A fast algorithm for time-dependent radiative transport equation based on integral formulation

arXiv2001.10050MaRDI QIDQ6333593

Publication date: 27 January 2020

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 O(M^{2+1/d} ) to 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.

Has companion code repository: https://github.com/lowrank/treecode_rte

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22) Numerical methods for partial differential equations, boundary value problems (65N99) Numerical algorithms for specific classes of architectures (65Y10)

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