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Bérenger/Maxwell with Discontinous Absorptions : Existence, Perfection, and No Loss

Laurence Halpern, Jeffrey Rauch (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

We analyse Bérenger’s split algorithm applied to the system version of the two dimensional wave equation with absorptions equal to Heaviside functions of x j , j = 1 , 2 . The methods form the core of the analysis [11] for three dimensional Maxwell equations with absorptions not necessarily piecewise constant. The split problem is well posed, has no loss of derivatives (for divergence free data in the case of Maxwell), and is perfectly matched.

Best N-term approximation in electronic structure calculations. II. Jastrow factors

Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We present a novel application of best N-term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions ( 2 ) near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best N-term approximation spaces A q α ( H 1 ) , we prove...

Best N-term approximation in electronic structure calculations I. One-electron reduced density matrix

Heinz-Jürgen Flad, Wolfgang Hackbusch, Reinhold Schneider (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We discuss best N-term approximation spaces for one-electron wavefunctions φ i and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces A q α ( H 1 ) for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted q spaces of wavelet coefficients to proof that both φ i and ρ are in A q α ( H 1 ) for all α > 0 with α = 1 q - 1 2 . Our proof is based on the...

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