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Articoli di riviste sul tema "Trefftz functions"

Autore: Grafiati

Pubblicato: 3 giugno 2025

Ultima modifica: 31 luglio 2025

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1

Borkowska, Dorota. "Application of Trefftz method for the solution of two-dimensional Poisson’s problem taking into account material properties." AUTOBUSY – Technika, Eksploatacja, Systemy Transportowe 19, no. 6 (2018): 363–67. http://dx.doi.org/10.24136/atest.2018.094.

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The aim of this paper is theoretical and numerical analysis of one of the nonsingular Trefftz method. Two-dimensional boundary value problem governed by Poisson’s equation is taken as the example. Domain boundary equation is obtained by transformation of classical formulation of the boundary problem with the use of weighted residual method. In this paper the original variation formulation is considered. The solution of the problem is assumed as the superposition of Trefftz functions, which satisfy Laplace’s equation. Taking the same functions as the weighting functions one obtains equations of

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2

Ku, Cheng-Yu, Chih-Yu Liu, Jing-En Xiao, Wei-Po Huang, and Yan Su. "A spacetime collocation Trefftz method for solving the inverse heat conduction problem." Advances in Mechanical Engineering 11, no. 7 (2019): 168781401986127. http://dx.doi.org/10.1177/1687814019861271.

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In this article, a novel spacetime collocation Trefftz method for solving the inverse heat conduction problem is presented. This pioneering work is based on the spacetime collocation Trefftz method; the method operates by collocating the boundary points in the spacetime coordinate system. In the spacetime domain, the initial and boundary conditions are both regarded as boundary conditions on the spacetime domain boundary. We may therefore rewrite an initial value problem (such as a heat conduction problem) as a boundary value problem. Hence, the spacetime collocation Trefftz method is adopted

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3

Wang, Ke Yong. "A Four-Node Hybrid-Trefftz Plane Elasticity Element with Fundamental Analytical Solutions." Advanced Materials Research 279 (July 2011): 194–99. http://dx.doi.org/10.4028/www.scientific.net/amr.279.194.

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A new four-node hybrid-Trefftz element is developed for plane elasticity problems. From the Airy stress function, the fundamental analytical solutions of the governing equation are derived as Trefftz functions for the intra-element (Trefftz) displacement field. Together with an independent frame displacement field along the element boundary, the element formulation is then constructed following the modified variational functional. Several numerical examples indicate that the proposed element exhibits good performance.

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4

Rjasanow, Sergej, and Steffen Weißer. "FEM with Trefftz trial functions on polyhedral elements." Journal of Computational and Applied Mathematics 263 (June 2014): 202–17. http://dx.doi.org/10.1016/j.cam.2013.12.023.

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5

Piasecka, Magdalena, Sylwia Hożejowska, Beata Maciejewska, and Anna Pawińska. "Time-Dependent Heat Transfer Calculations with Trefftz and Picard Methods for Flow Boiling in a Mini-Channel Heat Sink." Energies 14, no. 7 (2021): 1832. http://dx.doi.org/10.3390/en14071832.

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The intensification of heat transfer using two-phase boiling flow in mini-channels is widely used to dissipate the high heat fluxes in miniaturized electronic devices. However, the process itself is not fully recognized and still requires experimental studies and developing computation methods appropriate for them. The main aim of this work was the mathematical modeling of time-dependent heat transfer process in FC-72 flow boiling in a mini-channel heat sink with five parallel mini-channels of 1 mm depth. Channels have an asymmetrically heated wall while its outer temperature was measured by i

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6

REZAIEE-PAJAND, MOHAMMAD, MAJID YAGHOOBI, and MOHAMMAD KARKON. "HYBRID TREFFTZ FORMULATION FOR THIN PLATE ANALYSIS." International Journal of Computational Methods 09, no. 04 (2012): 1250053. http://dx.doi.org/10.1142/s0219876212500533.

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In this paper, two efficient elements are proposed by utilizing hybrid Trefftz method for the analysis of thin plate bending. The triangular element, THT, and the quadrilateral element, QHT, which have 9 and 12 degrees of freedom, respectively. Two independent displacement fields are defined for internal and boundary of the elements. The internal field is selected in such a way that it satisfies the governing equation of the thin plate. Boundary field is dependent on the nodal degrees of freedom via boundary interpolation functions. For deriving boundary interpolation functions, element's edge

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7

Frąckowiak, Andrzej, Agnieszka Wróblewska, and Michał Ciałkowski. "Trefftz numerical functions for solving inverse heat conduction problems." International Journal of Thermal Sciences 177 (July 2022): 107566. http://dx.doi.org/10.1016/j.ijthermalsci.2022.107566.

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8

Kompiš, Vladimı́r, Milan Toma, Milan Žmindák, and Marián Handrik. "Use of Trefftz functions in non-linear BEM/FEM." Computers & Structures 82, no. 27 (2004): 2351–60. http://dx.doi.org/10.1016/j.compstruc.2004.04.006.

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9

Zieliński, A. P. "On trial functions applied in the generalized Trefftz method." Advances in Engineering Software 24, no. 1-3 (1995): 147–55. http://dx.doi.org/10.1016/0965-9978(95)00066-6.

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10

Hochard, Ch, and L. Proslier. "A simplified analysis of plate structures using Trefftz-functions." International Journal for Numerical Methods in Engineering 34, no. 1 (1992): 179–95. http://dx.doi.org/10.1002/nme.1620340111.

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11

Kita, E., Y. Kataoka, and N. Kamiya. "First- and Second-Order Design Sensitivity Analysis Scheme Based on Trefftz Method." Journal of Mechanical Design 121, no. 1 (1999): 84–91. http://dx.doi.org/10.1115/1.2829434.

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This paper presents a new scheme for the first- and second-order design sensitivity analysis of the two-dimensional elastic problem by using Trefftz method. In the Trefftz method, the physical quantities are approximated by superposition of regular T-complete functions. Therefore, direct differentiation of the approximate expressions with respect to design parameters leads to the regular expressions of the sensitivities. The present schemes are applied to some examples in order to confirm the validity.

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12

Ku, Cheng-Yu, Chih-Yu Liu, Jing-En Xiao, Weichung Yeih, and Chia-Ming Fan. "A Spacetime Meshless Method for Modeling Subsurface Flow with a Transient Moving Boundary." Water 11, no. 12 (2019): 2595. http://dx.doi.org/10.3390/w11122595.

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In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the moving boundary is previously unknown. We solve the subsurface flow problems based on the Trefftz method, in which the Trefftz basis functions are obtained from the general solutions using the separation of variables. The solutions of the governing equation are then approximated numerically by the supe

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13

Mascotto, Lorenzo, Ilaria Perugia, and Alexander Pichler. "A nonconforming Trefftz virtual element method for the Helmholtz problem." Mathematical Models and Methods in Applied Sciences 29, no. 09 (2019): 1619–56. http://dx.doi.org/10.1142/s0218202519500301.

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We introduce a novel virtual element method (VEM) for the two-dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefftz functions, i.e. functions belonging to the kernel of the Helmholtz operator. The global trial and test spaces are not fully discontinuous, but rather interelement continuity is imposed in a nonconforming fashion. Although their functions are only implicitly defined, as typical of the VEM framework, they contain discontinuous subspaces made of functions known in closed form and with good approximation properties (pl

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14

Hożejowska, Sylwia, Robert Kaniowski, and Mieczysùaw E. Poniewski. "Application of adjustment calculus to the Trefftz method for calculating temperature field of the boiling liquid flowing in a minichannel." International Journal of Numerical Methods for Heat & Fluid Flow 24, no. 4 (2014): 811–24. http://dx.doi.org/10.1108/hff-01-2013-0022.

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Purpose – The purpose of this paper is to focus on the application of the Trefftz method to the calculation of the two-dimensional (2D) temperature field in the boiling refrigerant flow through an asymmetrically heated vertical minichannel with a rectangular cross-section. The considerations were limited to determining the temperature of the continuous phase – liquid for bubbly and bubbly-slug flow. The numerical solution found with the Trefftz methods was compared with the simplified solution. For nucleate boiling, heat transfer coefficient at the heating foil – liquid contact was determined.

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15

Reutskiy, S. "A boundary method of Trefftz type with approximate trial functions." Engineering Analysis with Boundary Elements 26, no. 4 (2002): 341–53. http://dx.doi.org/10.1016/s0955-7997(02)00006-1.

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16

Hożejowska, Sylwia, Magdalena Piasecka, and Artur Piasecki. "Development of a two-dimensional mathematical model of flow boiling heat transfer in micro- and minichannels." EPJ Web of Conferences 269 (2022): 01021. http://dx.doi.org/10.1051/epjconf/202226901021.

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The paper concerns flow boiling heat transfer in micro- and minichannels. In the mathematical model, the steady state heat transfer process in a single asymmetrically heated minichannel was considered. Calculations with the use of Trefftz functions were based on the data from own experiments. The temperature of the heater and the refrigerant were assumed to satisfy the Laplace equations and the energy equation respectively. The problem was solved by the Trefftz method using two sets of Trefftz functions. The known heater and refrigerant temperature distributions were used to determine the heat

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17

Qin, Qing-Hua. "Trefftz Finite Element Method and Its Applications." Applied Mechanics Reviews 58, no. 5 (2005): 316–37. http://dx.doi.org/10.1115/1.1995716.

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This paper presents an overview of the Trefftz finite element and its application in various engineering problems. Basic concepts of the Trefftz method are discussed, such as T-complete functions, special purpose elements, modified variational functionals, rank conditions, intraelement fields, and frame fields. The hybrid-Trefftz finite element formulation and numerical solutions of potential flow problems, plane elasticity, linear thin and thick plate bending, transient heat conduction, and geometrically nonlinear plate bending are described. Formulations for all cases are derived by means of

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18

Shang, Yan, Song Cen, and Wengen Ouyan. "New hybrid-Trefftz Mindlin–Reissner plate elements for efficiently modeling the edge zones near free/SS1 edges." Engineering Computations 35, no. 1 (2018): 136–56. http://dx.doi.org/10.1108/ec-04-2017-0123.

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Purpose The purpose of this paper is to propose a new finite element method (FEM) solving strategy for efficient analysis of the challenging edge effect problem in plate structures. Its main ideas are to develop special-purpose plate element models to effectively simulate the behaviors in the plate’s edge zones near free/SS1 edges. Design/methodology/approach These new elements are developed based on the hybrid-Trefftz element method. During their construction procedures, the analytical solutions of the edge effect problem, which are in exponential forms, are used to enhance the interior displ

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19

Liu, Chein-Shan. "Solving singular convection–diffusion equation by exponentially-fitted trial functions and adjoint Trefftz test functions." Journal of King Saud University - Science 30, no. 1 (2018): 100–105. http://dx.doi.org/10.1016/j.jksus.2016.09.011.

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20

HARARI, ISAAC, PARAMA BARAI, PAUL E. BARBONE, and MICHAEL SLAVUTIN. "THREE-DIMENSIONAL INFINITE ELEMENTS BASED ON A TREFFTZ FORMULATION." Journal of Computational Acoustics 09, no. 02 (2001): 381–94. http://dx.doi.org/10.1142/s0218396x01000577.

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Three-dimensional infinite elements for exterior problems of time-harmonic acoustics are developed. The infinite elements mesh only the outer boundary of the finite element domain and need not match the finite elements on the interface. A four-noded infinite element, based on separation of variables in spherical coordinates, is presented. Singular behavior of associated Legendre functions at the poles is circumvented. Numerical results validate the good performance of this approach.

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21

Ho ejowska, Sylwia. "Determining 2D temperature field in flow boiling with the use of Trefftz functions." EPJ Web of Conferences 213 (2019): 02026. http://dx.doi.org/10.1051/epjconf/201921302026.

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The paper proposes the use of Trefftz method to solve the triple coupled heat conduction problem in flow boiling of refrigerant in an asymmetrically heated minichannel. A mathematical model of heat transfer in a rectangular minichannel is suggested. Two sets of Trefftz functions were used to determine 2D temperature fields at a fluid flow in the minichannel tilted at a known angle. The procedure for the calculation of the liquid temperature was coupled with the process of determining temperature fields in two adjacent elements of the experimental stand with the minichannel, i.e. in the glass p

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22

Maciąg, Artur, and Krzysztof Grysa. "Trefftz Method of Solving a 1D Coupled Thermoelasticity Problem for One- and Two-Layered Media." Energies 14, no. 12 (2021): 3637. http://dx.doi.org/10.3390/en14123637.

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This paper discusses a 1D one-dimensional mathematical model for the thermoelasticity problem in a two-layer plate. Basic equations in dimensionless form contain both temperature and displacement. General solutions of homogeneous equations (displacement and temperature equations) are assumed to be a linear combination of Trefftz functions. Particular solutions of these equations are then expressed with appropriately constructed sums of derivatives of general solutions. Next, the inverse operators to those appearing in homogeneous equations are defined and applied to the right-hand sides of inh

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23

Piasecka, Magdalena, Kinga Strąk, and Beata Maciejewska. "The flow boiling heat transfer coefficient determination in a minichannel used the FEM combined with Trefftz functions." MATEC Web of Conferences 240 (2018): 01033. http://dx.doi.org/10.1051/matecconf/201824001033.

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The method of solving the inverse heat conduction problem, by means of the FEM with Trefftz-type basis functions, during flow boiling in a minichannel was shown. This basis functions were constructed with using the Hermite interpolation and Trefftz functions. The aim of the numerical calculations was to determine the local heat transfer coefficient on the basis of experimental data in a horizontally oriented minichannel. The refrigerant flowing along the minichannel (HFE-649 or HFE-7100) was heated by a thin enhanced plate by vibration-assisted laser texturing. The temperature on an outer smoo

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24

Pernet, Sebastien, Margot Sirdey, and Sebastien Tordeux. "Ultra-weak variational formulation for heterogeneous Maxwell problem in the context of high performance computing." ESAIM: Proceedings and Surveys 75 (December 2023): 96–121. http://dx.doi.org/10.1051/proc/202375096.

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Electromagnetic simulations on large domains require a huge memory consumption. Domain decomposition methods, based on Trefftz methods, could be an answer to this issue. In this paper, we associate to heterogeneous three-dimensional Maxwell equations one variational formulation which can be obtained either by upwind fluxes or Riemann traces. We associate to this variational formulation an iterative Trefftz Krylov solver. The poor conditioning due to the use of plane wave basis functions is bypassed thanks to a compression strategy. Moreover, the developed iterative solver is accelerated thanks

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25

Ku, Cheng-Yu, Chih-Yu Liu, Yan Su, Luxi Yang, and Wei-Po Huang. "Modeling Tide–Induced Groundwater Response in a Coastal Confined Aquifer Using the Spacetime Collocation Approach." Applied Sciences 10, no. 2 (2020): 439. http://dx.doi.org/10.3390/app10020439.

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This paper presents the modeling of tide–induced groundwater response using the spacetime collocation approach (SCA). The newly developed SCA begins with the consideration of Trefftz basis functions which are general solutions of the governing equation deriving from the separation of variables. The solution of the groundwater response in a coastal confined aquifer with an estuary boundary where the phase and amplitude of tide can vary with time and position is then approximated by the linear combination of Trefftz basis functions using the superposition theorem. The SCA is validated for severa

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26

Ku, Cheng-Yu, Li-Dan Hong, and Chih-Yu Liu. "Solving Transient Groundwater Inverse Problems Using Space–Time Collocation Trefftz Method." Water 12, no. 12 (2020): 3580. http://dx.doi.org/10.3390/w12123580.

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This paper presents a space–time meshfree method for solving transient inverse problems in subsurface flow. Based on the transient groundwater equation, we derived the Trefftz basis functions utilizing the method of separation of variables. Due to the basis functions completely satisfying the equation to be solved, collocation points are placed on the space–time boundaries. Numerical solutions are approximated based on the superposition theorem. Accordingly, the initial and boundary conditions are both regarded as space–time boundary conditions. Forward and inverse examples are conducted to va

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27

Mierzwiczak, Magdalena, Agnieszka Fraska, and Jakub K. Grabski. "Determination of the Slip Constant in the Beavers-Joseph Experiment for Laminar Fluid Flow through Porous Media Using a Meshless Method." Mathematical Problems in Engineering 2019 (April 8, 2019): 1–12. http://dx.doi.org/10.1155/2019/1494215.

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In the paper, a numerical simulation of the Beavers-Joseph experiment is presented. The simulation is based on a meshless method which is called the Trefftz method with the special purpose Trefftz functions. The porous medium is modeled as a regular array of fibers. Three kinds of arrays are taken under consideration: triangular, square, and hexagonal. Firstly, the permeability of the fibrous porous medium is determined by consideration of flow between an infinite array of fibers. In the next step the considered region is divided into two parts. The first half of the channel is a porous medium

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28

Stojek, Małgorzata. "Computation of Exterior Acoustics Problems in Two Dimensions by Trefftz-Type Finite Elements." Applied Mechanics and Materials 712 (January 2015): 17–22. http://dx.doi.org/10.4028/www.scientific.net/amm.712.17.

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The paper deals with the application of the so-called T-type finite elements [1] to the calculation of the exterior acoustic problems in two dimensions. The method is based on the use of asuitably truncated T-complete set of Trefftz functions over individual subdomains linked by means ofa least square procedure. The vertex singularities and the Sommerfeld radiation condition are readilyincorporated in the trial functions. In order to show the performance of the approach two examples ofcomputations for infinite cylinders (of circular and square cross section) are presented and comparedwith thos

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29

Sokała, Małgorzata. "Solutions of Two-Dimensional Wave Equation using some Form of the Trefftz Functions." Computational Methods in Science and Technology 14, no. 2 (2008): 111–22. http://dx.doi.org/10.12921/cmst.2008.14.02.111-122.

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Szybiński, B., and A. P. Zieliński. "Alternative T-complete systems of shape functions applied in analytical Trefftz finite elements." Numerical Methods for Partial Differential Equations 11, no. 4 (1995): 375–88. http://dx.doi.org/10.1002/num.1690110406.

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Ku, Cheng-Yu, Jing-En Xiao, and Chih-Yu Liu. "On Solving Nonlinear Moving Boundary Problems with Heterogeneity Using the Collocation Meshless Method." Water 11, no. 4 (2019): 835. http://dx.doi.org/10.3390/w11040835.

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In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary conditions. We adopt the collocation Trefftz method (CTM) to approximate the solution using Trefftz base functions, satisfying the Laplace equation. An iterative scheme in conjunction with the CTM for finding the phreatic line with over–specified nonlinear moving boundary conditions is developed. To deal with flow in the layered heterogeneous soil, the

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32

Chen, Lin, Wenzhi Xu, and Zhuojia Fu. "A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation." Mathematics 10, no. 6 (2022): 897. http://dx.doi.org/10.3390/math10060897.

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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. Unlike the traditional time discretization strategies, the proposed numerical scheme introduces the spatial–temporal radial Trefftz functions (STRTFs) as the basis functions for the spatial and temporal discretization of the transient wave equations. The STRTFs are constructed in the spatial–temporal domain, which is a combination of 3D Euclidean space and time into a 4D manifold. Mor

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Maciejewska, Beata, and Magdalena Piasecka. "Time-dependent study of boiling heat transfer coefficient in a vertical minichannel." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (2019): 2953–69. http://dx.doi.org/10.1108/hff-12-2018-0781.

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Purpose The purpose of this paper is to determine the time-dependent heat transfer coefficient during FC-72 flow boiling in a 1.7-mm-deep vertical and asymmetrically heated minichannel. Design/methodology/approach The temperature of the minichannel heated wall was recorded continuously with the use of thermocouples. The heat transfer coefficients for the subcooled and saturated boiling regions at the heated wall–fluid contact surface were calculated from the Robin boundary condition. Both the wall and fluid temperatures were obtained from the solution of the inverse nonstationary problems in t

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Faltinsen, Odd M., and Alexander N. Timokha. "On sloshing modes in a circular tank." Journal of Fluid Mechanics 695 (February 16, 2012): 467–77. http://dx.doi.org/10.1017/jfm.2012.38.

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AbstractEmploying the multipole-type functions given by Faltinsen & Timokha (J. Fluid Mech., vol. 665, 2010, pp. 457–479), we derive a Trefftz-type representation of the velocity potential for the liquid sloshing problem in a two-dimensional circular tank. This representation defines a continuation of the velocity potential into the ‘air’ area confined by the ‘dry’ tank surface. Its usage facilitates an effective approximation of the natural sloshing modes for all tank fillings.

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Grysa, Krzysztof, Artur Maciag, and Anna Pawinska. "Solving nonlinear direct and inverse problems of stationary heat transfer by using Trefftz functions." International Journal of Heat and Mass Transfer 55, no. 23-24 (2012): 7336–40. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.072.

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Cheung, Y. K., W. G. Jin, and O. C. Zienkiewicz. "Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions." Communications in Applied Numerical Methods 5, no. 3 (1989): 159–69. http://dx.doi.org/10.1002/cnm.1630050304.

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Piasecka, Magdalena, and Beata Maciejewska. "Application of the finite element method to the determining of boiling heat transfer coefficient for minichannel flow." Archives of Thermodynamics 34, no. 1 (2013): 55–69. http://dx.doi.org/10.2478/aoter-2013-0004.

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Abstract Miniature heat exchangers are used to provide higher cooling capacity for new technologies. This means a reduction in their size and cost but the identical power. The paper presents the method for determination of boiling heat transfer coefficient for a rectangular minichannel of 0.1 mm depth, 40 mm width and 360 mm length with asymmetric heating. Experimental research has focused on the transition from single phase forced convection to nucleate boiling, i.e., the zone of boiling incipience. The ‘boiling front’ location has been determined from the temperature distribution of the heat

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Galybin, A. N., and J. Irša. "On reconstruction of three-dimensional harmonic functions from discrete data." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, no. 2119 (2010): 1935–55. http://dx.doi.org/10.1098/rspa.2009.0471.

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This study presents an approach for reconstruction of harmonic functions in three dimensions from the finite number of field and surface measurements. The approach, based on the Trefftz method, performs reconstruction as the best fit to the data and provides smoothness of the reconstructed function. Two particular algorithms are proposed; the first one uses specific radial basis functions and the second one is of finite element type. Either of them can be applied to analyse different data types but the latter can handle larger problems. The data types considered in this study also cover direct

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Žmindák, Milan, Zoran Pelagić, and Martin Dudinsky. "MFS Heat Conduction Modeling of Composite Materials Reinforced by CNT-Fibers with Large Aspect Ratio." Applied Mechanics and Materials 420 (September 2013): 202–8. http://dx.doi.org/10.4028/www.scientific.net/amm.420.202.

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Carbon Nanotube (CNT) fibers, which are used to reinforce composite materials areoften associated within the aspect ratio values 103:1-106:1, sometimes even larger. The Method of Continuous Source Functions (MCSF) used for simulating fiber-matrix and fiber-fiber interaction uses 1D continuous source functions which are distributed along the fiber. The source functions serve as Trefftz (T-) functions, which can satisfy the governing equations which are inside the composite domain (composite matrix) and the boundary conditions on the fiber-matrix interfaces are satisfied through the collocation

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Grysa, Krzysztof, and Artur Maciag. "Trefftz method in solving the pennes’ and single-phase-lag heat conduction problems with perfusion in the skin." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 6 (2019): 3231–46. http://dx.doi.org/10.1108/hff-09-2018-0488.

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Purpose The purpose of this paper is to derive the Trefftz functions (T-functions) for the Pennes’ equation and for the single-phase-lag (SPL) model (hyperbolic equation) with perfusion and then comparing field of temperature in a flat slab made of skin in the case when perfusion is taken into account, with the situation when a Fourier model is considered. When considering the process of heat conduction in the skin, one needs to take into account the average values of its thermal properties. When in biological bodies relaxation time is of the order of 20 s, the thermal wave propagation appears

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Pawinska, Anna, and Sławomir Blasiak. "Temperature Identification in the Structural Elements of Non-Contacting Face Seals by Using Trefftz Functions." Transactions of the VŠB - Technical University of Ostrava, Mechanical Series 60, no. 2 (2014): 51–55. http://dx.doi.org/10.22223/tr.2014-2/1989.

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42

Imbert-Gerard, Lise-Marie. "Amplitude-based Generalized Plane Waves: New Quasi-Trefftz Functions for Scalar Equations in two dimensions." SIAM Journal on Numerical Analysis 59, no. 3 (2021): 1663–86. http://dx.doi.org/10.1137/20m136791x.

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43

Maciejewska, Beata, and Magdalena Piasecka. "A numerical solution to an inverse unsteady-state heat transfer problem involving the Trefftz functions." EPJ Web of Conferences 143 (2017): 02069. http://dx.doi.org/10.1051/epjconf/201714302069.

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44

Weißer, Steffen. "Arbitrary order Trefftz-like basis functions on polygonal meshes and realization in BEM-based FEM." Computers & Mathematics with Applications 67, no. 7 (2014): 1390–406. http://dx.doi.org/10.1016/j.camwa.2014.01.019.

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45

Hennuyer, C., N. Leconte, B. Langrand, and E. Markiewicz. "Interpolation functions of a hybrid-Trefftz perforated super-element featuring nodes on the hole boundary." Finite Elements in Analysis and Design 91 (November 2014): 40–47. http://dx.doi.org/10.1016/j.finel.2014.07.008.

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46

Maciejewska, Beata, Magdalena Piasecka, and Paweł Łabędzki. "Transient Subcooled Boiling in Minichannels: Experimental Study and Numerical Modelling Using Trefftz Functions and ADINA." Energies 18, no. 14 (2025): 3865. https://doi.org/10.3390/en18143865.

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Abstract (sommario):

This study focuses on the phenomenon of boiling heat transfer during fluid flow (Fluorinert FC-72) in minichannels. The research stand was built around a specially designed test section incorporating sets of aligned minichannels, each 1 mm deep. These channel arrays varied in number, comprising configurations with 7, 15, 17, 19, 21, and 25 parallel channels. The test section was vertically orientated with upward fluid flow. To address the heat transfer problem associated with transient flow boiling, two numerical approaches grounded in the finite element method (FEM) were employed. One used th

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47

Žmindák, Milan, Martin Dudinsky, and Zoran Pelagić. "Micro-Mechanical Analysis of Composites Reinforced with Discontinuous Fibers with Large Aspect Ratio." Applied Mechanics and Materials 420 (September 2013): 269–75. http://dx.doi.org/10.4028/www.scientific.net/amm.420.269.

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Abstract (sommario):

Properties of fiber composites reinforced with fibers greatly depend on the choice of fiber and matrix. Their mechanical properties and geometry influence the stress state in composite. In this paper the Method of Continuous Source Functions (MCSF) employing Trefftz Radial Basis Functions (TRBF) is presented. This method does not require any mesh. The focus will be given to the application of TRBF in form of dipoles to the simulation of composites reinforced with fibers of finite length with large aspect ratio. In presented example as well as in other linear problems, only nodes on the domain

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48

Liu, Chein-Shan, Zhuojia Fu, and Chung-Lun Kuo. "Multi-Dimensional Analytic Functions for Laplace Equations and Generalized Cauchy–Riemann Equations." Mathematics 13, no. 8 (2025): 1246. https://doi.org/10.3390/math13081246.

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Abstract (sommario):

A new concept of projective solution is introduced for the multi-dimensional Laplace equations. We project the field point onto a characteristic vector to obtain a projective variable, which can be used to reduce the Laplace equations to a second-order ordinary differential equation with only a leading term multiplied by the squared norm of the characteristic vector. The projective solutions involve characteristic vectors as parameters, which must be complex numbers to satisfy a null equation. Since the projective variable is a complex variable, we can construct the analytic function based on

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49

Maciag, Artur, and Anna Pawinska. "The solution of nonlinear direct and inverse problems for beam by means of the Trefftz functions." European Journal of Mechanics - A/Solids 92 (March 2022): 104476. http://dx.doi.org/10.1016/j.euromechsol.2021.104476.

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50

Liu, Chein-Shan. "A BIEM using the Trefftz test functions for solving the inverse Cauchy and source recovery problems." Engineering Analysis with Boundary Elements 62 (January 2016): 177–85. http://dx.doi.org/10.1016/j.enganabound.2015.10.004.

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