Computing the matrix sign and absolute value functions

Ndjinga, Michaël

doi:10.1016/j.crma.2007.11.028

Cited by 1 publication

(1 citation statement)

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“…It is possible to diagonalize A and to compute jAj using (35), but in practice this method is extremely costly. A more interesting method has been proposed in [29], which consists in computing a sequence of polynomial iterations based on the exact knowledge of the eigenvalues (or at last an explicit bound), and converging to the matrix sign if all the eigenvalues are real. However, this method also becomes costly when N A grows.…”

Section: An Efficient Methods For Approximating the Absolute Value Of mentioning

confidence: 99%

Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems

Tryoen

Maître

Ndjinga

et al. 2010

Journal of Computational Physics

121

106

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a b s t r a c tThis paper deals with stochastic spectral methods for uncertainty propagation and quantification in nonlinear hyperbolic systems of conservation laws. We consider problems with parametric uncertainty in initial conditions and model coefficients, whose solutions exhibit discontinuities in the spatial as well as in the stochastic variables. The stochastic spectral method relies on multi-resolution schemes where the stochastic domain is discretized using tensor-product stochastic elements supporting local polynomial bases. A Galerkin projection is used to derive a system of deterministic equations for the stochastic modes of the solution. Hyperbolicity of the resulting Galerkin system is analyzed. A finite volume scheme with a Roe-type solver is used for discretization of the spatial and time variables. An original technique is introduced for the fast evaluation of approximate upwind matrices, which is particularly well adapted to local polynomial bases. Efficiency and robustness of the overall method are assessed on the Burgers and Euler equations with shocks.

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Section: An Efficient Methods For Approximating the Absolute Value Of mentioning

confidence: 99%