On the Definition of Surface Potentials for Finite-Difference Operators

Journal of Scientific Computing

Volumn 18, Issue 2, 2003, Pages 155-189

  Tsynkov, S V ^a,b  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Boundary integral; Convolution; Dipole; Discontinuous solution; Distribution; Fundamental solution; Linear differential operator; Monopole; Single and double layer potentials; Surface density of the potential

Indexed keywords

BOUNDARY INTEGRALS; CALDERON POTENTIAL; DIFFERENCE POTENTIAL; DIPOLES; DISCONTINOUS SOLUTION; DOUBLE LAYER POTENTIAL; LINEAR DIFFERENCE OPERATOR; LINEAR DIFFERENTIAL OPERATORS; MONOPOLES; MULTI LAYER GRID BOUNDARY;

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONTROL SYSTEMS; DIFFERENTIATION (CALCULUS); FINITE DIFFERENCE METHOD; GREEN'S FUNCTION; PROBLEM SOLVING;

LINEAR ALGEBRA;

EID: 0043257725     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021111713715     Document Type: Article

References (21)

1. Calderon, A. P. (1963). Boundary-value problems for elliptic equations. In Proceedings of the Soviet-American Conference on Partial Differential Equations at Novosibirsk, Moscow, Fizmatgiz, pp. 303-304.
2. Kamenetskii, D. S. (1995). The Method of Difference Potentials: Certain Problems of Modified Calderon Potentials, Parts I-III, Technical Report 94-96, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, (In Russian).
3. Kamenetskii, D. S. (1998). Difference potentials and the parameterization of solutions of homogeneous difference equations. Comput. Math. Math. Phys. 38(11), 1754-1767.
4. Kamenetskii, D. S. (1999). Difference generalized Poincaré-Steklov operators and potentials with density from a space of jumps. Comput. Math. Math. Phys. 39(8), 1275-1282.
5. Kamenetskii, D. S. (2000). On one form of representing the difference potentials. Appl. Numer. Math. 33(1-4), 501-508.
6. Lončarić, J., Ryaben'kii, V. S., and Tsynkov, S. V. (2001). Active shielding and control of noise. SIAM J. Appl. Math. 62(2), 563-596.
7. Lončarić, J., and Tsynkov, S. V. (2002a). Quadratic optimization in the problems of active control of sound. Technical Report 2002-35, NASA/CR-2002-211939, ICASE, Hampton, VA, October 2002; submitted to SIAM J. Appl. Math..
8. Lončarić, J., and Tsynkov, S. V. (2002b). Optimization of acoustic source strength in the problems of active noise control. SIAM J. Appl. Math., to appear; also Technical Report 2002-11, NASA/CR-2002-211636, ICASE, Hampton, VA, May 2002.
9. Nelson, P. A., and Elliot, S. J. (1999). Active Control of Sound, San Diego, Academic Press.
10. Proskurowski, W., and Widlund. O. (1976). On the numerical solution of Helmholtz's equation by the capacitance matrix method. Math. Comp. 30, 433-468.
11. Ryaben'kii, V. S. (1971). The method of internal boundary conditions in the theory of boundary value difference problems. Russian Math. Surveys 26, 117-176.
12. Ryaben'kii, V. S. (1985). Boundary equations with projections. Russian Math. Surveys 40, 147-183.
13. Ryaben'kii, V. S. (1987). Difference Potentials Method for Some Problems of Continuous Media Mechanics, Moscow, Nauka. In Russian.
14. Ryaben'kii, V. S. (1995). A difference screening problem, Funct. Anal. Appl. 29, 70-71.
15. Ryaben'kii, V. S. (1998). A Nonlinear Difference Shielding Problem. In Bach, M., Constanda, C., Hsiao, G. C., Sandig, A.-M., and Werner, P. (eds.), Analysis, Numerics, and Applications of Differential and Integral Equations, Longman, Harlow, pp. 179-182.
16. Ryaben'kii, V. S. (2002). Method of Difference Potentials and Its Applications, Berlin, Springer-Verlag.
17. Seeley, R. T. (1966). Singular integrals and boundary value problems. Amer. J. Math. 88, 781-809.
18. Tikhonov, A. N., and Samarskii, A. A. (1963). Equations of Mathematical Physics, Oxford, Pergamon Press.
19. Veizman, R. I., and Ryaben'kii, V. S. (1997a). Difference problems of screening and simulation. Dokl. Akad. Nauk 354, 151-154.
20. Veizman, R. I., and Ryaben'kii, V. S. (1997b). Difference simulation problems. In Transactions of Moscow Mathematics Society, pp. 239-248.
21. Vladimirov, V. S. (1971). Equations of Mathematical Physics, New-York, Dekker.