1. Reflective conditions for radiative transfer in integral form with H-matrices.
- Author
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Pironneau, Olivier and Tournier, Pierre-Henri
- Subjects
- *
RADIATIVE transfer , *RADIATIVE transfer equation , *FINITE element method , *MULTIPLE scattering (Physics) , *ELECTROMAGNETIC radiation , *MATRIX multiplications - Abstract
In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective boundary conditions. The fixed point method to solve the system is shown to be monotone. The discretization is done with a P 1 Finite Element Method. The convolution integrals are precomputed at every vertex of the mesh and stored in compressed hierarchical matrices, using Partially Pivoted Adaptive Cross-Approximation. Then the fixed point iterations involve only matrix vector products. The method is O (N N 3 ln N) , with respect to the number of vertices, when everything is smooth. A numerical implementation is proposed and tested on two examples. As there are some analogies with ray tracing the programming is complex. • We present a method and a an algorithm using an H-matrix compression scheme to compute the temperature of a gas under electromagnetic radiations. • The method is now capable of handling reflective boundaries. • The paper improves on previously existing results and the numerical methods use state of the art computational tools. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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