Adaptive hp finite element computations of the scattering width output of Maxwell's equations

International Journal for Numerical Methods in Fluids

Volumn 43, Issue 8, 2003, Pages 953-978

  Ledger, P D ^a   Peraire, J ^b   Morgan, K ^a   Hassan, O ^a   Weatherill, N P ^a  

^a SWANSEA UNIVERSITY   (United Kingdom)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Arbitrary order edge elements; Electromagnetic scattering; Frequency domain; Goal orientated adaptivity; Output error bounds

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; ELECTROMAGNETIC WAVE SCATTERING; ERROR ANALYSIS; FINITE ELEMENT METHOD;

FINITE ELEMENT COMPUTATIONS;

MAXWELL EQUATIONS;

WAVE SCATTERING;

EID: 0344235608     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. 3 by finite element methods. SIAM Journal of Numerical Analysis 1978; 15:580-594.
2. 3. Numerische Mathematik 1980; 35:315-341.
3. 3. Numerische Mathematik 1986; 50:57-81.
4. Monk P. An analysis of Ńed́elec's method for the spatial discretization of Maxwell's equations. Journal of Computational and Applied Mathematics 1993; 47:101-121.
5. Monk P. On the p- and hp-extension of Ńed́elec's curl conforming elements. Journal of Computational and Applied Mathematics 1994; 53:117-137.
6. Demkowicz L, Rachowicz W. A 2D hp-adaptive finite element package for electromagnetics (2Dhp90em). TICAM Report 98-15, University of Texas at Austin, 1998.
7. Demkowicz L, Vardapetyan L. Modeling of electromagnetic/scattering problems using hp-adaptive finite elements. Computer Methods in Applied Mechanics and Engineering 1998; 152:103-124.
8. Ainsworth M, Coyle J. Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes. Computer Methods in Applied Mechanics and Engineering 2001; 190:6709-6733.
9. Ledger PD, Hassan O, Morgan K, Weatherill NP. PML and arbitrary order edge elements for electromagnetic scattering simulation. International Journal for Numerical Methods in Engineering 2002; 55:339-358.
10. Paraschivoiu M, Peraire J, Patera AT. A-posteriori finite element bounds for linear functional outputs of elliptic partial differential equations. Computer Methods in Applied Mechanics and Engineering 1997; 150:289-312.
11. Maday Y, Peraire J, Patera AT. A general formulation for a-posteriori bounds for output functionals of partial differential equations: application to the eigenvalue problem. Comptes Rendus des Seances de l'Academie des Sciences, Series I, Paris 1999; 328:823-828.
12. Peraire J, Patera AT. Asymptotic a-posteriori finite element bounds for the outputs of noncoercive problems: the Helmholtz and Burger's equations. Computer Methods in Applied Mechanics and Engineering 1999; 171:77-86.
13. Sarrate J, Peraire J, Patera AT. A-posteriori error bounds for nonlinear outputs of the Helmholtz equation. International Journal for Numerical Methods in Fluids 1999; 31:17-36.
14. Berenger J-P. A perfectly matched layer for the absorption of electromagentic waves. Journal of Computational Physics 1994; 114:185-200.
15. Ledger PD. Edge elements for waveguide and scattering problems. M.Sc. Thesis, University of Wales, Swansea, 1999.
16. Webb JP, Forghani B. Hierarchical scalar and vector tetrahedra. IEEE Transactions on Magnetics 1993; 29:1495-1498.
17. Abramowitz M, Stegun IA. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards, Washington, DC, 1964.
18. Kuzuoglu M, Mittra R. Investigation of nonplanar perfectly matched absorber for finite element mesh truncation. IEEE Transactions on Antennas and Propagation 1997; 45:474-486.
19. Stratton JA. Electromagnetic Theory. McGraw-Hill: New York, 1941.
20. Szab́o B, Babuska I. Finite Element Analysis. Wiley: New York, 1991.
21. Anderson E, Bai Z, Bischof C, Demmel J, Dongarra J, Du Choz J, Greenbaum A, Hammarling S, McKenney A, Ostrouchov S, Sorensen D. LAPACK Users Guide. SIAM: Philadelphia, 1992.
22. Ainsworth M, Senior B. Aspects of an adaptive hp-finite element method: adaptive strategy, conforming approximation and efficient solvers. Computer Methods in Applied Mechanics and Engineering 1997; 150: 65-87.
23. Ledger PD. Ph.D. Thesis, University of Wales, Swansea, 2002.
24. Demkowicz L. A-posteriori error analysis for steady state Maxwell's equations. In New Advances in Adaptive Computational Methods in Mechanics, Ladaveze P, Oden JT (eds). Elsevier: New York, 1998.
25. Peraire J, Patera AT. Bounds for linear functional outputs of coercive partial differential equations: local indicators and adaptive refinement. In New Advances in Adaptive Computational Methods in Mechanics, Ladaveze P, Oden JT (eds). Elsevier: New York, 1998.
26. Monk P. The near to far field transformation. International Journal for Computation and Mathematics in Electrical and Electronic Engineering 1995; 14:41-56.
27. Monk P, Suli E. The adaptive computation of far field patterns by a-posteriori error estimation of linear functionals. SIAM Journal of Numerical Analysis 1998; 36:251-274.
28. Monk P, Parott K. Phase accuracy and improved farfield estimates for 3-D edge elements on tetrahedral meshes. Journal of Computational Physics 2001; 170:614-641.
29. L̈ohner R, Morgan K, Zienkiewicz OC. Adaptive grid refinement for the compressible Euler equations. In Accuracy Estimates and Adaptive Refinements in Finite Element Computations, Babuska I et al. (eds). Wiley: Chichester, 1986; 281-297.