Due to the high dimensionality of the spaces where the problems are set, adapted discretization basis are often advocated in complex physical problems (Navier-Stokes equations, solid mecanics, ab initio electronic structure computations) to express the solution in terms of solution of similar (but easier to solve) problems. However, very few mathematical studies have been undertaken to asses the numerical properties of these approximations. Within this context, we will present in this paper an overview of the tools required to develop more rigorous reduced basis approaches for quantum chemistry: a posteriori numerical analysis and fast exponential decay of the n-width of the solution set.
Publié le : 2002-12-05
Classification:
reduced basis,
quantum chemistry,
Hartree-Fock equations,
ab initio chemistry,
a posteriori numerical analysis,
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA],
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]
@article{hal-00798475,
author = {Canc\`es, Eric and Le Bris, Claude and Maday, Yvon and Turinici, Gabriel},
title = {Towards Reduced Basis Approaches in ab initio Electronic Structure Computations},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00798475}
}
Cancès, Eric; Le Bris, Claude; Maday, Yvon; Turinici, Gabriel. Towards Reduced Basis Approaches in ab initio Electronic Structure Computations. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00798475/