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DTSTAMP:20221021T181552
DTSTART;TZID=America/Detroit:20221021T150000
DTEND;TZID=America/Detroit:20221021T160000
SUMMARY:Workshop / Seminar:Applied Interdisciplinary Mathematics (AIM) Seminar
DESCRIPTION: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))
UID:96563-21792891@events.umich.edu
URL:https://events.umich.edu/event/96563
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Mathematics
LOCATION:East Hall - 1084
CONTACT:
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