Search results for "Spectral method"
showing 10 items of 32 documents
Multi-domain spectral approach with Sommerfeld condition for the Maxwell equations
2021
We present a multidomain spectral approach with an exterior compactified domain for the Maxwell equations for monochromatic fields. The Sommerfeld radiation condition is imposed exactly at infinity being a finite point on the numerical grid. As an example, axisymmetric situations in spherical and prolate spheroidal coordinates are discussed.
General relativistic neutrino transport using spectral methods
2014
We present a new code, Lorene's Ghost (for Lorene's gravitational handling of spectral transport) developed to treat the problem of neutrino transport in supernovae with the use of spectral methods. First, we derive the expression for the nonrelativistic Liouville operator in doubly spherical coordinates (r, theta, phi, epsilon, Theta, Phi)$, and further its general relativistic counterpart. We use the 3 + 1 formalism with the conformally flat approximation for the spatial metric, to express the Liouville operator in the Eulerian frame. Our formulation does not use any approximations when dealing with the angular arguments (theta, phi, Theta, Phi), and is fully energy-dependent. This approa…
O(αs)corrections to the correlator of finite mass baryon currents
2000
We present analytical next-to-leading order results for the correlator of baryonic currents at the three-loop level with one finite mass quark. We obtain the massless and the HQET limit of the correlator from the general formula as particular cases. We also give explicit expressions for the moments of the spectral density.
Combining spectral and shock-capturing methods: A new numerical approach for 3D relativistic core collapse simulations
2005
We present a new three-dimensional general relativistic hydrodynamics code which is intended for simulations of stellar core collapse to a neutron star, as well as pulsations and instabilities of rotating relativistic stars. Contrary to the common approach followed in most existing three-dimensional numerical relativity codes which are based in Cartesian coordinates, in this code both the metric and the hydrodynamics equations are formulated and solved numerically using spherical polar coordinates. A distinctive feature of this new code is the combination of two types of accurate numerical schemes specifically designed to solve each system of equations. More precisely, the code uses spectra…
Singularity formation and separation phenomena in boundary layer theory
2009
In this paper we review some results concerning the behaviour of the incompressible Navier–Stokes solutions in the zero viscosity limit. Most of the emphasis is put on the phenomena occurring in the boundary layer created when the no-slip condition is imposed. Numerical simulations are used to explore the limits of the theory. We also consider the case of 2D vortex layers, i.e. flows with internal layers in the form of a rapid variation, across a curve, of the tangential velocity.
Singularities for Prandtl's equations.
2006
We used a mixed spectral/finite-difference numerical method to investigate the possibility of a finite time blow-up of the solutions of Prandtl's equations for the case of the impulsively started cylinder. Our toll is the complex singularity tracking method. We show that a cubic root singularity seems to develop, in a time that can be made arbitrarily short, from a class of data uniformely bounded in H^1.
Scattering resonances and Pseudospectrum : stability and completeness aspects in optical and gravitational systems
2022
The general context of this thesis is an effort to establish a bridge between gravitational andoptical physics, specifically in the context of scattering problems using as a guideline concepts andtools taken from the theory of non-self-adjoint operators. Our focus is on Quasi-Normal Modes(QNMs), namely the natural resonant modes of open leaky structures under linear perturbationssubject to outgoing boundary conditions. They also are referred to as scattering resonances.In the conservative self-adjoint case the spectral theorem guarantees the completeness andspectral stability of the associated normal modes. In this sense, a natural question in the non-self-adjoint setting refers to the char…
Experimental signatures of extreme optical fluctuations in lumped Raman fiber amplifiers
2012
International audience; In this work, we experimentally investigate several temporal and spectral methods to highlight extreme fluctuations which can develop during the Raman amplification of an ultrashort pulse train. Forward and backward pumping schemes are compared to dual pass configurations.
Contributions to the analysis and design of all-inductive filters with dielectric resonators
2003
In this work, three modern full-wave methods will be employed for the accurate analysis and efficient design of a novel family of all-inductive filters loaded with dielectric resonators. These techniques are the bi-orthonormal-basis combined with the orthonormal-basis method, the hybrid mode-matching/spectral method, and, finally, the BI-RME (Boundary Integral-Resonant Mode Expansion) method. Then, two prototypes of band-pass filters have been designed in this work using a CAD tool developed in the research groups implicated in this manuscript. The procedure described in this paper only involves a limited number of actual physical parameters at each step so that it is computationally very e…
Multidomain spectral method for the Gauss hypergeometric function
2018
International audience; We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobenius’ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line R∪∞, except for the singular points and cuts of the Rie…