Geodesic
Application of semiorthogonal spline wavelets and the Galerkin method to the numerical simulation of thin wire antennas
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 727-736 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Bubnov–Galerkin method based on spline wavelets is used to solve singular integral equations. For the resulting systems of linear algebraic equations, the properties of their coefficient matrices are examined. Sparse approximations of these matrices are constructed by applying a cutting barrier. The results are used to numerically analyze thin wire antennas. Numerical results are presented. 
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I. A. Blatov; N. V. Rogova. Application of semiorthogonal spline wavelets and the Galerkin method to the numerical simulation of thin wire antennas. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 5, pp. 727-736. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_5_a3/

[1] Blatov I. A., “On estimates of the inverse matrices elements for the Galerkin method for singular integral equation based on the splain wavelets”, Proc. Internat. conference on comput. math., v. 2, Novosibirsk, 2002, 356–361 | MR

[2] Beylkin G., Coifman R., Rochlin V., “Fast wavelet transforms and numerical algorithms”, Comm. Pure. Appl. Math., 44 (1991), 141–183 | DOI | MR | Zbl

[3] Ford J. M., Tyrtyshnikov E. E., “Combining Kroneker product approximation with discrete wavelet transforms to solve dense, functional-related systems”, SIAM J. Sci. Comp., 25:3 (2003), 961–981 | DOI | MR | Zbl

[4] Ford J. M., Tyrtyshnikov E. E., Oseledets I. V., “Matrix approximation with solves using tensor products and non-standard wavelet transforms related to irregular grids”, Russ. J. Numer. Anal. Math. Modelling, 19 (2004), 185–204 | DOI | MR | Zbl

[5] Oseledets I. V., Tyrtyshnikov E. E., “Priblizhennoe obraschenie matrits pri reshenii gipersingulyarnogo integralnogo uravneniya”, Zh. vychisl. matem. i matem. fiz., 45:2 (2005), 315–326 | MR | Zbl

[6] Dahmen W., Harbrecht H., Schneider R., “Compression techniques for boundary integral equation. Asymptotically optimal complexity estimates”, SIAM J. Numer. Analys., 43:6 (2006), 2251–227 | DOI | MR

[7] Dahmen W., Harbrecht H., Schneider R., “Adaptive methods for boundary integral equations: Complexity and convergence estimates”, Math. Comput., 76:259 (2007), 1243–1274 | DOI | MR | Zbl

[8] Blatov I. A., “Ob algebrakh operatorov s psevdorazrezhennymi matritsami i ikh prilozheniya”, Sibirskii matem. zhurnal, 37:1 (1996), 36–59 | MR | Zbl

[9] Pissanetski S., Tekhnologiya razrezhennykh matrits, Mir, M., 1988 | MR

[10] Dobeshi I., Desyat lektsii po veivletam, NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevsk, 2001

[11] Oseledets I. V., “Primenenie razdelennykh raznostei i B-splainov dlya postroeniya bystrykh diskretnykh preobrazovanii veivletovskogo tipa na neravnomernykh setkakh”, Matem. zametki, 77:5 (2005), 743–752 | DOI | MR | Zbl

[12] Chui Ch., Vvedenie v veivlety, Mir, M., 2002

[13] Stolnits E., DeRouz T., Salezin D., Veivlety v kompyuternoi grafike, Mir, M., 2002

[14] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Metody splain-funktsii, Nauka, M., 1981 | MR