Realistic behavior of deformable objects is essential for many applications in computer graphics, engineering, or medicine. Typical techniques are either based on mass-springdamper models, boundary element methods, finite difference methods, or finite element methods. These methods either lack accuracy or are computationally very expensive. If accuracy is required FEM computations use adaptive ...

Dougall's expansion is used in the expression for the volume element in tetrahedral coordinates, thereby lifting the spherical triangle restriction on the angles at the tetrahedral vertex. Application is made to the evaluation of matrix elements for the ground state of three-electron atoms.

Finite element methods for problems given in complex domains are often based on tetrahedral meshes. This paper demonstrates that the so–called rational Large Eddy Simulation model and a projection–based Variational Multiscale method can be extended in a straightforward way to tetrahedral meshes. Numerical studies are performed with an inf–sup stable second order pair of finite elements with dis...

In tetrahedral mesh generation, the constraints imposed by adaptive element size, good tetrahedral quality (shape measured by some local metric), and material boundaries are often in conflict. Attempts to satisfy these conditions simultaneously frustrate many conventional approaches. We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of p...

This application paper presents details of the technique we developed to produce an adaptive and quality tetrahedral finite element mesh model of a human heart. Beginning from a polygonal surface model consisting of twenty-two components, we first edit and convert it to volumetric gridded data. A component index for each cell edge and grid point is computed for assisting the boundary and materi...

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 ...

An unstructured nodal spectral-element method for the Navier-Stokes equations is developed in this paper. The method is based on a triangular and tetrahedral rational approximation and an easy-to-implement nodal basis which fully enjoys the tensorial product property. It allows arbitrary triangular and tetrahedral mesh, affording greater flexibility in handling complex domains while maintaining...