Results 51 to 60 of about 198 (145)
Sparsity comparison of polytopal finite element methods
Proceedings in Applied Mathematics and Mechanics, Volume 24, Issue 3, October 2024.Abstract In this work we compare crucial parameters for efficiency of different finite element methods for solving partial differential equations on polytopal meshes. We consider the virtual element method (VEM) and different discontinuous Galerkin (DG) methods, namely, the Hybrid DG and Trefftz DG methods.
Christoph Lehrenfeld +2 more
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Mathematics, 2022 In this paper, a novel semi-analytical collocation solver, the spatial–temporal radial Trefftz collocation method (STRTCM) is proposed to solve 3D transient wave equations with specified sound source excitations.
Lin Chen, Wenzhi Xu, Zhuojia Fu
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Projective Solutions Methods Automatically Satisfying the Stokes, Oseen and Brinkman Equations
MathematicsThe new projective solutions methods (PSMs) for solving the Stokes, Oseen, and Brinkman flow problems are presented in this paper. They automatically satisfy the governing equations and are therefore Trefftz-type methods.
Chein-Shan Liu +2 more
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Effectiveness of the Trefftz method in different engineering optimization procedures
Computer Assisted Methods in Engineering and Science, 2023 In a large class of linear, mathematically modelled engineering problems the Trefftz algorithms give accurate solutions in a relatively short computational time.
Andrzej P. Zieliński +2 more
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Trefftz spectral method for initial-boundary problems
Computer Assisted Methods in Engineering and Science, 2023 We describe a new Quasi Trefftz-type Spectral Method (QTSM) for solving boundary value and initial value problems. QTSM combines the properties of the Trefftz method with the spectral approach.
Sergei Lifits +2 more
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Structural inverse problems solved by the T -element approach
Computer Assisted Methods in Engineering and Science, 2022 Any direct boundary-value problem is defined in a certain area Ω by a system of differential equations and respective set of boundary conditions. In structural inverse problems the above conditions can be partly unknown.
Adam Wróblewski, Andrzej P. Zieliński
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Solving thermoelasticity problems by means of Trefftz functions
Computer Assisted Methods in Engineering and Science, 2017 The paper presents a new method of approximate solving of the two- and three-dimensional thermoelasticity problems in a finite body. The method presented here can be used for solving direct and inverse problems as well.
A. Maciąg
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A numerical solution to an inverse unsteady-state heat transfer problem involving the Trefftz functions [PDF]
EPJ Web of Conferences, 2017 This paper shows the results concerning flow boiling heat transfer in an asymmetrically heated vertical minichannel. The heated element for FC-72 Fluorinert flowing in that minichannel was a thin foil. The foil surface temperature was monitored continuously at 18 points by K-type thermocouples from the outer foil surface. Fluid temperature and pressure
Maciejewska Beata, Piasecka Magdalena
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2D wave polynomials as base functions in modified FEM
Computer Assisted Methods in Engineering and Science, 2022 The paper presents solutions of a two-dimensional wave equation by using Trefftz functions. Two ways of obtaining different forms of these functions are shown.
Artur Maciąg +2 more
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Amplitude-based Generalized Plane Waves: new Quasi-Trefftz functions for scalar equations in 2D
CoRR, 2020 Generalized Plane Waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisfy the Trefftz property, i.e. they are not exact solutions to the governing equation, they instead satisfy a quasi-Trefftz property: they are only approximate solutions.
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