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Improving the quality of meshes for the simulation of semiconductor devices using Lepp‐based algorithms
Author(s) -
Hitschfeld N.,
Villablanca L.,
Krause J.,
Rivara M. C.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.767
Subject(s) - delaunay triangulation , polygon mesh , vertex (graph theory) , isosceles triangle , algorithm , constrained delaunay triangulation , chew's second algorithm , triangle mesh , voronoi diagram , mathematics , surface triangulation , boundary (topology) , topology (electrical circuits) , computer science , geometry , combinatorics , graph , mathematical analysis
This paper discusses a new post‐process algorithm for generating valid Delaunay meshes for the Box‐method (finite‐volume method) as required in semiconductor device simulation. In such an application, the following requirements must be considered: (i) in critical zones of the device, edges aligned with the flow of the current (anisotropic meshes) are needed; (ii) boundary and interface triangles with obtuse angles opposite to the boundary/interfaces are forbidden; (iii) large obtuse angles in the interior of the device must be destroyed and (iv) interior vertices with high vertex‐edge connectivity should be avoided. By starting from a fine Delaunay mesh that satisfies condition (i), the algorithm produces a Delaunay mesh that fully satisfies condition (ii) and satisfies conditions (iii) and (iv) according to input tolerance parameters γ and c , where γ is a maximum angle tolerance value and c is a maximum vertex‐edge connectivity tolerance value. Both to destroy any target interior obtuse triangle t and any target high vertex‐edge connectivity, a Lepp–Delaunay algorithm is used. The elimination of obtuse angles opposite to the boundary and/or interfaces is done either by longest edge bisection or by the generation of isosceles triangles. The Lepp–Delaunay algorithm allows a natural improvement of the input mesh by inserting a few points in some existing edges of the current triangulation. Examples of the use of the algorithm over Delaunay constrained meshes generated by a normal offsetting approach will be shown. A comparison with an orthogonal refinement method followed by Voronoi point insertion is also included. Copyright © 2003 John Wiley & Sons, Ltd.