Quadruple and octuple layer potentials in two dimensions I: Analytical apparatus

Applied and Computational Harmonic Analysis

Volumn 14, Issue 1, 2003, Pages 47-74

  Kolm, Petter ^a   Jiang, Shidong ^b   Rokhlin, Vladimir ^b  

^a YALE UNIVERSITY   (United States)

^b Yale University   (United States)

Author keywords

Hypersingular integral equations; Laplace equation; Potential theory; Pseudo differential operators

Indexed keywords

BOUNDARY VALUE PROBLEMS; ELASTIC WAVES; GREEN'S FUNCTION; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; MAXWELL EQUATIONS; PROBLEM SOLVING;

COMPUTATIONAL ELECTROMAGNETICS; MATHEMATICAL PHYSICS;

LAPLACE TRANSFORMS;

EID: 0242573575     PISSN: 10635203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1063-5203(03)00004-6     Document Type: Article

References (20)

1. A. J. Burton, G.F. Miller, The application of integral equation methods to the numerical solution of some exterior boundary-value problems, Proc. Roy. Soc. London A 323 (1971) 201-210.
2. H. Cheng, V. Rokhlin, N. Yarvin, Non-linear optimization, quadrature, and interpolation, Tech. Rep. YALEU/DCS/RR-1169, Computer Science Department, Yale University, 1998.
3. D. Colton, R. Kress, Integral Equation Methods in Scattering Theory, John Wiley & Sons, 1983.
4. M.P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, New York, 1976.
5. M.A. Epton, B. Dembart, Multipole translation theory for the 3-D Laplace and Helmholtz equations, SIAM J. Sci. Comp. 10 (1995) 865-897.
6. L. Greengard, V. Rokhlin, A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numer. 6 (1997) 229-269.
7. J. Hadamard, Lectures on the Cauchy's Problem in Linear Partial Differential Equations, Dover, 1952.
8. S. Kapur, V. Rokhlin, High-order corrected trapezoidal rules for singular functions, SIAM J. Numer. Anal. 34 (1997) 1331-1356.
9. Y. Katznelson, An Introduction to Harmonic. Analysis, Dover, 1976.
10. P. Kolm, V. Rokhlin, Numerical quadratures for singular and hypersingular integrals, Tech. Rep. YALEU/DCS/RR-1190, Computer Science Department, Yale University, 2000.
11. P. Kolm, V. Rokhlin, Quadruple and Octuple Layer Potentials in Two Dimensions II: Numerical Techniques, in preparation.
12. R. Kress, Linear Integral Equations, Springer, 1989.
13. J.R. Mautz, R.F. Harrington, H-field, E-field, and combined field solutions for conducting bodies of revolution, AEU 32 (1978) 157-164.
14. S.G. Mikhlin, Integral Equations and Their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology, Pergamon Press, 1957.
15. A.F. Peterson, The "Interior resonance" problem associated with surface integral equations of electromagnetics: Numerical consequences and a survey of remedies, J. Electromagn. Waves Appl. 10 (1990) 293-312.
16. V. Rokhlin, End-point corrected trapezoidal quadrature rules for singular functions, Comput. Math. Appl. 20 (1990) 51-62.
17. A. Sidi, M. Israeli, Quadrature methods for periodic singular and weakly singular Fredholm integral equations, J. Sci. Comp. 3 (1988) 201-231.
18. J. Song, W.C. Chew, The fast Illinois solver code: Requirements and scaling properties, IEEE Comput. Sci. Engrng. (1998) 19-23.
19. R.L. Wheeden, A. Zygmund, Measure and Integral: An Introduction to Real-Analysis, Dekker, 1977.
20. Y. Yan, I.H. Sloan, On integral equations of the first kind with logarithmic kernels, J. Integral Equations Appl. 1 (1988) 549-579.