Finite element analysis of a scattering problem
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- by A. K. Aziz and R. Bruce Kellogg PDF
- Math. Comp. 37 (1981), 261-272 Request permission
Abstract:
A finite element method for the solution of a scattering problem for the reduced wave equation is formulated and analyzed. The method involves a reformulation of the problem on a bounded domain with a nonlocal boundary condition. The space of trial functions includes piecewise polynomial functions and functions arising from spherical harmonics.References
-
M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, U. S. Government Printing Office, Washington, D. C., 1965.
- M. S. Agranovič, Elliptic singular integro-differential operators, Uspehi Mat. Nauk 20 (1965), no. 5 (125), 3–120 (Russian). MR 0198017
- A. K. Aziz (ed.), The mathematical foundations of the finite element method with applications to partial differential equations, Academic Press, New York-London, 1972. MR 0347104 P. W. Barber, "Resonance electromagnetic absorption by non spherical dielectric objects," IEEE Trans. Microwave Theory. Tech, 1977, pp. 373-381.
- Jöran Bergh and Jörgen Löfström, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin-New York, 1976. MR 0482275 Peter Bettess "Infinite elements," Internat. J. Numer. Methods Engrg., v. 11, 1977, pp. 53-64. F. Brezzi & C. Johnson, On the Coupling of Boundary Coupling and the Finite Element Method, Dept. of Computer Science, Chalmers University of Technology, Report 77.15R, 1977.
- P. Grisvard, Caractérisation de quelques espaces d’interpolation, Arch. Rational Mech. Anal. 25 (1967), 40–63 (French). MR 213864, DOI 10.1007/BF00281421 B. G. Guru & K. N. Chen, "Experimental and theoretical studies on electromagnetic fields induced inside finite biological bodies," IEEE Trans. Microwave Theory Tech., v. 24, 1976, pp. 433-440. S. P. Marin, A Finite Element Method for Problems Involving the Helmholtz Equation in 2-Dimensional Exterior Regions, Doctoral Thesis, Carnegie-Mellon University, 1978. C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves, Springer-Verlag, New York, 1969.
- C. Müller and H. Kersten, Zwei Klassen vollständiger Funktionensysteme zur Behandlung der Randwertaufgaben der Schwingungsgleichung $\Delta U+k^{2}U=0$, Math. Methods Appl. Sci. 2 (1980), no. 1, 48–67 (German, with English summary). MR 561378, DOI 10.1002/mma.1670020106
- James M. Ortega, Numerical analysis. A second course, Computer Science and Applied Mathematics, Academic Press, New York-London, 1972. MR 0403154
- Alfred H. Schatz, An observation concerning Ritz-Galerkin methods with indefinite bilinear forms, Math. Comp. 28 (1974), 959–962. MR 373326, DOI 10.1090/S0025-5718-1974-0373326-0
- G. W. Stewart, Introduction to matrix computations, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. MR 0458818 J. A. Stratton, Electromagnetic Theory, McGraw-Hill, New York, 1941. K. Yosida, Functional Analysis, Grundlehren der Math. Wissenschaften, vol. 123, Springer-Verlag, Berlin and New York, 1975.
- O. C. Zienkiewicz, D. W. Kelly, and P. Bettess, The coupling of the finite element method and boundary solution procedures, Internat. J. Numer. Methods Engrg. 11 (1977), no. 2, 355–375. MR 451784, DOI 10.1002/nme.1620110210 A. K. Aziz, M. R. Dorr & R. B. Kellogg, A New Approximation Method for the Helmholtz Equation in an Exterior Domain, Technical Report, UMBC, 1981.
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 37 (1981), 261-272
- MSC: Primary 65N30; Secondary 35J05
- DOI: https://doi.org/10.1090/S0025-5718-1981-0628694-2
- MathSciNet review: 628694