Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

A Double Spherical Harmonic Solution to the Radiative Transport Equation

Sean Horan
Saturday, April 25, 2020
11:00 am - 11:50 am
Virtual via Zoom

Talk Abstract:

The propogation of radiant energy inside a scattering and absorbing medium on mezzo to macro scales is governed by the radiative transport equation. Solutions to this integal-differential equation are of great use in biomedical optics, computer graphics, reactor physics and other application. These solutions have generally taken two forms: computationally expensive Monte Carlo simulations which provide high degrees of detail and more efficient, deterministic solutions which provide significantly less accuracy, often used to construct functionals of radiant energy rather than the energy itself. Here I present a new, deterministic solution to this equation based on a double spherical harmonic basis. This method provides a far higher level of detail in reconstructing radiant energy as a function of position and angle than previous deterministic methods. The accuracy of reconstruction in biologically relevant cases compares better to a Monte Carlo "gold standard" than any other fast deterministic method and computes its solutions tens of thousands to millions of times faster than these gold standards..

About the Speaker:

Sean is a 5th year graduate student working on applied mathematics.

Refreshments:

Pizza will be served after the talk.