Boundary-conforming coordinates with grid line control for acoustic scattering from complexly shaped obstacles

Numerical Methods for Partial Differential Equations

Volumn 23, Issue 6, 2007, Pages 1445-1467

  Vlllamlzar, Vianey ^a   Weber, Matthew ^b  

^a BRIGHAM YOUNG UNIVERSITY   (United States)

^b LDS Business College Library   (United States)

Author keywords

Acoustic scattering; Boundary singularities; Elliptic grid generation; Finite difference time domain method; Grid line control; Radar cross section

Indexed keywords

EID: 35948965266     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20235     Document Type: Article

References (30)

1. 1 V. Villamizar and O. Rojas, Time‐dependent numerical method with boundary‐conforming curvilinear coordinates applied to wave interactions with prototypical antennas, J Comput Phys 177 ( 2002), 1–36.
2. 2 V. Villamizar, G. Kriegsmann, and E. Resis, Acoustic scattering from baffled membranes that are backed by elastic cavities, Wave Motion 14 ( 1991), 299–320.
3. 3 V. Villamizar and R. Jimenez, Scattering cross section of a cylinder at the interface of two acoustic media, J. A. DeSanto, editor, Proceedings of 4th International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena, SIAM, Colorado, 1998, pp. 641.
4. 4 V. Villamizar, Elastic scattering from a viscous incompressible fluid sphere at low reynolds number, SIAM J of Appl Math 50 ( 1990), 16–32.
5. 5 J. C. Gomez and V. Villamizar, Response of a viscous incompressible fluid cyclinder at low reynolds number to an incident plane compressional elastic wave, SIAM J of Appl Math 56 ( 1996), 372–387.
6. 6 K. S. Yee, Numerical solution of intial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans Antennas Propagation 14 ( 1966), 302–307.
7. 7 A. Taflove, Advances in computational electrodynamics. The finite‐difference time‐domain method, Artech House, 1998.
8. 8 A. C. Cangellaris and D. B. Wright, Analysis of the numerical error caused by the stairstepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena, IEEE Trans Antennas Propogat 39 ( 1991), 1518–1525.
9. 9 R. Holland, Pitfalls of staircase meshing, IEEE Trans Electromag Compat 35 ( 1993), 434–439.
10. 10 J. B. Schneider and K. L. Shlager, FDTD simulations of TEM horns and the implications for staircased representations, IEEE Trans Antennas Propogat 45 ( 1997), 1830–1838.
11. 11 G. Ryskin and L. G. Leal, Orthogonal mapping, J Comp Phys 50 ( 1983), 71–100.
12. 12 L. Eca, 2D orthogonal grid generation with boundary point distribution control, J Comput Phys 125 ( 1996), 440–453.
13. 13 V. Villamizar and M. Weber, Scattering cross section of non‐smooth cylindrical obstacles of arbitraty shape, H. Haddar and J. H. Hesthaven, editors, Proceedings of 7th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Waves 2005, Rhode Island, 2005, pp. 167.
14. 14 A. Winslow, Numerical solution of the quasilinear poisson equations in a nonuniform triangle mesh, J Comp Phys 2 ( 1967), 149–172.
15. 15 F. Collino, T. Fouquet, and P. Joly, Conservative space‐time mesh refinement methods for the FDTD solution of maxwell's equations, J Comput Phys 211 ( 2006), 9–35.
16. 16 V. Villamizar, O. Rojas, and J. Mabey, Generation of curvilinear coordinates on multiply connected regions with boundary singularities, J Comput Phys ( 2006), doi:10.1016/j.jcp.2006.09.028.
17. 17 C. S. Morawetz, The limiting amplitude principle, Comm Pure Appl Math 15 ( 1962), 349–361.
18. 18 P. Knupp and S. Steinberg, Fundamentals of grid generation, CRC Press, 1993.
19. 19 D. Givoli, Non‐reflecting boundary conitions: a review, J Comp Phys 94 ( 1991), 1–29.
20. 20 D. Givoli, Numerical methods for problems in infinite domains, Elsevier Science Publishers, Amsterdam, 1992.
21. 21 A. Bayliss and E. Turkel, Boundary conditions for the numerical solution of elliptic equations in exterior regions, SIAM J Appl Math 42 ( 1982), 430.
22. 22 T. Hagstrom and S. I. Hariharan, A formulation of asymptotic and exact boundary conditions using local operators, Appl Num Math 5 ( 1998), 1–14.
23. 23 C. L. Wang and K. Tang, Non‐self overlapping hermite interpolation mapping: a practical solution for structured quadrilateral meshing, Comput Aided Des 37 ( 2005), 271–283.
24. 24 A. R. Mitchell, Computational methods in partial differential equations, Wiley, 1969.
25. 25 G. Sewell, The numerical solution of ordinary and partial differential equations, Wiley, 2005.
26. 26 O. P. Bruno and E. M. Hyde, Higher‐order fourier approximation in scattering by two‐dimensionalm, inhomogeneous media, SIAM J Numer Anal 42 ( 2005), 2298–2319.
27. 27 F. Ihlenburg, Finite element analysis of acoustic scattering, Springer Verlag, 1998.
28. 28 R. Kress, Numerical analysis, Springer Verlag, 1998.
29. 29 P. M. Knuupp and N. Robidoux, A framework for variational grid generation: conditioning the jacobian matrix with matrix norms, SIAM J Sci Comput 21 ( 2000), 2009–2047.
30. 30 E. Manoha, R. Guenanff, S. Redonnet, and M. Terracol, Acoustic scattering from complex geometries, AIAA, editor, 10th AIAA/CEAS Aeroacoustics Conference AIAA, Manchester, Great Britain, 2004, pp. 1553.