In this paper, the inverse Cauchy problem for Laplace equation defined in an arbitrary plane domain is investigated by using the collocation Trefftz method (CTM) with a better postconditioner. We first introduce a multiple-scale Rk in the T-complete functions as a set of bases to expand the trial solution. Then, the better values of Rk are sought by using the concept of an equilibrated matrix, ...

In this paper, the inverse Cauchy problem for Laplace equation defined in an arbitrary plane domain is investigated by using the collocation Trefftz method (CTM) with a better postconditioner. We first introduce a multiple-scale Rk in the T-complete functions as a set of bases to expand the trial solution. Then, the better values of Rk are sought by using the concept of an equilibrated matrix, ...

In this paper, we develop T-Trefftz Voronoi Cell Finite Elements (VCFEM-TTs) for micromechanical modeling of composite and porous materials. In addition to a homogenous matrix in each polygon-shaped element, three types of arbitrarily-shaped heterogeneities are considered in each element: an elastic inclusion, a rigid inclusion, or a void. In all of these three cases, an inter-element compatibl...

This paper shows the essential unity between the known approximation procedures to differential equations. The boundary type approximations associated with Trefftz are shown to be a particular form of the weighted residual approximation and can provide a very useful basis for generating hybrid 'finite elements'. These can be used in combination with other finite element approaches.

This paper discusses a domain-based formulation for hybrid-Trefftz thick plate elements. The formulation can be applied to triangular and quadrilateral elements, and enables an analytical formulation of these elements to be used. Techniques for improving the computational efficiency are explored, and a simple and accurate triangular element is formulated in this manner.