In the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary condit...

This paper considers the technological aspects of the finite volume element method for the numerical solution of partial differential equations on simplicial grids in two and three dimensions. We derive new classes of integration formulas for the exact integration of generic monomials of barycentric coordinates over different types of fundamental shapes corresponding to a barycentric dual mesh....

A mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized/extended FEM. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and co...

A generalized framework is presented that extends the classical theory of finite-difference summation-by-parts (SBP) operators to include a wide range of operators, where the main extensions are i) non-repeating interior point operators, ii) nonuniform nodal distribution in the computational domain, iii) operators that do not include one or both boundary nodes. Necessary and sufficient conditio...

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

We show how to solve hyperbolic equations numerically on unbounded domains by means of compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate in combination with compactification. Based on this idea, we present a new layer method, called hyperboloidal layers. Accuracy and efficiency of thi...