Practical aspects of higher-order numerical schemes for wave propagation phenomena

International Journal for Numerical Methods in Engineering

Volumn 45, Issue 12, 1999, Pages 1849-1869

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

^a AIR FORCE RESEARCH LABORATORY   (United States)

^b UNIVERSITY OF IDAHO   (United States)

Author keywords

Compact differencing; Filtering; High order; Wave propagation

Indexed keywords

COMPUTER TECHNIQUE; ELECTROMAGNETIC WAVE; MATHEMATICAL METHOD; WAVE PROPAGATION;

ELECTROMAGNETIC RADIATION; MATHEMATICAL METHOD; WAVE PROPAGATION;

EID: 0032844977     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19990830)45:12<1849::AID-NME657>3.0.CO;2-4     Document Type: Article

References (32)

1. Shang JS, Gaitonde D. Characteristic-based, time-dependent Maxwell equations solvers on a general curvilinear frame. AIAA Journal 1995; 33:491-498.
2. Taflove A. Re-inventing electromagnetics: supercomputing solution of Maxwell's equations via direct time integration on space grids. Computing Systems in Engineering 1992; 3:1-4.
3. Lele SK. Compact finite difference schemes with spectral-like resolution. Journal of Computational Physics 1992; 103:16-42.
4. Tam CKW, Webb JC. Dispersion-relation-preserving finite difference schemes for computational Acoustics. Journal of Computational Physics 1993; 107:262-281.
5. Hirsh RS. Higher order accurate difference solutions of fluid mechanics problems by a compact differencing Technique. Journal of Computational Physics 1975; 19:90-109.
6. Young JL, Gaitonde D, Shang JS. A fourth-order compact difference scheme for Maxwell's equations. IEEE AP-S International Symposium 1997; 3:1992-1995.
7. Young JL, Gaitonde D, Shang JS. Towards the construction of a fourth-order difference scheme for transient EM wave simulation:staggered grid approach. IEEE Transactions on Antennas and Propagation 1997; 45:1573-1580.
8. Gaitonde D, Shang JS. Optimized compact-difference-based finite-volume schemes for linear wave phenomena. Journal of Computational Physics 1997; 138:617-643.
9. Gustafsson B, Kreiss HO, Sundstrom A. Stability theory of difference approximations for mixed initial boundary value problems. II. Mathematics of Computation 1972; 26:649-686.
10. Carpenter MH, Gottlieb D, Abarbanel S. The stability of numerical boundary treatments for compact high-order finite-difference schemes. Journal of Computational Physics 1993; 108:272-295.
11. Kreiss HO, Wu L. On the stability definition of difference approximations for the initial boundary value problem. Applied Numerical Mathematics 1993; 12:213-228.
12. Vichnevetsky R. Propagation through numerical mesh refinement for hyperbolic equations. Mathematics and Computers in Simulation 1981; XXIII:344-353.
13. Gustafsson B, Olsson P. Fourth-order difference methods for hyperbolic IBVPs. Journal of Computational Physics 1995; 117:300-317.
14. Carpenter MH, Gottlieb D, Abarbanel S. Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact systems. Journal of Computational Physics 1994; 111:220-236.
15. Jurgens HM, Zingg DW. Implementation of a high-accuracy finite-difference scheme for linear wave phenomena. Proceedings of the International Conference on Spectral and High-Order Methods, June 1995.
16. Harten A, Engquist B, Osher S, Chakravarthy SR. Uniformly high order accurate essentially non-oscillatory schemes, III. Journal of Computational Physics 1987; 71:231-303.
17. Conte SD, de Boor C. Elementary Numerical Analysis - An Algorithmic Approach. McGraw-Hill Book Company: New York, 1980.
18. Vichnevetsky R, Bowles JB. Fourier analysis of numerical approximations of hyperbolic equations. SIAM Studies in Applied Mathematics 1982.
19. Harrington RR. Time-Harmonic Electromagnetic Fields. McGraw-Hill Book Company: New York, 1961.
20. Thompson JF, Warsi ZUA, Mastin CW. Numerical Grid Generation. North-Holland: New York, 1985.
21. Casper J, Atkins HL. A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems. Journal of Computational Physics 1993; 106:62-76.
22. Fung K-Y, Man RSO, Davis S. Implicit high-order compact algorithm for computational acoustics. AIAA Journal, 1996; 34:2029-2038.
23. Tuttle Jr DF. Network Synthesis, vol. 1. John Wiley and Sons: New York, 1958.
24. Vichnevetsky R. Numerical filtering for partial differential equations. Numerical Applications Memorandum. Rutgers University, NAM 156, November 1974.
25. Kennedy CA, Carpenter MH. Several new numerical methods for compressible shear-layer simulations. Applied Numerical Mathematics 1994; 14:397-433.
26. Gaitonde D, Shang JS. High-order finite-volume schemes in wave propagation phenomena. AIAA Paper 96-2335, June 1996.
27. Gaitonde DV, Visbal MR. High-order schemes for Navier-Stokes equations: algorithm and implementation into FDL3DI. Technical Report AFRL-VA-WP-TR-1998-3060. Air Force Research Laboratory, Wright-Patterson AFB, 1998.
28. Yee KS. Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antenna and Propagation 1966; 14:302-307.
29. Shlager KL, Maloney JG, Ray SL, Peterson AF. Relative accuracy of several finite-difference time-domain methods in two and three-dimensions. IEEE Transactions on Antenna and Propagation 1993; 41:1732-1737.
30. Gaitonde DV. Optimized schemes for time-domain electromagnetics. IEEE AP-S International Symposium, Montreal Quebec, July 1997.
31. Blaschak JG. Radiation Boundary Conditions. Ph.D. Thesis, Northwestern University, Evanston, IL, 1988.
32. Gustafsson B. The convergence rate for difference approximations to mixed initial boundary value problems. Mathematics of Computation 1975; 29:396-406.