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Fast Algorithms for Composite Materials

Published online by Cambridge University Press:  10 February 2011

L. Greengard
L. Greengard*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012
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Abstract

We briefly review recently developed fast algorithms for the evaluation of electrostatic fields in composite materials consisting of a collection of piecewise homogeneous inclusions embedded in a uniform background. These algorithms are based on combining a suitable boundary integral equation with the fast multipole method and a conjugate gradient-like iterative method. The CPU time required grows linearly with the number of points in the discretization of the interface between the inclusions and the background material, bringing large-scale calculations within practical reach.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 408: Symposium P – Materials Theory, Simulations, and Parallel Algorithms , 1995 , 93
Copyright
Copyright © Materials Research Society 1996

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References

1. Barnes, J. and Hut, P., Nature 324, 446 (1986).Google Scholar
2. Beylkin, G., Coifman, R. and Rokhlin, V., Comm. Pure and Appl. Math. 44, 141 (1991).Google Scholar
3. Brandt, A. and Lubrecht, A. A., J. Comput. Phys. 90, 348 (1990).Google Scholar
4. Brebbia, C. A., Telles, J. C. F., and Wrobel, L. C., Boundary element techniques, Springer Verlag, Berlin, 1983.Google Scholar
5. Carrier, J., Greengard, L., and Rokhlin, V., Siam J. Sci. Stat. Comput. 9, 669 (1988).Google Scholar
6. Cheng, H. and Greengard, L., DOE/CMCL Report 95–005, New York University, 1995.Google Scholar
7. Greenbaum, A., Greengard, L., and Mayo, A., Physica D 60, 216 (1992).Google Scholar
8. Greengard, L., The Rapid Evaluation of Potential Fields in Particle Systems, MIT Press, Cambridge, 1988.Google Scholar
9. Greengard, L., Kropinski, M. C., and Mayo, A., J. Comput. Phys., to appear.Google Scholar
10. Greengard, L. and Moura, M., Acta Numerica, 379 (1994).Google Scholar
11. Greengard, L. and Rokhlin, V., J. Comput. Phys. 73, 325 (1987).Google Scholar
12. Greengard, L. and Rokhlin, V., Chemica Scripta 29A, 139 (1989).Google Scholar
13. Helsing, J., J. Mech. Phys. Solids 43, 815 (1995).Google Scholar
14. Helsing, J., Report Number TRITA-NA-9406, Department of Numerical Analysis and Computing Science, Royal Institute of Technology, Stockholm, 1994.Google Scholar
15. Hetherington, J. and Thorpe, M. F. Proc. R. Soc. Lond. A 438, 591 (1992).Google Scholar
16. Jaswon, M. A. and Symm, G. T., Integral Equation Methods in Potential Theory and Elastostatics, Academic Press, New York, 1977.Google Scholar
17. Nabors, K. and White, J. IEEE Trans. on Circuits and Systems 39, 946 (1992).Google Scholar
18. Phan-Thien, N. and Kim, S., Microstructures in Elastic Media, Oxford University Press, New York, 1994.Google Scholar
19. Rokhlin, V., J. Comput. Phys. 60, 187 (1985).Google Scholar
20. Saad, Y. and Schultz, M. H. SIAM J. Sci. Stat. Comput. 7, 856 (1986).Google Scholar
21. Sherman, D. I., Nonhomogeneity in Elasticity and Plasticity, Pergamon Press, Oxford, 1959.Google Scholar
22. Theocaris, P. S. and loakimidis, N. I., Q. Jl. Mech. Appl. Math. 30, 437 (1977).Google Scholar
23. Van Bladel, J., Electromagnetic Fields, McGraw-Hill, New York, 1964.Google Scholar