Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics

IEEE Transactions on Antennas and Propagation

Volumn 45, Issue 3, 1997, Pages 316-328

  Hsiao, George C ^a   Kleinman, Ralph E ^a  

^a UNIVERSITY OF DELAWARE   (United States)

Author keywords

Integral equation methods; Numerical analysis

Indexed keywords

CALCULATIONS; ERRORS; ESTIMATION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; MAXWELL EQUATIONS; NUMERICAL ANALYSIS; THREE DIMENSIONAL;

ELECTRIC FIELD INTEGRAL EQUATIONS; GALERKIN METHOD; MAGNETIC FIELD INTEGRAL EQUATION; SOBOLEV SPACES;

ELECTROMAGNETIC FIELD THEORY;

EID: 0031097479     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/8.558648     Document Type: Article

References (41)

1. ME. M. KennaughMultipole field expansions and their use in approximate solutions of electromagnetic scattering problems, Ph.D. dissertation, Ohio State Univ., Dept. Elect. Eng., 1959.
2. MM. G. AndreasenScattering from parallel metallic cylinders with arbitrary cross-section, IEEE Trans. Antennas Propagat., vol. AP-12, pp. 746-754, Nov. 1964.
3. MJ. H. RichmondScattering by a dielectric cylinder of arbitrary cross section shape, Proc. IEEE, vol. 3, pp. 334-341, Aug. 1965.
4. MR. F. HarringtonField Computation by Moment Methods. New York: Macmillan, 1968.
5. MG. C. HsiaoR. E. Kleinman, R. X. Li, and P. M. van den Berg, Residual error-A simple and sufficient estimate of actual error in solutions of boundary integral equations, in Computational Engineering with Boundary Elements, Vol. 1: Fluid and Potential Problems, S. Grilli, C. A. Brebbia, and A. H. D. Cheng, Eds. Boston, MA: Computational Mechanics Publ., 1990, pp. 73-83.
6. MG. C. Hsiao and R. E. KleinmanFeasible error estimates in boundary element methods, Boundary Element Technology VII, C. A. Brebbia and M. S. Ingber, Eds. Boston, MA: Computational Mechanics Publ., 1991, pp. 875-886.
7. MP. M. van den BergA. P. M. Zwamborn, G. C. Hsiao, and R. E. Kleinman, Iterative solutions of first kind integral equations, Direct and Inverse Boundary Value Problems, R. E. Kleinman, R. Kress, and E. Martensen, Eds. Frankfurt, Germany: Lang, 1991, pp. 213-232.
8. MG. C. Hsiao and R. E. KleinmanError analysis in numerical solution of acoustic integral equations, Int. J. Numer. Meth. Eng., vol. 37, pp. 2921-2933, 1994.
9. MError control in numerical solution of boundary integral equations ACES, vol. 11, no. 1, pp. 32-36, 1996.
10. MM. FeistauerG. C. Hsiao, and R. E. Kleinman, Asymptotic and a posteriori estimates for boundary element solutions of hypersingular integral equations, SIAM J. Numer. Anal, vol. 33, pp. 666-685, Apr. 1996.
11. ME. F. KuesterComputable error bounds for variational functionals of solutions of a convolution integral equation of the first kind, Wave Motion, vol. 22, 171-185, 1995.
12. MY. G. SmirnovOn the Fredholm problem for the diffraction by a plane, but perfectly conducting screen, Sov. Phy. Dokl, vol. 36, pp. 512-513, July 1991.
13. MFredhomness of systems of pseudo differential equations in the problem of diffraction on a bounded screen Differential Equal., vol. 28, pp. 130-136, 1991.
14. MSolvability of integrodifferential equations in the problem of diffraction by a perfectly conducting plane screen Sov. J. Comm. Tech. Elec., vol. 37, pp. 118-121, 1992.
15. MOn the solvability of vector problems of diffraction in regions that are connected to an aperture in the screen Computat. Math. Mathem. Phys., vol. 33, pp. 1263-1273, 1993.
16. MOn the solvability of vector integrodifferential equations in the problem of the diffraction of an electromagnetic field by screens of arbitrary shape Computat. Math. Mathem. Phys., vol. 34, no. 10, pp. 1265-1276, 1994.
17. MA. S. Il'lnskiy and Yu. G. SmirnovIntegral equations for problems of wave diffraction at screens, Sov. J. Communicat. Tech. Elect., vol. 39, no. 4, 129-136, 1994.
18. MJ. A. Stratton and L. J. ChuDiffraction theory of electromagnetic waves, Phy. Rev., vol. 56, pp. 99-107, July 1939.
19. MW. V. IgnatowskyDiffraktion and reflexion, abgeleitet aus den Maxwellscher Gliechungen, Ann. D. Phys., vol. 23, pp. 875-906, 1907; vol. 25, pp. 99-117, 1908.
20. MD. Colton and R. KressIntegral Equation Methods in Scattering Theory. New York: Wiley, 1984.
21. MA. J. Poggio and E. K. MillerIntegral equation solutions of three-dimensional scattering problems, in Computer Techniques for Electromagnetics, R. Mittra, Ed. Oxford: Pergamon, 1973, pp. 159-264.
22. MA. W. MaueZur Formuliering, eines allgemenen Beugungsproblems durch eine Integralgleichung, Z. Phys., vol. 126, no. 7, pp. 601-618, 1949.
23. MF. H. MurrayConductors in an electromagnetic field, Amer. J. Mathem., vol. 53, pp. 275-288, 1931.
24. MJ. R. Mautz and R. F. HarringtonH-field, E-field, and combinedfield solutions for conducting bodies of revolution, Arch. Elektron Übertragungstech., Electron. Commun., vol. 32, no. 4, pp. 159-164, 1978.
25. MA. D. YaghjianAugmented electric-and-magnetic integral equations, Radio Sei., vol. 16, pp. 987-1001, Nov./Dec. 1981.
26. MG. JostIntegral equations with modified fundamental solution in time-harmonic electromagnetic scattering, IMA J. Applicat. Mathem., vol. 40, pp. 129-143, 1988.
27. MA. de La BourdonnayeSome formulations coupling finite element and integral equation methods for Helmholtz equation and electromagnetism, Numer. Mathem., vol. 69, pp. 257-268, 1995.
28. 1/2 (F) et nature de lopérateur de Steklov-Poincaré du problème extérieur de l'électomagnétisme Note CR.A.S.t.316, Série I., 1993, pp. 369-372.
29. MC. MirandaPartial Differential Equations of Elliptic Type, 2nd ed. New York: Springer-Verlag, 1970.
30. MJ. L. Lions and E. MagenesNon-Homogeneous Boundary Value Problems and Applications. Berlin: Springer, 1972, vol. I.
31. MA. BendaliNumerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method-Part 1 : The continuous problem; Part 2: The discrete problem, Mathem. Computat., vol. 43, p. 167, 1984.
32. MT. AbboudEtude mathématique et numérique de quelques problèmes de diffraction d'ondes électromagnéques, thesis, L'Ecole Polytech., Palaiseau, France, 1991.
33. MV. LevillainCouplage éléments finis-équations de Maxwell en milieu hétérogène, Ph.D. thesis, École Polytech., 1991.
34. MT. Abboud and J. C. NedelecElectromagnetic waves in inhomogeneus medium, Centre de Mathém. Appliquées de l'École Polytech., Rapoert Interne, p. 203.
35. MT. Abboud and F. StarlingScattering of an electromagnetic wave by a screen, in Boundary Value Problems and Integral Equations in Non-Smooth Domains, Lecture Notes in Pure and Applied Mathematics. New York: Marcel Dekker, 1995, vol. 167, pp. 1-17.
36. MR. Dautray and J. L. LionsMathematical analysis and numerical methods for science and technology, Spectral Theory and Applications. New York: Springer-Verlag, 1990, vol. 3.
37. MM. KernÉtude mathématique et numérique d'un modèle de propagation du champ électrique en unilieu conducteur tridimensionel, Ph.D. thesis, LÉcole Polytech., Palaiseau, France, 1991.
38. MS. G. MikhlinMultidimensional Singular Integrals and Integral Equations. New York: Pergamon, 1965.
39. MD. S. JonesAcoustic and Electromagnetic Waves. Oxford: Clarendon, 1986.
40. MM. Abramowitz and L. A. StegunHandbook of Mathematical Functions with Formulas, Graphs, and Mathmatical Tables, Nat. Bureau Standards, 1964.
41. MI. StakgoldGreen's Functions and Boundary Value Problems. New York: Wiley, 1979.