On the implementation of a multi-region Trefftz-collocation formulation for 2-D potential problems

Leitão, Vitor M.A.

doi:10.1016/s0955-7997(97)00045-3

Cited by 14 publications

(9 citation statements)

References 14 publications

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“…As the homogeneous part of the equations is well taken care of, all that remains to be done is the (approximate) enforcement of the boundary conditions. The traditional way to achieve this is by collocation (Leitão [2,3], Sensale and Rodriguez [4]). This means selecting a set of (boundary) points and forcing the approximation to satisfy, locally, the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Trefftz collocation for frequency domain elastodynamic problems

Leitão

Sensale

Rodriguez

2009

Mesh Reduction Methods

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A Trefftz collocation method is proposed for the analysis of two-dimensional elastodynamic problems subjected to steady-state time-harmonic loads. Trefftz methods are characterized by the use of a superposition of a number of actual solutions of the homogeneous part of governing equations, the so-called T(Trefftz)-functions. This leads to high quality approximations where the unknowns are the weights of each of the T-functions considered. The unknowns are found by matching the approximations to the boundary conditions by following a standard collocation approach.The numerical implementation of the method is briefly described and results are obtained for two anti-plane elastodynamic problems. The results compare quite favourably to other results available in the literature whereby Galerkin and collocation boundary element methods were used.

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Section: Introductionmentioning

confidence: 99%

Trefftz collocation for frequency domain elastodynamic problems

Leitão

Sensale

Rodriguez

2009

Mesh Reduction Methods

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“…[2]) on one side, and the Trefftz method (be it the collocation, e.g. [3,4], or the Galerkin approaches, e.g. [5][6][7]) on the other side, rely on the use of specific knowledge about the solution of the PDE being analysed.…”

Section: Introductionmentioning

confidence: 99%

Generalized finite differences using fundamental solutions

Leitão¹

2009

Numerical Meth Engineering

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SUMMARYIt is well known that solutions for linear partial differential equations may be given in terms of fundamental solutions. The fundamental solutions solve the homogeneous equation exactly and are obtained from the solution of the inhomogeneous equation where the inhomogeneous term is described by a Dirac delta distribution. Fundamental solutions are the building blocks of the boundary element method and of the method of fundamental solutions and are traditionally used to build boundary-only global approximations in the domain of interest. In this work the same characteristic of the fundamental solutions, that of solving the homogeneous equation exactly, is used but not to build a global approximation. On the contrary, local approximations are built in such a manner that it is possible to construct finite difference operators that are free from any form of structured grid.

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“…[17]), using a domain decomposition technique (c.f. [16]). The application of domain decomposition techniques together with meshless methods has been a subject of recent research in other contexts (e.g.…”

Section: Introductionmentioning

confidence: 99%