The development of an hp-adaptive finite element procedure for electromagnetic scattering problems

Finite Elements in Analysis and Design

Volumn 39, Issue 8, 2003, Pages 751-764

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

^a SWANSEA UNIVERSITY   (United Kingdom)

^b Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

A posteriori error estimation; hp adaptivity; Maxwell's equations; N d lec's curl conforming elements; Reduced order model

Indexed keywords

COMPUTER SIMULATION; ELECTROMAGNETISM; MAXWELL EQUATIONS; PROBLEM SOLVING; SCATTERING;

ELECTROMAGNETIC SCATTERING PROBLEMS;

FINITE ELEMENT METHOD;

EID: 0037404313     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(03)00057-X     Document Type: Conference Paper

References (30)

1. Peraire J., Vahdati M., Morgan K., Zienkiewicz O.C. Adaptive remeshing for compressible flow calculations. J. Comput. Phys. 72:1987;449-466.
2. Peraire J., Perió J., Morgan K. Adaptive re-meshing for three-dimensional compressible flow computations. J. Comput. Phys. 103:1992;269-285.
3. Morgan K., Hassan O., Peraire J. A time domain unstructured grid approach to the simulation of electromagnetic scattering in piecewise homogeneous media. Comput. Meth. Appl. Mech. Eng. 134:1996;17-36.
4. E. Darve, R. Löhner, Advanced structured-unstructured solver for electromagnetic scattering from multimaterial objects, AIAA Paper 97-0863, 1997.
5. Morgan K., Brookes P.J., Hassan O., Weatherill N.P. Parallel processing for the simulation of problems involving scattering of electromagnetic waves. Comput. Methods Appl. Mech. Eng. 152:1998;157-174.
6. 3 by finite element methods SIAM J. Numer. Anal. 15:1978;580-594.
7. 3 Numer. Math. 35:1980;315-341.
8. 3 Numer. Math. 50:1986;57-81.
9. Monk P. Analysis of a finite element method for Maxwell's equations. SIAM J. Numer. Anal. 29:1992;714-729.
10. 3 SIAM J. Appl. Math. 55:1995;1324-1344.
11. L. Demkowicz, W. Rachowicz, A 2D hp-adaptive finite element package for electromagnetics (2Dhp90em), TICAM Report 98-15, University of Texas at Austin, 1998.
12. Demkowicz L., Vardapetyan L. Modeling of electromagnetic/scattering problems using hp-adaptive finite elements. Comput. Methods Appl. Mech. Eng. 152:1998;103-124.
13. Ainsworth M., Coyle J. Hierarchic hp-edge element families for Maxwell's equations on hybrid quadrilateral/triangular meshes. Comput. Methods Appl. Mech. Eng. 190:2001;6709-6733.
14. Ledger P.D., Morgan K., Hassan O., Weatherill N.P. Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML. Int. J. Numer. Methods Eng. 55:2002;339-358.
15. P.D. Ledger, An hp-adaptive finite element procedure for electromagnetic scattering problems, Ph.D. Thesis, University of Wales, Swansea, 2001.
16. Ainsworth M., Oden J.T. A Posteriori Error Estimation in Finite Element Analysis. 2000;Wiley, New York.
17. Demkowicz L. A posteriori error analysis for steady state Maxwell's equations. Ladaveze P., Oden J.T. New Advances in Adaptive Computational Methods in Mechanics. 1998;Elsevier, Amsterdam.
18. Paraschivoiu M., Peraire J., Patera A.T. A posteriori finite element bounds for linear functional output of elliptic partial differential equations. Comput. Meth. Appl. Mech. Eng. 150:1997;289-312.
19. Maday Y., Peraire J., Patera A.T. A general formulation for a posteriori bounds for output functionals of partial differential equations. application to the eigenvalue problem C.R. Acad. Sci. Paris. 328 Ser. I:1999;823-828.
20. Peraire J., Patera A.T. Asymptotic a posteriori finite element bounds for the outputs of noncoercive problems. the Helmholtz and Burgers equations Comput. Methods Appl. Mech. 171:1999;77-86.
21. Sarrate J., Peraire J., Patera A.T. A posteriori error bounds for nonlinear outputs of the Helmholtz equation. Int. J. Numer. Methods Fluids. 31:1999;17-36.
22. P.D. Ledger, J. Peraire, K. Morgan, O. Hassan, N.P. Weatherill, Adaptive hp finite element computations of the scattering width output of Maxwell's equations, Int. J. Numer. Methods Fluids 42 (2003), in press.
23. K.E. Wilcox, J.D. Paduano, J. Peraire, Low order aerodynamic models for aeroelastic control of turbomachines, AIAA Paper 99-1467, 1999.
24. Wilcox K.E., Peraire J., White J. An Arnoldi approach for generation of reduced order models for turbmachinery. Comput. Fluids. 31:2002;369-389.
25. Machiels L., Maday Y., Patera A.T. Output bounds for reduced-order approximations of partial differential equations. Comput. Methods Appl. Mech. Eng. 190:2001;3413-3426.
26. Y. Maday, A.T. Patera, D.V. Rovas, A reduced-basis output bound method for noncoercive linear problems, Technical Report, Laboratoire d'Analyse Numérique, Universite Paris VI, 2000.
27. Berenger J.-P. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114:1994;185-200.
28. Kuzuoglu M., Mittra R. Investigation of nonplanar perfectly matched absorber for finite element mesh truncation. IEEE Trans. Antennas Propagation. 45:1997;474-486.
29. Stratton J.A. Electromagnetic Theory. 1941;McGraw-Hill, New York.
30. Peraire J., Patera A.T. Bounds for linear functional outputs of coercive partial differential equations: local indicators and adaptive refinement. Ladaveze P., Oden J.T. New Advances in Adaptive Computational Mechanics. 1998;Elsevier, Amsterdam.