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Sparse grids for the Schrödinger equation
Published online by Cambridge University Press: 16 June 2007
Abstract
We present a sparse grid/hyperbolic cross discretization for many-particle problems.It involves the tensor product of a one-particle multilevel basis. Subsequent truncation of the associated series expansion then results in a sparse grid discretization.Here, depending on the norms involved, different variants of sparse grid techniques for many-particle spaces can be derivedthat, in the best case, result in complexities and error estimates which are independent of the number of particles.Furthermore we introduce an additional constraint which gives antisymmetric sparse grids which are suited to fermionic systems. We apply the antisymmetric sparse grid discretization to the electronic Schrödinger equationand compare costs, accuracy, convergence rates and scalability with respect to the number of electrons present in the system.
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- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 2: Special issue on Molecular Modelling , March 2007 , pp. 215 - 247
- Copyright
- © EDP Sciences, SMAI, 2007
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