Chebyshev Polynomial Approximation for Distributed Signal Processing

Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals collected by sensor networks. The proposed method features approximations of the graph Fourier multipliers by shifted Chebyshev polynomials, whose recurrence relations make them readily amenable to distributed computation. We demonstrate how the proposed method can be used in a distributed denoising task, and show that the communication requirements of the method scale gracefully with the size of the network.Comment: 8 pages, 5 figures, to appear in the Proceedings of the IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), June, 2011, Barcelona, Spai

A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry

We develop a high-order kinetic scheme for entropy-based moment models of a one-dimensional linear kinetic equation in slab geometry. High-order spatial reconstructions are achieved using the weighted essentially non-oscillatory (WENO) method, and for time integration we use multi-step Runge-Kutta methods which are strong stability preserving and whose stages and steps can be written as convex combinations of forward Euler steps. We show that the moment vectors stay in the realizable set using these time integrators along with a maximum principle-based kinetic-level limiter, which simultaneously dampens spurious oscillations in the numerical solutions. We present numerical results both on a manufactured solution, where we perform convergence tests showing our scheme converges of the expected order up to the numerical noise from the numerical optimization, as well as on two standard benchmark problems, where we show some of the advantages of high-order solutions and the role of the key parameter in the limiter

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