We present an advanced algorithm for an extraction tool to compute inductances of interconnect structures. As already pointed out [Proc. Third Int. Conf. Modeling Simul. Microsyst. (2000) 416] the pursued energy concept leads to a 6-fold integral which can also be evaluated by use of the Monte Carlo method. A classical implementation of the Monte Carlo method, where the whole geometry has to be...

We propose a multilevel preconditioning strategy for the iterative solution of large sparse linear systems arising from a nite element discretization of the radiation di usion equations. In particular, these equations are solved using a mixed nite element scheme in order to make the discretization discontinuous, which is imposed by the application in which the di usion equation will be embedded...

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store the information necessary for random access, we suggest 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neig...

A method for optimising a pre-existing mesh of tetrahedral ®nite elements is described. It is based on a series of mesh connectivity and node position searches of the landscape de®ning mesh quality. A Riemannian metric, re¯ecting the a posteriori error measure, is used to calculate element size and shape. A functional is de®ned which embodies both shape and size quality of an element with respe...

Abstract This work continues the series of papers in which new approach of constructing alge braic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general grid is proposed The linear system arising from the mixed meth ods is rst algebraically condensed to a symmetric positive de nite system for Lagrange multipliers which cor...

In a previous paper (Kim and Bathe, 2013) [1], we introduced a scheme to improve finite element displacement and stress solutions by the use of interpolation covers. In the present paper we show how the scheme can be used to automatically improve finite element solutions. As in Ref. (Kim and Bathe, 2013) [1], we focus on the use of the low-order finite elements for the analysis of solids, namel...

In some of the engineering problems, it is necessary to analyze the three-dimensional temperature profiles. In order to solve a typical problem numerically, the three-dimensional temperature diffusion equation is chosen as the mathematical model. The finite volume formulation is derived using Galerkin approach for the mesh of tetrahedral elements, which facilitates solving temperature problems ...

A parallel tetrahedral mesh adaptation code is expanded to treat general, mixed-element unstructured meshes comprised of any combination of basic element types. Emphasis is placed on developing conforming mesh modification methods that are solver-independent. Specific developments include the implementation of a treatment for viscous, high aspect ratio near wall tetrahedra, and cell subdivision...

The paper presents a parallel direct solver for multi-physics problems. The solver is dedicated for solving problems resulting from adaptive Finite Element Method computations. The concept of finite element is actually replaced by the concept of the node. The computational mesh consists of several nodes, related to element vertices, edges, faces and interiors. The ordering of unknowns in the so...

The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to gener...