PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main interest lies in modeling the spectral line polarization produced by scattering processes and the Hanle and Zeeman effects. One of the difficulties is that the plasma of a stellar atmosphere can be highly inhomogeneous and dynamic, which implies the need to solve the non-equilibrium problem of the generation and transfer of polarized radiation in realistic three-dimensional (3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel radiative transfer code we have developed for the simulation of the spectral line polarization caused by scattering processes and the Hanle and Zeeman effects in 3D models of stellar atmospheres. The numerical method of solution is based on the non-linear multigrid iterative method and on a novel short-characteristics formal solver of the Stokes-vector transfer equation which uses monotonic B\'ezier interpolation. Therefore, with PORTA the computing time needed to obtain at each spatial grid point the self-consistent values of the atomic density matrix (which quantifies the excitation state of the atomic system) scales linearly with the total number of grid points. Another crucial feature of PORTA is its parallelization strategy, which allows us to speed up the numerical solution of complicated 3D problems by several orders of magnitude with respect to sequential radiative transfer approaches, given its excellent linear scaling with the number of available processors. The PORTA code can also be conveniently applied to solve the simpler 3D radiative transfer problem of unpolarized radiation in multilevel systems.Comment: 15 pages, 15 figures, to appear in Astronomy and Astrophysic

Cumulative reports and publications through December 31, 1988

This document contains a complete list of ICASE Reports. Since ICASE Reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Cumulative reports and publications through December 31, 1990

This document contains a complete list of ICASE reports. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available

Parallel-in-Time Simulation of an Electrical Machine using MGRIT

We apply the multigrid-reduction-in-time (MGRIT) algorithm to an eddy current simulation of a two-dimensional induction machine supplied by a pulse-width-modulation signal. To resolve the fast-switching excitations, small time steps are needed, such that parallelization in time becomes highly relevant for reducing the simulation time. The MGRIT algorithm is well suited for introducing time parallelism in the simulation of electrical machines using existing application codes, as MGRIT is a non-intrusive approach that essentially uses the same time integrator as a traditional time-stepping algorithm. We investigate effects of spatial coarsening on MGRIT convergence when applied to two numerical models of an induction machine, one with linear material laws and a full nonlinear model. Parallel results demonstrate significant speedup in the simulation time compared to sequential time stepping, even for moderate numbers of processors.Comment: 14 page

Functional a posteriori error estimates for parabolic time-periodic boundary value problems

The paper is concerned with parabolic time-periodic boundary value problems which are of theoretical interest and arise in different practical applications. The multiharmonic finite element method is well adapted to this class of parabolic problems. We study properties of multiharmonic approximations and derive guaranteed and fully computable bounds of approximation errors. For this purpose, we use the functional a posteriori error estimation techniques earlier introduced by S. Repin. Numerical tests confirm the efficiency of the a posteriori error bounds derived

Cumulative reports and publications

A complete list of Institute for Computer Applications in Science and Engineering (ICASE) reports are listed. Since ICASE reports are intended to be preprints of articles that will appear in journals or conference proceedings, the published reference is included when it is available. The major categories of the current ICASE research program are: applied and numerical mathematics, including numerical analysis and algorithm development; theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and computer science