Formal Solutions for Polarized Radiative Transfer. III. Stiffness and Instability

Janett, Gioele; Paganini, Alberto

doi:10.3847/1538-4357/aab3d9

Cited by 18 publications

(27 citation statements)

References 25 publications

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“…solver, the latter is exactly equivalent to a Hermite method (Auer 2003;Ibgui et al 2013). The accuracy of these methods has been recently analyzed in great detail for the polarized case by Janett et al (2017) and Janett & Paganini (2018). We found an unfortunate mistake in the transcription of the cubic Bezier integration coefficients reported by de la Cruz Rodríguez & Piskunov (2013).…”

Section: Formal Solution Of the Radiative Transfer Equationmentioning

confidence: 85%

STiC: A multiatom non-LTE PRD inversion code for full-Stokes solar observations

Rodríguez

Danilović

Uitenbroek

2019

A&A

116

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The inference of the underlying state of the plasma in the solar chromosphere remains extremely challenging because of the nonlocal character of the observed radiation and plasma conditions in this layer. Inversion methods allow us to derive a model atmosphere that can reproduce the observed spectra by undertaking several physical assumptions. The most advanced approaches involve a depth-stratified model atmosphere described by temperature, line-of-sight velocity, turbulent velocity, the three components of the magntic field vector, and gas and electron pressure. The parameters of the radiative transfer equation are computed from a solid ground of physical principles. In order to apply these techniques to spectral lines that sample the chromosphere, nonlocal thermodynamical equilibrium effects must be included in the calculations. We developed a new inversion code STiC (STockholm inversion Code) to study spectral lines that sample the upper chromosphere. The code is based on the RH forward synthesis code, which we modified to make the inversions faster and more stable. For the first time, STiC facilitates the processing of lines from multiple atoms in non-LTE, also including partial redistribution effects (PRD) in angle and frequency of scattered photons. Furthermore, we include a regularization strategy that allows for model atmospheres with a complex depth stratification, without introducing artifacts in the reconstructed physical parameters, which are usually manifested in the form of oscillatory behavior. This approach takes steps toward a node-less inversion, in which the value of the physical parameters at each grid point can be considered a free parameter. In this paper we discuss the implementation of the aforementioned techniques, the description of the model atmosphere, and the optimizations that we applied to the code. We carry out some numerical experiments to show the performance of the code and the regularization techniques that we implemented. We made STiC publicly available to the community.

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Section: Formal Solution Of the Radiative Transfer Equationmentioning

confidence: 85%

STiC: A multiatom non-LTE PRD inversion code for full-Stokes solar observations

Rodríguez

Danilović

Uitenbroek

2019

A&A

116

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“…Providing at least second-order accurate derivatives, both methods can reach fourth-order accuracy. Janett & Paganini (2018) demonstrated their proximity to L-stability. Similarly to the cubic Hermitian method, DELO-Bézier methods require the calculation of numerical derivatives that increases the total computational effort.…”

Section: Quadratic and Cubic Delo-bézier Methodsmentioning

confidence: 94%

“…Moreover, Ibgui et al (2013) explained that the calculation of numerical derivatives proposed by Steffen (1990) is sensibly slower than the one proposed by Fritsch & Butland (1984). However, the derivatives provided by Fritsch & Butland (1984) are second-order accurate on uniform grids only and they drop to first-order accuracy on non-uniform grids (see Janett & Paganini 2018). For this reason, the version by Steffen (1990) is used here.…”

Section: Cubic Hermitian Methodsmentioning

confidence: 99%

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Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems

Janett

Steiner

Belluzzi

2018

ApJ

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The numerical computation of reliable and accurate Stokes profiles is of great relevance in solar physics. In the synthesis process, many actors play a relevant role: among them the formal solver, the discrete atmospheric model, and the spectral line. This paper tests the performances of different numerical schemes in the synthesis of polarized spectra for different spectral lines and atmospheric models. The hierarchy between formal solvers is enforced, stressing the peculiarities of high-order and low-order formal solvers. The density of grid points necessary for reaching a given accuracy requirement is quantitatively described for specific situations.

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“…For instance, the problem cannot be reduced to simple quadratures (see Landi Degl 'Innocenti & Landolfi 2004). Moreover the radiative transfer equation for polarized light exhibits stiff behavior, and numerical schemes face instability issues (Janett & Paganini 2018). An extensive analysis of the numerical solution of the polarized radiative transfer equation is given by Janett et al (2017a,b), who characterized several exponential integrators (DELO methods) and high-order formal solvers.…”

Section: Polarized Radiative Transfer Equationmentioning

confidence: 99%

Discontinuities in numerical radiative transfer

Janett

2019

A&A

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Observations and magnetohydrodynamic simulations of solar and stellar atmospheres reveal an intermittent behavior or steep gradients in physical parameters, such as magnetic field, temperature, and bulk velocities. The numerical solution of the stationary radiative transfer equation is particularly challenging in such situations, because standard numerical methods may perform very inefficiently in the absence of local smoothness. However, a rigorous investigation of the numerical treatment of the radiative transfer equation in discontinuous media is still lacking. The aim of this work is to expose the limitations of standard convergence analyses for this problem and to identify the relevant issues. Moreover, specific numerical tests are performed. These show that discontinuities in the atmospheric physical parameters effectively induce first-order discontinuities in the radiative transfer equation, reducing the accuracy of the solution and thwarting high-order convergence. In addition, a survey of the existing numerical schemes for discontinuous ordinary differential systems and interpolation techniques for discontinuous discrete data is given, evaluating their applicability to the radiative transfer problem.

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Formal Solutions for Polarized Radiative Transfer. III. Stiffness and Instability

Cited by 18 publications

References 25 publications

STiC: A multiatom non-LTE PRD inversion code for full-Stokes solar observations

STiC: A multiatom non-LTE PRD inversion code for full-Stokes solar observations

Formal Solutions for Polarized Radiative Transfer. IV. Numerical Performances in Practical Problems

Discontinuities in numerical radiative transfer

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