In this paper, application of the eXtended Finite Element Method (X-FEM) is considered for the structural optimization of continuum structures using an isoline/isosurface topology optimization algorithm. First, the methodology is described for 2D design domains in which the design boundary is represented by isolines of strain energy density (SED) in a fixed-grid design space. The optimization a...

Numerical 3D formulations using scalar  and vector A potentials are examined for magnetic fields, with emphasis on the finite difference (FDM) and finite element (FEM) methods using nodal and facet elements. It is shown that for hexahedral elements the FDM equations may be presented in a form similar to the FEM equations; to accomplish this the coefficients defining volume integrals in FEM nee...

We describe a hybrid method which combines the boundary element method (BEM) and the finite element method (FEM) to compute circuit models for layout dependent capacitances. The method can handle irregularities in the stratification of the layout of the integrated circuits (IC’s). New in the method are the models for the interface between the regions where the BEM and the FEM are applied. We sh...

Computer Tomography (CT) and in particular super fast, 64 and 256 detector CT has rapidly advanced over recent years, such that high resolution cardiac imaging has become a reality. In this paper, we provide a solution to the problem of automatically constructing three dimensional (3D) finite-element mesh models (FEM) of the human heart directly from high resolution CT. Our overall computationa...

This paper describes the concurrent multi-frontal direct solver algorithm for a multi-physics Finite Element Method (FEM). The multi-physics FEM utilizes different element sizes as well as polynomial orders of approximation over element edges, faces, and interiors (element nodes). The solver is based on the concept of a node, and management of unknowns is realized at the level of nodes. The sol...

A set of Shock Wave Lithotripsy(SWL) related experimental observations including 3D dynamic crack propagation, reported in literature, are simulated with the aim of understanding the fragmentation of kidney stone with SWL. Extracorporeal shock wave lithotripsy (ESWL) is the fragmentation of kidney stones by focusing an ultrasonic pressure pulse onto the stones. 3D models with fine discretizatio...

Power transformer analysis and design focusing on the equivalent circuit parameter evaluation by magnetic field numerical calculation is presented. Two kinds of numerical techniques are examined: the threedimensional (3D) finite element method (FEM), adopting a particular reduced scalar potential formulation and the 3D mixed finite element-boundary element (FEM-BEM) method. The methods are vali...

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...

Finite element methods (FEM) are generally used in cardiac 3D-electromechanical modeling. For FEM modeling, a step of a suitable mesh construction is required, which is non-trivial and time-consuming for complex geometries. A meshless method is proposed to avoid meshing. The smoothed particle hydrodynamics (SPH) method was used to solve an electrophysiological model on a left ventricle extracte...