The hp version of the finite element method (hp-FEM) combined with adaptive mesh refinement is a particularly efficient method for solving partial differential equations because it can achieve a convergence rate that is exponential in the number of degrees of freedom. hp-FEM allows for refinement in both the element size, h, and the polynomial degree, p. Like adaptive refinement for the h versi...

A higher order large-domain hybrid finite element – method of moments (FEM-MoM) technique is presented. The discretization and solving FEM and MoM parts of the problem and the coupling of the two methods is described. A benchmark example of analysis of a scatterer with pronounced curvature at resonant frequency is given, demonstrating accuracy and robustness of the presented hybrid technique.

We present a model of fracture formation on surfaces of bilayered materials. The model makes it possible to synthesize patterns of fractures induced by growth or shrinkage of one layer with respect to another. We use the finite element method (FEM) to obtain numerical solutions. This paper improves the standard FEM with techniques needed to efficiently capture growth and fractures.

The proposed research for the Computational Engineering and Sciences (CES) option of the Computational and Applied Mathematics (CAM) Ph.D. program is in the area of tetrahedral/hexahedral finite element meshing from volumetric imaging data with defined boundaries. The proposed research work is to extract adaptive tetrahedral and hexahedral finite element meshes with guaranteed quality directly ...

The analysis of adhesively bonded joints started in 1938 with the closed-form model of Volkersen. The equilibrium equation of a single lap joint led to a simple governing differential equation with a simple algebraic equation. However, if there is yielding of the adhesive and/or the adherends and substantial peeling is present, a more complex model is necessary. The more complete is an analysis...

dynamic analysis of two-dimensional elasticity problems using the isogeometric analysis method and its comparison with the finite element method is the subject of this research. for this purpose, formulation of the governing differential equation is obtained by using the b-spline basis functions. some numerical examples employing consistent and lumped mass matrices are presented in order to com...

In this paper, we present a time integration scheme applied to the Discontinuous Galerkin finite element method (DG-FEM, [1]) for the computation of electromagnetic fields in the interior of three-dimensional structures. This approach is also known as Arbitrary High-Order Derivative Discontinuous Galerkin (ADER-DG, [2, 3]). By this method, we reach arbitrary high accuracy not only in space but ...

In this paper we present an overview of the possibilities of the finite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diffusion-reaction, fluid mechanics and fluid-structure interaction solved with th...

For the purpose of identifying the sound transmission characteristics of honeycomb sandwich panels that are commonly used in aircraft industries, Finite Element Method (FEM) combined with Boundary Element Method (BEM) has been widely used. However, the latter approach is not always applicable to high frequency analysis since it requires a large number of FEM/BEM meshes resulting in high computa...

In this paper we describe a hybrid element method which combines the boundary element method (BEM) and the finite element method (FEM) to calculate circuit models for layout dependent capacitances. The method can handle irregularities in the stratification of the layout of the integrated circuits (IC’s). We present a stand-alone extraction program which we developed for validation and testing p...