Solving eigenvalues problems for Helmholtz equation by point-source method
https://doi.org/10.12737/20227
Abstract
References
1. Fairweather, G., Karageorghis, A. The method of fundamental solutions for elliptic boundary value problems. Ad. Vol. Comput. Math., 1998, vol. 9, pp. 69–95.
2. Alves, C.J.S., Chen, C.S. A new method of fundamental solutions applied to nonhomogeneous elliptic problems. Advances in Computational Mathematics, 2005, vol. 23, pp. 125–142.
3. Knyazev S.Y. Ustoychivost' i skhodimost' metoda tochechnykh istochnikov polya pri chislennom reshenii kraevykh zadach dlya uravneniya Laplasa. [Stability and Convergence of Point-Source Field Method at Numerical Solution to Boundary Value Problems for Laplace Equation]. Russian Electromechanics, 2010, no. 1, pp. 3–12 (in Russian).
4. Knyazev, S.Y., Shcherbakova, E.E., Yengibaryan, A.A. Chislennoe reshenie kraevykh zadach dlya uravneniya Puassona metodom tochechnykh istochnikov polya. [Numerical solution of the boundary problems with Poisson equation by point-source method.] Vestnik of DSTU, 2014. Vol. 14. No. 2(77). pp. 15–20 (in Russian).
5. Knyazev S.Y., Shcherbakova E.E. Reshenie trekhmernykh kraevykh zadach dlya uravneniy Laplasa s pomoshch'yu metoda diskretnykh istochnikov polya. [The Decision of the Three-Dimensional Boundary Value Problems for the Laplace Equation Using the Method of Discrete Sources of the Field.] Russian Electromechanics, 2015, no. 5, pp. 25–30 (in Russian).
6. Bakhvalov, Y.A., Knyazev, S.Y., Shcherbakov, A.A., Shcherbakova, E.E. Pogreshnost' metoda tochechnykh istochnikov pri modelirovanii potentsial'nykh poley v oblastyakh s razlichnoy konfiguratsiey. [Errors of Point Source Method under Simulation of Potential Fields in Areas with Different Shape Configuration.] Russian Electromechanics, 2012, no. 5, pp. 17–21 (in Russian).
7. Knyazev, S.Y., Shcherbakova, E.E., Zaichenko, A.N. Sravnitel'nyy analiz dvukh variantov metoda kollokatsiy pri chislennom modelirovanii potentsial'nykh poley. [A Comparative Analysis of the Two Variants of the Collocation in Numerical Modeling of Potential Fields.] Russian Electromechanics, 2014, no. 1, pp. 17–19 (in Russian).
8. Knyazev, S.Y., Shcherbakova, E.E. Reshenie zadach teplo i massoperenosa s pomoshch'yu metoda tochechnykh istochnikov polya. [Solving problems of heat and mass transfer by the point source method.]University News. North- Caucasian region. Technical Sciences Series, 2006, no. 4, pp. 43–47 (in Russian).
9. Knyazev, S.Y., Pustovoyt, V.N., Shcherbakova, E.E. Modelirovanie poley uprugikh deformatsiy s primeneniem metoda tochechnykh istochnikov. [Modeling the elastic strain fields by point-source method.] Vestnik of DSTU, 2015, vol. 15, no. 1(80), pp. 29– 38 (in Russian).
10. Knyazev, S.Y., Pustovoyt, V.N., Shcherbakova, E.E. Modelirovanie trekhmernykh poley uprugikh deformatsiy s pomoshch'yu metoda tochechnykh istochnikov. [Modeling of three-dimensional elastic strain fields by point-source method.] Vestnik of DSTU, 2015, vol. 15, no. 4 (83), pp. 13–23 (in Russian).
11. Knyazev, S.Y., Shcherbakova, E.E., Shcherbakov, A.A. Sravnitel'nyy analiz razlichnykh variantov ispol'zovaniya metoda tochechnykh istochnikov polya pri modelirovanii temperaturnykh poley. [A comparative analysis of various variants of the point source method application in the temperature field simulation.] Physical and mathematical system modeling: Proc. XII Int. Workshop. Voronezh, 2014, pp. 52–56 (in Russian).
12. Lunin, L.S., Knyazev, S.Y., Seredin, B.M., Polukhin, A.S., Shcherbakova, E.E. Issledovanie stabil'nosti termomigratsii ansamblya lineynykh zon s pomo-shch'yu trekhmernoy komp'yuternoy modeli, postroennoy na osnove metoda tochechnykh istochnikov polya. [The study of stability of thermomigration of an ensemble of linear zones using a threedimensional computer model constructed on the basis of the field point sources method.] Vestnik SSC RAS, 2015, vol. 11, number 4, pp. 9–15 (in Russian).
13. Knyazev, S.Y., Shcherbakova, E.E., Shcherbakov, A.A. Matematicheskoe modelirovanie poley uprugikh deformatsiy metodom tochechnykh istochnikov polya. [Mathematical modeling of elastic deformation fields by the point source method.] Mathematical Methods in Engineering and Technologies, 2015, no. 5 (75), pp. 21–23 (in Russian).
14. Knyazev S.Y., Shcherbakova E.E., Shcherbakov A.A. Komp'yuternoe modelirovanie potentsial'nykh poley metodom tochechnykh istochnikov. [Computer modeling of potential fields by the point source method.] Rostov-on-Don: DSTU Publ. Centre, 2012, 156 p. (in Russian).
15. Knyazev, S.Y. Metod tochechnykh istochnikov dlya komp'yuternogo modelirovaniya fizicheskikh poley v zadachakh s podvizhnymi granitsami: dis. …doktora tekhn. nauk. [Point source method for computer modeling of physical fields in moving boundary problems: Dr.Sci. (Eng.) diss.] Novocherkassk, 2011, 342 p. (in Russian)
16. Knyazev, S.Y., Shcherbakova, E.E. Chislennoe issledovanie stabil'nosti termomigratsii ploskikh zon. [Numerical study of thermomigration stability of flat bands.] Russian Electromechanics, 2007, no. 1, pp. 14–19 (in Russian).
17. Bakhvalov, Y.A., Knyazev, S.Y., Shcherbakov, A.A. Matematicheskoe modelirovanie fizicheskikh poley metodom tochechnykh istochnikov. [Mathematical modeling of physical fields by a method of dot sources.] Bulletin of the Russian Academy of Sciences: Physics, 2008, vol. 72, no. 9, pp. 1259–1261 (in Russian).
18. Knyazev, S.Y. Chislennoe reshenie uravneniy Puassona i Gel'mgol'tsa s pomoshch'yu metoda tochechnykh istochnikov. [Numerical solution of Poisson and Helmholtz equations using the point source method.] Russian Electromechanics, 2007, no. 2, pp. 77–78 (in Russian).
19. Knyazev, S.Y., Shcherbakova, E.E., Zaichenko, A.N. Chislennoe reshenie kraevykh zadach dlya neodnorodnykh uravneniy Gel'mgol'tsa metodom tochechnykh istochnikov polya. [Numerical solution for inhomogeneous Helmholtz equation by the point source method.] Russian Electromechanics, 2014, no. 4, pp. 14–19 (in Russian).
20. Abramowitz, A., Stegun, L. Spravochnik po spetsial'nym funktsiyam. [Handbook of Mathematical Functions.]. Moscow, Nauka, 1979, 832 p. (in Russian).
21. Polyanin, A.D. Spravochnik po lineynym uravneniyam matematicheskoy fiziki. [Handbook of linear equations in mathematical physics.] Moscow, Fizmatlit, 2001, 576 p. (in Russian).
Review
For citations:
Shcherbakova E.E. Solving eigenvalues problems for Helmholtz equation by point-source method. Vestnik of Don State Technical University. 2016;16(3):87-95. (In Russ.) https://doi.org/10.12737/20227