Practical aspects of high-order accurate finite-volume schemes for electromagnetics

35th Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 1997, Pages

  Gaitonde, Datta V ^a   Shang, Joseph S ^a   Young, Jeffrey L ^b  

^a WRIGHT PATTERSON AIR FORCE BASE   (United States)

^b UNIVERSITY OF IDAHO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER ANALYSIS; MAXWELL EQUATIONS;

CANONICAL PROBLEMS; FINITE VOLUME SCHEMES; MULTIPLE DIMENSIONS; NUMERICAL EXPERIMENTS; OPTIMIZATION AND PERFORMANCE; ORDER OF ACCURACY; RECONSTRUCTION OPERATORS; TRANSFORMED DOMAIN;

AEROSPACE ENGINEERING;

EID: 84982318160     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (34)

1. J.S. Shang and D. Gaitonde. Characteristic-Based, Time-Dependent Maxwell Equations Solvers on a General Curvilinear Frame. AIAA Journal, 33(3): 491-498, March 1995.
2. S.K. Lele. Compact Finite Difference Schemes with Spectral-like Resolution. Journal of Computational Physics, 103: 16-42, 1992.
3. C.K.W. Tarn and J.C. Webb. Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics. Journal of Computational Physics, 107: 262-281,1993.
4. Chen. C.L. and Y. Liu. Analysis of Numerical Approaches for Acoustic Equations. AIAA Paper 93-4324, 1993.
5. Z. Haras and S. Ta’asan. Finite Difference Schemes for Long-Tune Integration. Journal of Computational Physics, 114: 265-279,1994.
6. D.W. Zingg, H. Lomax, and H. Jurgens. An Optimized Finite-Difference Scheme for Wave Propagation Problems. AIAA Paper 93-0459, 1993.
7. D. Gaitonde and J.S. Shang. High-Order Finite-Volume Schemes in Wave Propagation Phenomena. AIAA Paper 96-2335, 1996.
8. A. Harten, B. Engquist, S. Osher, and S.R. Chakravarthy. Uniformly High Order Accurate Essentially Non-oscillatory Schemes, III. Journal of Computational Physics, 71: 231-303, 1987.
9. R.S. Hirsh. Higher Order Accurate Difference Solutions of Fluid Mechanics Problems by a Compact Differencing Technique. Journal of Computational Physics, 19: 90-109, 1975.
10. K.S. Yee. Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media. IEEE Trans. Antennas and Propagation, 14: 302-307,1966.
11. V. Shankar, A.H. Mohammadian, and W.F. Hall. A CFD-Based Finite-Volume Procedure for Computational Electromagnetics - Interdisciplinary Applications for CFD Methods, AIAA Paper 89-1987, 1989.
12. D.J. Fyfe. Economical Evaluation of Runge-Kutta Formulae. Math. Comput., 20: 392-398, 1966.
13. A.A. Wray. Minimal Storage Time-Advancement Schemes for Spectral Methods. NASA Ames Research Center, 1995.
14. W.H. Enright. Analysis of Error Control Strategies for Continuous Runge-Kutta Methods. SIAM J. Numer. Anal., 26(3): 588-599, June 1989.
15. D.W. Zingg. Runge-Kutta Methods for Linear Problems. AIAA Paper 95-1756-CP, 1995.
16. J. Casper and H.L. Atkins. A Finite-Volume High-Order ENO Scheme for Two-Dimensional Hyperbolic Systems. Journal of Computational Physics, 106: 62-76, 1993.
17. B. Gustafsson, H. O. Kreiss, and A. Sundstrom. Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II. Math. Comp., 26: 649-686,1972.
18. M.H. Carpenter, D. Gottlieb, and S. Abarbanel. The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes. Journal of Computational Physics, 108: 272-295, 1993.
19. H.S. Kreiss and L. Wu. On the Stability Definition of Difference Approximations for the Initial Boundary Value Problem. Appl. Num. Math., 12(1/3): 213, May 1993.
20. R. Vichnevetsky. Propagation Through Numerical Mesh Refinement for Hyperbolic Equations. Math, and Comp. in Simulation, XXIIL 344-353, 1981.
21. B. Gustafsson and P. Olsson. Fourth-Order Difference Methods for Hyperbolic IBVPs. Journal of Computational Physics, 117: 300-317, 1995.
22. M.H. Carpenter, D. Gottlieb, and S. Abarbanel. Time-Stable Boundary Conditions for Finite-Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Systems. Journal of Computational Physics, 111(2): 220-, April 1994.
23. H.M. Jurgens and D.W Zingg. Implementation of a High-Accuracy Finite-Difference Scheme for Linear Wave Phenomena. Proceedings of the Internat. Conf. on Spectral and High-Order Methods, June 1995.
24. R.R. Harrington. Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Co., New York, 1961.
25. A. Sommerfeld. Electrodynamics. Academic Press Inc., New York, 1952.
26. S.D. Conte and C. de Boor. Elementary Numerical Analysis - An Algorithmic Approach. McGraw-Hill Book Company, 1980.
27. Y.S. Weber. Investigations on the Properties of a Finite-Volume, Time-Domain Method for Computational Electromagnetics. AIAA Paper 95-1964, 1995.
28. J.F. Thompson, Z.U.A. Warsi, and C.W Mastin. Numerical Grid Generation. North-Holland, New York, 1985.
29. K-Y. Fung, R.S.O Man, and S. Davis. Implicit High-Order Compact Algorithm for Computational Acoustics. AIAA J., 34(10): 2029-2038, Oct. 1996.
30. R. Vichnevetsky. Numerical Filtering for Partial Differential Equations. Numerical Applications Memorandum, (NAM 156), November 1974.
31. R. Vichnevetsky and J.B. Bowles. Fourier Analysis of Numerical Approximations of Hyperbolic Equations. SIAM Studies in Applied Mathematics, 1982.
32. B. Gustafsson. The Convergence Rate for Difference Approximations to Mixed Initial Boundary Value Problems. Math. Comp., 29(130): 396-406, 1975.
33. R.F. Harrington. Field Computation by Moment Methods. Macmillan, New York, 1968.
34. J.S. Shang and D. Gaitonde. On High Resolution Schemes for Tune-Dependent Maxwell Equations. AIAA Paper 96-0832, Jan. 1996.