Volume 1, Issue 2
A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation

Hongkai Zhao & Yimin Zhong

CSIAM Trans. Appl. Math., 1 (2020), pp. 346-364.

Published online: 2020-07

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  • Abstract

In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity from $\mathcal{O}$($M$2+1/$d$) to $\mathcal{O}$($M$1+1/$d$log$M$), where $M$ is the number of points in the physical domain. The error analysis is presented and numerical experiments are performed to validate our algorithm.

  • Keywords

Radiative transport equation, volume integral equation, treecode algorithm.

  • AMS Subject Headings

45K05, 65N22, 65N99, 65R20, 65Y10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CSIAM-AM-1-346, author = {Hongkai Zhao , and Yimin Zhong , }, title = {A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {2}, pages = {346--364}, abstract = {

In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity from $\mathcal{O}$($M$2+1/$d$) to $\mathcal{O}$($M$1+1/$d$log$M$), where $M$ is the number of points in the physical domain. The error analysis is presented and numerical experiments are performed to validate our algorithm.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0012}, url = {http://global-sci.org/intro/article_detail/csiam-am/17182.html} }
TY - JOUR T1 - A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation AU - Hongkai Zhao , AU - Yimin Zhong , JO - CSIAM Transactions on Applied Mathematics VL - 2 SP - 346 EP - 364 PY - 2020 DA - 2020/07 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0012 UR - https://global-sci.org/intro/article_detail/csiam-am/17182.html KW - Radiative transport equation, volume integral equation, treecode algorithm. AB -

In this work, we introduce a fast numerical algorithm to solve the time-dependent radiative transport equation (RTE). Our method uses the integral formulation of RTE and applies the treecode algorithm to reduce the computational complexity from $\mathcal{O}$($M$2+1/$d$) to $\mathcal{O}$($M$1+1/$d$log$M$), where $M$ is the number of points in the physical domain. The error analysis is presented and numerical experiments are performed to validate our algorithm.

Hongkai Zhao & Yimin Zhong. (2020). A Fast Algorithm for Time-Dependent Radiative Transport Equation Based on Integral Formulation. CSIAM Transactions on Applied Mathematics. 1 (2). 346-364. doi:10.4208/csiam-am.2020-0012
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