Effectiveness of nonsingular solutions of the boundary problems based on Trefftz methods

Brański, A.; Borkowska, Dorota

doi:10.1016/j.enganabound.2015.04.016

Cited by 10 publications

(8 citation statements)

References 33 publications

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“…Metoda OS;TT była podstawą badań m. in. w pracach [4], [5], w których porównywano jej efektywność z innymi wersjami metody. Wymienione prace zawierają przykłady implementacji metody do rozwiązywania zagadnień potencjału opisanych równaniem Laplace'a.…”

Section: Wstępunclassified

Application of Trefftz method for the solution of two-dimensional Poisson’s problem taking into account material properties

Borkowska

2018

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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 the Galerkin version of the Trefftz method with symbolic name OS;TT. The paper contains the theoretical analysis of the OS;TT method which is confirmed with numerical example. .

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Section: Wstępunclassified

Application of Trefftz method for the solution of two-dimensional Poisson’s problem taking into account material properties

Borkowska

2018

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“…and I p is the identity matrix or diagonal matrix made from identity matrix where p-th diagonal element can be set to 0, which reflects the fact that one of the weighting functions can be the first one from the set (4). Having in mind that in such case p-th row of H is a zero vector one can write…”

Section: Scalability Of the Matrices Of The Scaled Boundariesmentioning

confidence: 99%

“…With the use of weighted residual method and employing different weighting functions one can obtain different versions of indirect Trefftz method, i.e. collocation, Galerkin or least squares version [2,3,4,5]. Systems of equations constituted by these methods are then solved for unknown parameters, so that solution approximated by the series of linearly independent functions satisfies the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The scalability of the matrices in direct Trefftz method in 2D Laplace problem

Borkowski

2016

Engineering Analysis with Boundary Elements

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This paper presents an interesting property of the matrices that may be obtained with the use of direct Trefftz method. It is proved analytically for 2D Laplace problem that values of the elements of matrices describing the capacitance of two scaled domains are inversely proportional to the scalability factor. As an example of the application the capacitance extraction problem is chosen. Concise description of the algorithm in which the scalability property can be utilized is given. Furthermore some numerical results of the algorithm are presented.

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“…However, this BEM needs costly numerical calculations of singular and nearly singular integrals (Sladek, Sladek, 1998;Sladek et al, 2000). Recently, the BEM, based on the Trefftz functions (they are nonsingular), is developed in (Brański et al, 2012;Borkowski, 2015;Brański, Borkowska, 2015a;2015b). Unfortunately, the construction of the mesh of the boundary in the BEM is a bit difficult.…”

Section: Introductionmentioning

confidence: 99%

Archives of Acoustics

Brański

Prędka

2018

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An efficiency of the nonsingular meshless method is analyzed in an acoustic indoor problem. The solution is assumed in the form of the series of radial bases functions. The Hardy's multiquadratic functions, as the bases, are taken into account. The room acoustic field with uniform, impedance walls is considered. The representative, rectangular cross section of the room is chosen. Practical combinations of acoustic boundary conditions, expressed through absorption coefficient values, are considered. The classical formulation of the boundary problem is used. It is established any coefficient in the multiquadratic functions depend on the number of influence points, the frequency and the absorption coefficient. All approximate results are calculated in relation to the exact ones. This way, it is proved that the meshless method based on the multiquadratic functions is simple and efficient method in the description of the complicated acoustic boundary problems for the low and medium ranges of frequency.

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Effectiveness of nonsingular solutions of the boundary problems based on Trefftz methods

Cited by 10 publications

References 33 publications

Application of Trefftz method for the solution of two-dimensional Poisson’s problem taking into account material properties

Application of Trefftz method for the solution of two-dimensional Poisson’s problem taking into account material properties

The scalability of the matrices in direct Trefftz method in 2D Laplace problem

Archives of Acoustics

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