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Applied Interdisciplinary Mathematics (AIM) Seminar

Numerical Solution of the Steady State Fokker-Planck Equation
Friday, October 21, 2022
3:00-4:00 PM
1084 East Hall Map
The Fokker-Planck equation (FPE) has important applications to radiative transfer, for example ion and photon transport in biological tissue. The equation describes the radiation intensity for a given choice of absorption and scattering coefficients. This work proposes finite-difference methods for the steady state Fokker-Planck equation in one space dimension and two angle variables (polar µ, azimuthal θ). The talk focuses on a direct method based on a Crank-Nicolson discretization of the transport term in the FPE. Two problems are considered. In the first problem, the solution is independent of the azimuthal angle θ and convergence is studied with respect to grid refinement. In the second problem, the dependence on the azimuth angle θ is not neglected; using Fourier techniques, the problem is divided into a set of θ-independent problems whose absorption coefficients become singular, which requires a modification of the scheme. Finally, preliminary results using this method will be presented for the time-dependent FPE. Speaker(s): Nizomjon Jumaniyazov (Tashkent University of Information Technologies (Urgench branch))
Building: East Hall
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics, Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics