$ G 0 / K 0 . Ghost distributions, and in particular their Harish

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16

Zhou, Yicheng, Zhenzhou Lu, Yan Shi, Changcong Zhou, and Wanying Yun. "Variational Bayesian inference-based polynomial chaos expansion: Application to time-variantreliability analysis." Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, October 26, 2021, 1748006X2110555. http://dx.doi.org/10.1177/1748006x211055534.

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In the time-variant systems, random variables, stochastic processes, and time parameter are regarded as the inputs of time-variant computational model. This results in an even more computationally expensive model what makes the time-variant reliability analysis a challenging task. This paper addresses the problem by presenting an active learning strategy using polynomial chaos expansion (PCE) in an augmented reliability space. We first propose a new algorithm that determines the sparse representation applying statistical threshold to determine the significant terms of the PCE model. This adapt

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17

Gomes, Lorena Leocádio, Felicio Bruzzi Barros, Samuel Silva Penna, and Roque Luiz da Silva Pitangueira. "Geometrically nonlinear analysis by the generalized finite element method." Engineering Computations ahead-of-print, ahead-of-print (2020). http://dx.doi.org/10.1108/ec-10-2019-0478.

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Purpose The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations. Design

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