Multilevel domain decomposition for electronic structure calculations

Barrault, Maxime; Cancès, Éric; Hager, William W.; Bris, Claude Le

doi:10.1016/j.jcp.2006.06.049

Cited by 32 publications

(39 citation statements)

References 26 publications

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“…In this case, N is of the order of the number of electrons of the system and the best known methods use variations of the SCF fixed point iteration, which involve computing N eigenvalues and eigenvectors of a symmetric K × K matrix [2,4]. The challenge is to develop methods that scale linearly with respect to N , preserving possible sparsity of X and ∇f (X) and being efficient in the absence of gap between eigenvalues N and N + 1 of ∇f (X) [24,25,26,27].…”

Section: Matricial Optimization Problemmentioning

confidence: 99%

Inexact restoration method for minimization problems arising in electronic structure calculations

et al. 2010

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An inexact restoration (IR) approach is presented to solve a matricial optimization problem arising in electronic structure calculations. The solution of the problem is the closed-shell density matrix and the constraints are represented by a Grassmann manifold. One of the mathematical and computational challenges in this area is to develop methods for solving the problem not using eigenvalue calculations and having the possibility of preserving sparsity of iterates and gradients. The inexact restoration approach enjoys local quadratic convergence and global convergence to stationary points and does not use spectral matrix decompositions, so that, in principle, large-scale implementations may preserve sparsity. Numerical experiments show that IR algorithms are competitive with current algorithms for solving closed-shell Hartree-Fock equations and similar mathematical problems, thus being a promising alternative for problems where eigenvalue calculations are a limiting factor.

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Section: Matricial Optimization Problemmentioning

confidence: 99%

Inexact restoration method for minimization problems arising in electronic structure calculations

et al. 2010

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“…In [2] and [3] we develop a multilevel domain decomposition algorithm for electronic structure calculations which has been extremely eective in computing electronic structure for large, linear polymer chains. Both the computational cost and memory requirement scale linearly with the number of atoms.…”

Section: Introductionmentioning

confidence: 99%

“…Although this algorithm has been very eective in practice, a theory establishing convergence has not yet been developed. The algorithm in [2,3] was motivated by a related decomposition algorithm for a quadratic programming problem with an orthogonality constraint. In this paper, we develop a convergence theory for the decomposition algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…The problem which must be solved in electronic structure calculations is more general than (1) and the multilevel algorithm developed in [2,3] is more complex than (2). For example, in electronic structure calculations, H 1 and H 2 could be of dierent dimensions and the orthogonality condition x T 1 x 2 = 0 in (1) would be replaced by the more general condition x T 1 Px 2 = 0 where P is rectangular.…”

Section: Introductionmentioning

confidence: 99%

“…For example, in electronic structure calculations, H 1 and H 2 could be of dierent dimensions and the orthogonality condition x T 1 x 2 = 0 in (1) would be replaced by the more general condition x T 1 Px 2 = 0 where P is rectangular. Nonetheless, the algorithm studied in this paper was the basis for the more general algorithm developed in [2,3], and our analysis is an initial step towards justifying and understanding the convergence properties of the more general algorithm.…”

Section: Introductionmentioning

confidence: 99%

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