110 research outputs found
STiC -- A multi-atom non-LTE PRD inversion code for full-Stokes solar observations
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 magnetic field vector, and gas and electron pressure. The
parameters of the radiative transfer equation are computed from a solid ground
of physical principles. To apply these techniques to spectral lines that sample
the chromosphere, NLTE effects must be included in the calculations.
We developed a new inversion code STiC to study spectral lines that sample
the upper chromosphere. The code is based the RH synthetis 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. Furthermore, we include a
regularization strategy that allows for model atmospheres with a complex
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.Comment: Accepted for publication in Astronomy & Astrophysic
Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics
International audienceThe fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles
Modeling a Spheroidal Particle Ensemble and Inversion by Generalized Runge-Kutta Regularizers from Limited Data
Extracting information about the shape or size of non-spherical aerosol particles from limited optical radar data is a well-known inverse ill-posed problem. The purpose of the study is to figure out a robust and stable regularization method including an appropriate parameter choice rule to address the latter problem. First, we briefly review common regularization methods and investigate a new iterative family of generalized Runge–Kutta filter regularizers. Next, we model a spheroidal particle ensemble and test with it different regularization methods experimenting with artificial data pertaining to several atmospheric scenarios. We found that one method of the newly introduced generalized family combined with the L-curve method performs better compared to traditional methods
Combining Analytic Preconditioner and Fast Multipole Method for the 3-D Helmholtz Equation
International audienceThe paper presents a detailed numerical study of an iterative solution to 3-D sound-hard acoustic scattering problems at high frequency considering the Combined Field Integral Equation (CFIE). We propose a combination of an OSRC preconditioning technique and a Fast Multipole Method which leads to a fast and efficient algorithm independently of both a frequency increase and a mesh refinement. The OSRC-preconditioned CFIE exhibits very interesting spectral properties even for trapping domains. Moreover, this analytic preconditioner shows highly-desirable advantages: sparse structure, ease of implementation and low additional computational cost. We first investigate the numerical behavior of the eigenvalues of the related integral operators, CFIE and OSRC-preconditioned CFIE, in order to illustrate the influence of the proposed preconditioner. We then apply the resolution algorithm to various and significant test-cases using a GMRES solver. The OSRC-preconditioning technique is combined to a Fast Multipole Method in order to deal with high-frequency 3-D cases. This variety of tests validates the effectiveness of the method and fully justifies the interest of such a combination
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