A typical problem in engineering is to find a numerical solution to a partial differential equation (or a coupled set thereof), given a number of boundary conditions, and the usual approach of solving the problem starts by discretizing the domain into elementary volumes. In this paper, we focus on mesh generation suitable for the solution of field problems in arbitrary VLSI structures. We assume that the problem cannot be easily reduced to a lower dimensionality by exploiting symmetry or regularity, so that the problem-domain is intrinsically threedimensional. Also, we assume that the selected numerical technique (e.g., the finite element method) requires a three-dimensional discretization (as opposed to a surface-discretization). Surveys on mesh generation are given in [2] and [5]. The mesh generator described in this paper is based on techniques from the Delaunay-based mesh generation literature. The main benefit of these techniques is that the quality of the resulting meshes can be guaranteed, and, equally important, that the meshes are still small enough to be practically useful. An additional advantage is that computation of the mesh is efficient in practice. In general, mesh computation is much faster than solving the subsequent numerical problems. An example mesh generated by our implementation is shown in Figure 1.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
van der Kolk, K.J., van der Meijs, N.P. (2007). On the Implementation of a Delaunay-based 3-dimensional Mesh Generator. In: Ciuprina, G., Ioan, D. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71980-9_40
Download citation
DOI: https://doi.org/10.1007/978-3-540-71980-9_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71979-3
Online ISBN: 978-3-540-71980-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)