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We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stii lower order term that approximates the original system with a small dissipative correction. The new system can be solved(More)
On Time-Splitting Spectral Approximations for the Schrödinger Equation in the Semiclassical Regime Weizhu Bao,∗ Shi Jin,† and Peter A. Markowich‡ ∗Department of Computational Science, National University of Singapore, Singapore 117543; †Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706; and ‡Institute of Mathematics,(More)
  • Shi Jin
  • SIAM J. Scientific Computing
  • 1999
Many kinetic models of the Boltzmann equation have a diiusive scaling that leads to the Navier-Stokes type parabolic equations as the small scaling parameter approaches zero. In practical applications, it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter, from the rareeed kinetic regimes(More)
This paper investigates the uplink achievable rates of massive multiple-input multiple-output (MIMO) antenna systems in Ricean fading channels, using maximal-ratio combining (MRC) and zero-forcing (ZF) receivers, assuming perfect and imperfect channel state information (CSI). In contrast to previous relevant works, the fast fading MIMO channel matrix is(More)
We develop a level set method for the computation of multi-valued physical observables (density, velocity, energy, etc.) for the high frequency limit of symmetric hyperbolic systems in any number of space dimensions. We take two approaches to derive the method. The first one starts with a decoupled system of an eikonal eikonal for phase S and a transport(More)
In this paper we study the performance of time-splitting spectral approximations for general nonlinear Schrödinger equations (NLS) in the semiclassical regimes, where the Planck constant ε is small. The time-splitting spectral approximation under study is explicit, unconditionally stable and conserves the position density in L1. Moreover it is(More)
We study several schemes of rst or second-order accuracy based on kinetic approximations to solve pressureless and isothermal gas dynamics equations. The pressureless gas system is weakly hyperbolic, giving rise to the formation of density concentrations known as delta-shocks. For the isothermal gas system, the innnite speed of expansion into vacuum leads(More)
This paper analyzes MIMO systems with multichannel beamforming in Ricean fading. Our results apply to a wide class of multichannel systems which transmit on the eigenmodes of the MIMO channel. We first present new closed-form expressions for the marginal ordered eigenvalue distributions of complex noncentral Wishart matrices. These are used to characterize(More)
In this paper we study energy efficient joint power allocation and beamforming for coordinated multicell multiuser downlink systems. The considered optimization problem is in a non-convex fractional form and hard to tackle. We propose to first transform the original problem into an equivalent optimization problem in a parametric subtractive form, by which(More)