Determination of the diffusion coefficient
- 55 Downloads
A multilevel algorithm for solving the inverse problem for the diffusion equation by the optimization method using Laguerre functions is considered. Numerical calculations are carried out for Maxwell’s equations in a one-dimensional formulation in the diffusion approximations. Using the known solution, we find the medium’s conductivity distribution at some point of space. The function of the Laguerre harmonics is minimized by Newton’s method and the conjugate gradients technique. We investigate the influence of the form of the source of the electromagnetic waves and its spectrum on the solution’s accuracy for the inverse problem. The accuracy of this solution obtained by a multi-level algorithm and using conventional single-level algorithms is compared.
Keywordsdiffusion coefficient Maxwell’s equations multilevel method Laguerre’s method
Unable to display preview. Download preview PDF.
- 1.L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon, New York, 1984).Google Scholar
- 2.Electrical Prospecting. Geophysicist’s Manual, Ed. by G. Tarkhov (Nedra, Moscow, 1980) [in Russian].Google Scholar
- 3.J. Beck, B. Blackwell, and C. St.-Clair, Inverse Heat Conduction Ill-Posed Problem (Wiley, New York, 1985; Mir, Moscow, 1989).Google Scholar
- 4.A. N. Tikhonov and V. Ya. Arsenin, Solution of Ill-Posed Problems (Wiley, New York, 1977; Nauka, Moscow, 1979).Google Scholar
- 6.F. P. Vasil’ev, Numerical Methods for Solving Extremal Problems (Nauka, Moscow, 1980), p. 518 [in Russian].Google Scholar
- 10.A. F. Mastryukov, “Inverse solution to the diffusion equation using the Laguerre spectral transform,” Mat. Model., No. 9, 15–26 (2007).Google Scholar
- 15.A. F. Mastryukov, “Recovery of two-dimensional conductivity of medium by optimization method,” Geol. Geofiz., No. 3, 686–692 (1997).Google Scholar
- 18.M. I. Epov, V. L. Mironov, S. A. Komarov, and K. V. Muzalevskii, “Ultrabroadband electromagnetic wave propagation in hydrocarbon reservoirs in the presence of an oil-water interface,” Russ. Geol. Geophys., No. 1, 46 (2009).Google Scholar