Frequency and time domain electromagnetic scattering simulations employing higher order edge elements

Computer Methods in Applied Mechanics and Engineering

Volumn 194, Issue 2-5 SPEC. ISS., 2005, Pages 105-125

  Ledger, P D ^a   Morgan, K ^b   Hassan, O ^b  

^a ETH ZURICH   (Switzerland)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

2D time domain; 3D frequency domain; Arbitrary order edge elements; Unstructured meshes

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); FREQUENCY DOMAIN ANALYSIS; INTERFACES (MATERIALS); LINEAR EQUATIONS; TIME DOMAIN ANALYSIS;

ELECTROMAGNETIC SCATTERING; LOWER ORDER APPROXIMATIONS;

ELECTROMAGNETIC WAVE SCATTERING;

ELECTROMAGNETIC TECHNIQUE; FINITE ELEMENT METHOD;

EID: 10444246642     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2004.05.011     Document Type: Article

References (44)

1. 3 Numer. Math. 35 1980 315-341
2. 3 Numer. Math. 50 1986 57-81
3. G. Mur Edge elements their advantages and their disadvantages IEEE Trans. Magn. 30 1994 57-81
4. D. Sun J. Manges X. Yuan Z. Cendes Spurious modes in electromagnetics IEEE Antennas Propagat. Mag. 37 1995 12-24
5. A. Deraemaeker I. Babuska P. Boullard Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions Int. J. Numer. Methods Engrg. 46 1999 471-499
6. I. Babuska F. Ihlenburg E.T. Paik S. Sauter A generalised finite element method for solving the Helmholtz equation in two-dimensions with minimal pollution Comput. Methods Appl. Mech. Engrg. 128 1995 325-359
7. I.M. Babuska S.A. Sauter Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? SIAM Rev. 42 2000 451-484
8. F. Ihlenburg I. Babuska Finite element solution of the Helmholtz equation with high wave number. Part II: The hp-version of the FEM SIAM J. Numer. Anal. 31 1997 315-358
9. M. Ainsworth Discrete dispersion relationship for hp version finite element approximation at high wave number SIAM J. Numer. Anal. 42 2004 553-575
10. G.S. Warren W.R. Scott An investigation of numerical dispersion in the vector finite element method using quadrilateral edge elements IEEE Trans. Antennas Propagat. 42 1994 1502-1508
11. M. Ainsworth J. Coyle Hierarchic p-edge element families for Maxwell's equations on hybrid quadrilateral and triangular meshes Comput. Methods Appl. Mech. Engrg. 190 2001 103-124
12. M. Ainsworth Dispersive properties of high order Nédélec/edge element approximation of the time-harmonic Maxwell equations Phil. Trans. Roy. Soc. Series A 362 2004 471-493
13. R. Hiptmair, P.D. Ledger, A quadrilateral edge element scheme with minimum dispersion, Research Report 2003-17, Seminar for Applied Mathematics, ETH, Zurich, Switzerland
14. G.S. Warren W.R. Scott Numerical dispersion in the finite element method using three-dimensional edge elements Microwave Opt. Technol. Lett. 18 1998 423-429
15. P. Monk A.K. Parrott Phase accuracy computations and improved far field estimates for 3-D edge elements on tetrahedral meshes J. Comput. Phys 170 2001 614-641
16. L. Demkowicz L. Vardetyan Modelling of electromagnetic absorption/scattering problems using hp adaptive finite elements Comput. Methods Appl. Mech. Engrg. 152 1998 103-124
17. W. Rachowicz L. Demkowicz Three dimensional hp-adaptive finite element package for electromagnetics Int. J. Numer. Methods Engrg. 53 2002 147-180
18. M. Ainsworth J. Coyle Conditioning of hierarchic p-version Nédélec elements on meshes of curvilinear quadrilaterals and hexahedra SIAM J. Numer. Anal. 41 2003 731-750
19. M. Ainsworth J. Coyle Hierarchic finite element bases on unstructured tetrahedral meshes Int. J. Numer. Methods Engrg. 58 2003 2103-2130
20. J.P. Webb Heirachical vector basis functions of arbitrary order for triangular and tetrahedral finite elements IEEE Trans. Antennas Propagat. 47 1999 1244-1253
21. W. Cecot W. Rachowicz L. Demkowicz An hp-adaptive finite element method for electromagnetics. Part 3: A three-dimensional infinite element for Maxwell's equations Int. J. Numer. Methods Engrg. 57 2003 899-921
22. J.-P. Berenger A perfectly matched layer for the absorption of electromagnetic waves J. Comput. Phys. 114 1994 185-300
23. Z.S. Sacks D.M. Kingsland R. Lee J.-F. Lee A perfectly matched anisotropic absorber for use as an absorbing boundary condition IEEE Trans. Antennas Propagat. 43 1995 1460-1463
24. P.D. Ledger K. Morgan O. Hassan N.P. Weatherill Arbitrary order edge elements for electromagnetic scattering problems using hybrid meshes and a PML Int. J. Numer. Methods Engrg. 55 2002 339-358
25. W. Cecot L. Demkowicz W. Rachowicz A two dimensional infinite element for Maxwell's equations Comput. Methods Appl. Mech. Engrg. 188 2000 625-643
26. P. Monk The Finite Element Method for Maxwell's Equations 2003 Oxford University Press Oxford
27. A. Taflove S.C. Hagness Computational Electrodynamics: The Finite-Difference Time-Domain Method 2nd ed. 2000 Artech House Boston
28. F. Kikuchi Mixed and penalty formulations for the finite element analysis of an eigenvalue problem in electromagnetism Comput. Methods Appl. Mech. Engrg. 64 1987 509-521
29. P.D. Ledger An hp adaptive finite element procedure for electromagnetic scattering problems. Ph.D. thesis, Department of Civil Engineering, University of Wales, Swansea, 2002
30. J.A. Stratton Electromagnetic Theory 1941 McGraw-Hill New York
31. W.J. Gordon C. Hall Construction of curvilinear coordinate systems and applications to mesh generation Int. J. Numer. Methods Engrg. 7 1973 461-477
32. B. Szabó I. Babuska Finite Element Analysis 1991 John Wiley and Sons New York
33. G.E.M. Karniadakis J.P. Sherwin Spectral/hp Element Methods for CFD 1999 Oxford University Press
34. J. Coyle, P.D. Ledger, Evidence of exponential convergence in the computation of Maxwell eigenvalues, Comput. Methods Appl. Mech. Engrg., to appear
35. C.A. Balanis Advanced Engineering Electromagnetics 1989 John Wiley & Sons New York
36. Harwell Fortran Library
37. G.L.F. Sleijpen D.R. Fokkema BiCGSTAB(ℓ) for linear equations involving unsymmetric matrices with complex spectrum Electron. Trans. Numer. Anal. 1 1993 11-32
38. G.L.G. Sleijpen H.A. van der Vorst Maintaining convergence properties of BiCGSTAB methods in finite precision arithematic Numer. Algorithms 10 1995 203-223
39. G.L.G. Sleijpen H.A. van der Vorst Reliable updated residuals in hybrid bi-CG methods Computing 56 1996 141-163
40. G.C. Cohen Higher Order Numerical Methods for Transient Wave Equations 2002 Springer-Verlag Berlin
41. P. Monk A comparison of finite element methods for the time dependent Maxwell equations. In: G. Cohen (Ed.). Mathematical and Numerical Aspects of Wave Propagation Phenomena 1991 SIAM Philadelphia 80-88
42. C.W. Gear Numerical initial boundary value problems in ordinary differential equations 1971 Prentice-Hall
43. B.M. Irons Application of a theorem on eigenvalues to finite element problems (CR/132/70), University of Wales, Department of Civil Engineering, Swansea, UK, 1970
44. U. Kangro R. Nicolaides Spurious fields in time-domain computations of scattering problems IEEE Trans. Antennas Propagat. 45 1997 228-234