Abstract
Yee’s scheme for the solution of the Maxwell equations [1] and the MAC algorithm for the solution of the Navier-Stokes equations [2] are examples of co-volume solution techniques. Co-volume methods, which are staggered in both time and space, exhibit a high degree of computationally efficiency, in terms of both CPU and memory requirements compared to, for example, a finite element time domain method (FETD). The co-volume method for electromagnetic (EM) waves has the additional advantage of preserving the energy and, hence, maintaining the amplitude of plane waves. It also better approximates the field near sharp edges, vertices and wire structures, without the need to reduce the element size. Initially proposed for structured grids, Yee’s scheme can be generalized for unstructured meshes and this will enable its application to industrially complex geometries [3].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
1. Yee K (1996) Numerical solution of initial boundary value problem involving Maxwell's equation in isotropic media, IEEE Trans Antennas and Propagation 14:302–307
2. Churbanov A (2001) An unified algorithm to predict compressible and incompressible flows. In: CD Proceedings of the ECCOMAS Computational Fluid Dynamics Conference, Swansea, Wales, UK
3. Morgan K, Hassan O, Peraire J (1996) A time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media, Computer Methods in Applied Mechanics and Engineering 134:17–36
4. Bern M, Chew L.P, Eppstein D, and Ruppert J (1995) Dihedral bounds for mesh generation in high dimensions. In: 6th ACM-SIAM Symposium on Discrete Algorithms, 189–196.
5. Peraire J, Vahdati M, Morgan K, Zienkiewicz O (1987) Adaptive remeshing for compressible flow computations, Journal of Computational Physics 72:449–466
6. George P, Borounchaki H (1998) Delaunay Triangulation and Meshing. Application to Finite Elements, Hermes, Paris
7. Marcum D, Weatherill N (1995) Aerospace applications of solution adaptive finite element analysis, Computer Aided Geometric Design, Elsevier, 12:709–731
8. Frey W, Field D (1991) Mesh relaxation: a new technique for improving triangulation, Int J Numer Meth in Engineering 31:1121–1133
9. Sazonov I, Wang D, Hassan O, Morgan K, Weatherill N (2006) A stitching method for the generation of unstructured meshes for use with co-volume solution techniques, Computer Methods in Applied Mechanics and Engineering 195/13–16:1826–1845
10. Du Q, Faber V, Gunzburger M (1999) Centroidal Voronöý Tessellations: Applications and Algorithms, SIAM Review 41/4:637–676
11. Lloyd S (1982) Least square quantization in PCM. IEEE Trans Infor Theory 28:129–137
12. Taove A, Hagness S.C. (2000) Computational electrodynamics: the finite-difference time domain method. 2nd ed., Artech House, Boston.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this paper
Cite this paper
Sazonov, I., Hassan, O., Morgan, K., Weatherill, N.P. (2006). Smooth Delaunay-Voronoï Dual Meshes for Co-Volume Integration Schemes. In: Pébay, P.P. (eds) Proceedings of the 15th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34958-7_30
Download citation
DOI: https://doi.org/10.1007/978-3-540-34958-7_30
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34957-0
Online ISBN: 978-3-540-34958-7
eBook Packages: EngineeringEngineering (R0)