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Related papers: Enhancing SfePy with Isogeometric Analysis

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In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel…

Numerical Analysis · Mathematics 2025-06-19 Gareth Hardwick , Senwei Liang , Haizhao Yang

In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…

Numerical Analysis · Mathematics 2025-05-06 Tianlong He , Philippe Karamian-Surville , Daniel Choï

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence…

Numerical Analysis · Mathematics 2021-03-23 Fleurianne Bertrand , Daniele Boffi , Gonzalo G. de Diego

The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…

Numerical Analysis · Mathematics 2023-11-27 Alireza Daneshyar , Stefan Kollmannsberger

In this paper we analyze a space-time unfitted finite element method for the discretization of scalar surface partial differential equations on evolving surfaces. For higher order approximations of the evolving surface we use the technique…

Numerical Analysis · Mathematics 2024-11-26 Arnold Reusken , Hauke Sass

We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…

Numerical Analysis · Mathematics 2023-01-25 Jennifer E. Fromm , Nils Wunsch , Ru Xiang , Han Zhao , Kurt Maute , John A. Evans , David Kamensky

We study the spectral approximation properties of isogeometric analysis with local continuity reduction of the basis. Such continuity reduction results in a reduction in the interconnection between the degrees of freedom of the mesh, which…

Numerical Analysis · Mathematics 2018-12-27 Vladimir Puzyrev , Quanling Deng , Victor Calo

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite…

Computational Engineering, Finance, and Science · Computer Science 2017-09-19 Zeger Bontinck , Jacopo Corno , Herbert De Gersem , Stefan Kurz , Andreas Pels , Sebastian Schöps , Felix Wolf , Carlo de Falco , Jürgen Dölz , Rafael Vázquez , Ulrich Römer

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…

Numerical Analysis · Mathematics 2020-07-24 Mehdi Elasmi , Christoph Erath , Stefan Kurz

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…

Numerical Analysis · Mathematics 2019-12-12 Stefano Berrone , Andrea Borio , Alessandro D'Auria

The scaled boundary finite element method (SBFEM) is a semi-analytical computational scheme, which is based on the characteristics of the finite element method (FEM) and combines the advantages of the boundary element method (BEM). This…

Numerical Analysis · Mathematics 2024-10-22 Yang Yang , Zongliang Zhang , Yelin Feng

We extend the softFEM idea to isogeometric analysis (IGA) to reduce the stiffness (consequently, the condition numbers) of the IGA discretized problem. We refer to the resulting approximation technique as softIGA. We obtain the resulting…

Numerical Analysis · Mathematics 2022-11-09 Quanling Deng , Pouria Behnoudfar , Victor M. Calo

In this paper the isogeometric Nystr\"om method is presented. It's outstanding features are: it allows the analysis of domains described by many different geometrical mapping methods in computer aided geometric design and it requires only…

Numerical Analysis · Computer Science 2015-06-15 Jürgen Zechner , Benjamin Marussig , Gernot Beer , Thomas-Peter Fries

In this paper, a symmetrized two-scale finite element method is proposed for a class of partial differential equations with symmetric solutions. With this method, the finite element approximation on a fine tensor product grid is reduced to…

Numerical Analysis · Mathematics 2022-06-01 Pengyu Hou , Fang Liu , Aihui Zhou

Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…

Numerical Analysis · Mathematics 2024-02-27 Jennifer E. Fromm , Nils Wunsch , Kurt Maute , John A. Evans , Jiun-Shyan Chen

The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions,…

Numerical Analysis · Mathematics 2021-04-07 Karolinne O. Coelho , Philippe R. B. Devloo , Sonia M. Gomes

Isogeometric Analysis (IGA) is a computational technique for the numerical approximation of partial differential equations (PDEs). This technique is based on the use of spline-type basis functions, that are able to hold a global smoothness…

Numerical Analysis · Mathematics 2020-09-04 Álvaro Pé de la Riva , Carmen Rodrigo , Francisco J. Gaspar

The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…

Numerical Analysis · Mathematics 2018-08-03 Christoph Lehrenfeld , Maxim A. Olshanskii

This paper presents a novel approach for solving fourth-order phase-field models in brittle fracture mechanics using the Interior Penalty Finite Element Method (IP-FEM). The fourth-order model improves numerical stability and accuracy…

Numerical Analysis · Mathematics 2025-04-15 Tian Tian , Chen Chunyu , Wei Huayi

The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…

Numerical Analysis · Mathematics 2025-02-06 Victor Dominguez , Alejandro Duque