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Adaptive finite element simulation of the time-dependent simplified \(P_N\) equations. (English) Zbl 1368.65191

Summary: The steady-state simplified \(P_N\) approximation to the radiative transfer equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified \(P_N\) equations have been derived by an asymptotic analysis similar to the asymptotic derivation of the steady-state \(SP_N\) equations [M. Frank et al., J. Comput. Phys. 226, No. 2, 2289–2305 (2007; Zbl 1128.65107)]. In this paper, we present computational results for the time-dependent \(SP_N\) equations in two dimensions, obtained by using an adaptive finite element approach. Several numerical comparisons with other existing models are shown.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
78A60 Lasers, masers, optical bistability, nonlinear optics
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
85A25 Radiative transfer in astronomy and astrophysics

Citations:

Zbl 1128.65107

Software:

KARDOS; RODAS
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Full Text: DOI arXiv

References:

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