PIER | |
Progress In Electromagnetics Research | ISSN: 1070-4698, E-ISSN: 1559-8985 |
Home > Vol. 28 > pp. 231-252
A Detailed Examination of the Finite-Volume, Time-Domain Method for Maxwell's EquationsBy J. L. Young, R. O. Nelson, and D. V. Gaitonde
Citation:
References:
2. Palaniswamy, S., W. F. Hall, and V. Shankar, "Numerical solution to Maxwell’s equations in the time domain on nonuniform grids," Radio Sci., Vol. 31, No. 4, 1996. 3. Madsen, N. K. and R. W. Ziolkowski, "A three-dimensional modified finite volume technique for Maxwell’s equations," Electromagnetics, Vol. 10, 147-161, 1990. 4. Anderson, W. K., J. L. Thomas, and B. van Leer, "A comparison of finite volume flux vector splittings for the Euler equations," AIAA 23rd Aerospace Sciences Meeting, AIAA-85-0122, Reno, NV, Jan. 1985.
5. Richtmyer, R. and K. Morton, Difference Methods for Initial-Value Problems, Wiley, New York, 1967.
6. Harrington, R. F., Time-Harmonic Electromagnetic Fields, McGraw-Hill, New York, 1961.
7. Gaitonde, D., J. Shang, and J. L. Young, "Practical aspects of higher-order numerical schemes for wave propagation phenomena," Intl. J. Num. Methods in Engr., Vol. 45, 1849-1869.
8. Anderson, D. A., J. C. Tannehill, and R. H. Pletcher, Computational Fluid and Mechanics and Heat Transfer, Taylor & Francis, Bristol, PA, 1984.
9. Ray, S. L., "Grid decoupling in finite element solutions of Maxwell’s equations," IEEE Trans. Ant. Propagat., Vol. 40, No. 4, 1992. 10. Shang, J. S. and D. Gaitonde, Characteristic-based, timedependent maxwell equation solvers on a general curvilinear fram, Vol. 33, No. 3, 491-498, AIAA Journal, 1995.
11. Al-Khafaji, A. W., Numerical Methods in Engineering Practice, Holt, Rinehart and Winstron, New York, 1986.
12. Gaitonde, D. and J. S. Shang, "Optimized compact-differencebased finite-volume schemes for linear wave phenomena," J. Comp. Phys., Vol. 138, 617-643, 1997. 13. Gottlieb, D. and B. Yang, "Comparisons of staggered and nonstaggered schemes for Maxwell’s equations," 12 Annual Rev. of Progress in Appl. Comp. Electromagn., 1122-1131, Monterrey, CA, 1996.
14. Thomas, L. H., "Elliptic problems in linear difference equations over a network," Watson Sci. Comput. Lab. Rept., Columbia University, New York, 1949.
15. Gustafsson, B., "The convergence rate for difference approximations to mixed initial boundary value problems," Math. Comp., Vol. 29, 396-406, 1975. 16. Zhao, L. and A. C. Cangellaris, "GT-PML: Generalized theory of perfectly matched layers and its application to the reflectionless truncation of finite-difference time-domain grids ," IEEE Trans. Microwave Theory Tech., Vol. 44, No. 12, 1996. 17. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Cambridge University Press, Cambridge, 1986.
18. Fyfe, D. J., "Economical evaluation of Runge-Kutta formulae ," Math. Comput., Vol. 20, 392-398, 1966. 19. Williamson, J. H., "Low-storage Runge-Kutta schemes," J. Comp. Physics., Vol. 35, 48-56, 1980. 20. Shang, J., A perspective of computational electromagnetics in the time domain, 28th AIAA Plasmadynamics & Lasers Conference, AIAA 97-2356, Atlanta, GA, June 1997.
|