The paper presents a hybrid-Trefftz element approach for the numerical solution of transient linear heat conduction problems. In the proposed method, the transient heat conduction equation is first discretized with respect to time and then the resulting set of elliptic equations is solved by the corresponding time independent hybrid Trefftz element approach. At the end of the paper, the propose...

A Trefftz collocation method (TCM) is proposed for solving three-dimensional (3D) linear-elastic boundary value problems. By using the Papkovich-Neuber (P-N) general solutions, Trefftz trial functions are expressed in terms of cylindrical harmonics. Both non-singular and singular harmonic functions are included, facilitating the study of interior and exterior problems. To mitigate the problem o...

This paper discusses the use of wave based prediction methods for the analysis of steady-state interior acoustic problems. Conventional element based prediction methods, such as the Finite Element Method (FEM), are commonly used, but are restricted to low-frequency applications. The Wave Based Method (WBM) is an alternative deterministic technique which is based on the indirect Trefftz approach...

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. Concis...

In recent years the hybrid-Trefftz finite element (hT-FE) model, which originated in the work by Jirousek and his collaborators and makes use of an independently defined auxiliary inter-element frame, has been considerably improved. It has indeed become a highly efficient computational tool for the solution of difficult boundary value problems In parallel and to a large extent independently, a ...

A recently developed wave based method (WBM) has proven to be a computationally efficient tool for analysing steady-state lowand mid-frequency acoustic problems. The method is based on an indirect Trefftz approach, in that the dynamic pressure field is approximated by wave functions, which are exact solutions of the governing Helmholtz equation. Several case studies have shown that the WBM exhi...

In this paper, we explore three different ways of developing T-Trefftz finite elements of quadrilateral as well as polygonal shapes. In all of these three approaches, in addition to assuming an inter-element compatible displacement field along the element boundary, an interior displacement field for each element is independently assumed as a linear combination of T-Trefftz trial functions. In a...

Trefftz methods are high-order Galerkin schemes in which all discrete functions elementwise solution of the PDE to be approximated. They viable only when is linear and its coefficients piecewise-constant. We introduce a “quasi-Trefftz” discontinuous (DG) method for discretisation acoustic wave equation with piecewise-smooth material parameters: approximate solutions. show that new enjoys same e...

For several elasticity problems, solution representations for the displacements and stresses are available. The solution representations are given in terms of “arbitrary” complex valued functions. For any choice of the complex functions, the governing differential equations are automatically satisfied. Complex solution representations are therefore useful for applications of the Trefftz method....

Solution representations are available for severeal differential equations. For elasticity problems some of the solution representations are considered in this paper. The solution representations can be used for a systematic construction of Trefftz functions for the derivation of Trefftz-type finite elements. For the example of a thick plate a set of Trefftz functions is presented.