ACA accelerated high order BEM for Maxwell problems

Computational Mechanics

Volumn 51, Issue 4, 2013, Pages 431-441

  Rjasanow, Sergej ^a   Weggler, Lucy ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

Adaptive Cross Approximation; Boundary Element Methods; High order methods

Indexed keywords

ITERATIVE METHODS; MAXWELL EQUATIONS;

ADAPTIVE CROSS APPROXIMATION; HIGH-ORDER; HIGH-ORDER BOUNDARY ELEMENT METHODS; HIGH-ORDER METHODS; LINEAR COMPLEXITY; MEMORY REQUIREMENTS; SUB-MATRICES; TEST SPACE;

BOUNDARY ELEMENT METHOD;

EID: 84877115208     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-012-0731-9     Document Type: Conference Paper

References (21)

1. Balanis C (1989) Advanced engineering electromagnetics, engineering. Wiley, New York
2. Beatson RK, Cherrie JB, Mouat CT (1999) Fast fitting of radial basis functions: methods based on preconditioned GMRES iteration. Adv Comput Math 11: 253-270
3. Bebendorf M (2000) Approximation of boundary element matrices. Numer Math 86(4): 565-589
4. Bebendorf M, Grzhibovskis R (2006) Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation. Math Methods Appl Sci 29: 1721-1747
5. Bebendorf M, Rjasanow S (2003) Adaptive low-rank approximation of collocation matrices. Computing 70(1): 1-24
6. Bespalov A, Heuer N, Hiptmair R (2010) Convergence of the natural hp-BEM for the electric field integral equation on polyhedral surfaces. SIAM J Numer Anal 48(4):1518-1529
7. Buffa A, Ciarlet P Jr (2001) On traces for functional spaces related to Maxwell's equations. I. An integration by parts formula in Lipschitz polyhedra. Math Methods Appl Sci 24(1): 9-30
8. Buffa A, Costabel M, Sheen D (2002) On traces for H(curl, Ω) in Lipschitz domains. J Math Anal Appl 276(2): 845-867
9. Buffa A, Hiptmair R, von Petersdorff T, Schwab C (2003) Boundary element methods for Maxwell transmission problems in Lipschitz domains. Numer Math 95(3): 459-485
10. Demkowicz L (2007) Computing with hp-adaptive finite elements. Vol. 1. Applied mathematics and nonlinear science series. Chapman & Hall/CRC, Boca Raton
11. Demkowicz L, Kurtz J, Pardo D, Paszyński M, Rachowicz W, Zdunek A (2008) Computing with hp-adaptive finite elements. Vol. 2. Applied mathematics and nonlinear science series. Chapman & Hall/CRC, Boca Raton
12. FEKO ESS, Comprehensive electromagnetic solutions
13. Harrington R (2001) Time-harmonic electromagnetic fields. Wiley-IEEE Press, New York
14. Kurz S, Rain O, Rjasanow S (2002) The adaptive cross approximation technique for the 3D boundary element method. IEEE Trans Magn 38(2): 421-424
15. 3. Numer Math 35(3): 315-341
16. 3. Numer Math 50(1): 57-81
17. Nédélec JC (2001) Acoustic and electromagnetic equations. Springer, New York
18. Rjasanow S, Steinbach O (2007) The fast solution of boundary integral equations. Mathematical and analytical techniques with applications to engineering. Springer, New York
19. Schöberl J, Zaglmayr S (2005) High order N édélec elements with local complete sequence properties. COMPEL 24(2): 374-384
20. Stephan EP, Maischak M, Leydecker F (2007) An hp-adaptive finite element/boundary element coupling method for electromagnetic problems. Comput Mech 39(5): 673-680
21. Weggler L (2011) High order boundary element methods. Dissertation, Saarland University