Three-dimensional wave polynomials
TL;DR: In this article, a power series expansion technique was used to solve the three-dimensional homogeneous and finite body of a certain shape using wave polynomials and their derivatives in Cartesian, spherical, and cylindrical coordinate systems.
read more
Abstract: We demonstrate a specific power series expansion technique to
solve the three-dimensional homogeneous and
inhomogeneous wave equations. As solving functions, so-called wave
polynomials are used. The presented method is useful for a finite
body of certain shape. Recurrent formulas to improve efficiency
are obtained for the wave polynomials and their derivatives in a
Cartesian, spherical, and cylindrical coordinate system. Formulas
for a particular solution of the inhomogeneous wave equation are
derived. The accuracy of the method is discussed and some typical
examples are shown.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Solving nonlinear direct and inverse problems of stationary heat transfer by using Trefftz functions
TL;DR: In this paper, a nonlinear differential operator is resolved into a linear and nonlinear part, and the nonlinearity is treated as an inhomogeneity for the linear operator.
51
Direct and inverse heat transfer in non-contacting face seals
Slawomir Blasiak,Anna Pawinska +1 more
TL;DR: In this paper, the authors developed a mathematical model of a non-contacting face seal describing the phenomenon of heat transfer in the system: sealing rings -fluid film, which is used to separate the working agent from the external environment.
36
The usage of wave polynomials in solving direct and inverse problems for two-dimensional wave equation
TL;DR: In this paper, a wave polynomials (Trefftz functions for wave equation) were used to obtain an approximate solution of the direct and inverse problems for two-dimensional wave equation (two space variables and time).
26
Solution of the direct and inverse problems for beam
Artur Maciag,Anna Pawinska +1 more
TL;DR: In this paper, an approximate method of solving direct and inverse problems described by Bernoulli-Euler inhomogeneous equation of vibrations of a beam is presented, where a semianalytical solution is approximated by a linear combination of the Trefftz functions (T-functions, solving functions).
Solving Direct and Inverse Thermoelasticity Problems by Means of Trefftz Base Functions for Finite Element Method
Krzysztof Grysa,Artur Macia¸g +1 more
TL;DR: In this paper, the authors presented the application of the Trefftz functions method to solving direct and inverse problems of elasticity and thermoelasticity, where the system of equations for displacements is reduced to a system of wave equations.
16
References
Trefftz method: Fitting boundary conditions
A. P. Zieliński,Ismael Herrera +1 more
TL;DR: In this paper, the convergence of the Collatz error measures and the conditioning of the solution matrices are investigated in detail, and various ways of fitting the boundary conditions in the T-complete functions method are presented.
121
Solution of the two-dimensional wave equation by using wave polynomials
Artur Macig,Jörg Wauer +1 more
TL;DR: In this paper, a power-series-expansion technique was used to solve approximately the two-dimensional wave equation, where wave polynomials were used as solving functions.
Heat polynomials method in solving the direct and inverse heat conduction problems in a cylindrical system of coordinates
Sylwia Futakiewicz,L. Hozejowski +1 more
- 01 Jan 1998
TL;DR: In this paper, heat polynomials in a cylindrical and polar coordinate system were used to solve direct and inverse problems of heat conduction in a cylinder, and numerical results were presented and discussed.
11