Numerical simulation of 2D electrodynamic problems with unstructured triangular meshes

We present a generalization of standard leap-frog plus Yee mesh approach for Cauchy problem in electrodynamics simulations on unstructured triangulated mesh. The presented approach still inherits from finite-difference time-domain and do not use techniques developed in finite-volume time-domain approach. In the paper the whole flow from mesh creation to actual simulation is presented. The proposed computation flow is parallel ready and can be implemented for distributed systems (computation servers, graphical processing units, etc.). We studied the influence of non-regular triangulation on stability and dispersion properties of numerical solution.

Using Discrete and Continuous Models to Solve Nanoporous Flow Optimization Problems

We consider using a discrete network model in combination with continuous nonlinear optimization models to solve the problem of optimizing channels in nanoporous materials. The problem and the hierarchical optimization algorithm are described in [2]. A key feature of the model is the fact that we use the edges of the finite element grid as the locations of the channels. The focus here is on the use of the discrete model within that algorithm. We develop several approximations to the relevant flow and a greedy algorithm for quickly generating a “good” tree connecting all of the nodes in the finite-element mesh to a designated root node. We also consider Metropolis-Hastings (MH) improvements to the greedy result. We consider both a regular triangulation and a Delaunay triangulation of the region, and present some numerical results.

Generating Offsets That Are Homologous to Their Skeletons

In this paper we present a method for generating an offset surface from a subcomplex of a regular triangulation such that the surface has the same topology as the subcomplex. We assume that a subcomplex has been generated by specifying input points and their weights. The subcomplex may contain points, lines, triangles, and tetrahedra based on the values of the weights. The offset from the subcomplex, or skeleton, is restricted to lie inside a union of balls centered around the input points with radii related to the weights of the input points. This restriction forces the offset and the skeleton to have the same homology. The homology groups are easy to compute for the skeleton. In this way, a designer can impose both geometric and topological constraints on a model. Also, the skeleton can be thought of as a graph to which design information can be attached; for instance, we show how the portion of the offset surface associated with each input point can be easily identified and used in lumped parameter analysis for simulations. Functional representations of a design might also be attached to the skeleton as well.

A Skeletal Topological Modeler Based on Bounding Spheres

Solid modelers are most frequently used when the final shape of the object to be modeled is known. One reason for this is the amount of input required on the part of designers to create even simple models. We propose a modeler requiring only weighted points to be specified. The connectivity of the points is determined based on proximity and the value of the weight at each point. The connected diagram — a subcomplex of the regular triangulation of the input points known as an alpha shape — serves as a skeleton for an offset surface which becomes the solid model. Functional representations of a design might also be attached to the skeleton as well.