Modified Broyden’s method for accelerating convergence in self-consistent calculations

Johnson, Duane D.

doi:10.1103/physrevb.38.12807

Cited by 547 publications

(309 citation statements)

References 13 publications

Supporting

Mentioning

306

Contrasting

Unclassified

Order By: Relevance

“…There are two particular members in the generalized Broyden family (28): the Type-I method (27) and the Type-II method (16). The latter corresponds to Anderson mixing (24) which is therefore a Type-II method.…”

Section: Anderson's Familymentioning

confidence: 99%

“…The generalized Broyden's first method (27) and generalized Broyden's second method (16) are two particular members in this family. Note that if F k is square and nonsingular, then…”

Section: The Minimizer Of E(jmentioning

confidence: 99%

“…Type-I methods differ from each other by how the set of secant equations is chosen. We call Type-II methods, those methods that update G k by (16) by minimizing the change of the approximate inverse Jacobian in the Frobenius norm. Likewise, Type-II methods differ from each other by how the set of secant equations is chosen.…”

Section: The Minimizer Of E(jmentioning

confidence: 99%

See 2 more Smart Citations

Two classes of multisecant methods for nonlinear acceleration

Fang

Saad

2008

Numerical Linear Algebra App

246

264

View full text Add to dashboard Cite

Many applications in science and engineering lead to models which require solving large-scale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasi-Newton methods that implicitly update the approximate Jacobian or inverse Jacobian to satisfy a certain secant condition.We present two classes of multisecant methods which allows to take into account a variable number of secant equations at each iteration. The first is the Broyden-like class, of which Broyden's family is a subclass, and Anderson mixing is a particular member. The second class is that of the nonlinear Eirola-Nevanlinna-type methods.This work was motivated by a problem in electronic structure calculations, whereby a fixed point iteration, known as the self-consistent field (SCF) iteration, is accelerated by various strategies termed 'mixing'.

show abstract

Section: Anderson's Familymentioning

confidence: 99%

“…The generalized Broyden's first method (27) and generalized Broyden's second method (16) are two particular members in this family. Note that if F k is square and nonsingular, then…”

Section: The Minimizer Of E(jmentioning

confidence: 99%

See 1 more Smart Citation

Two classes of multisecant methods for nonlinear acceleration

Fang

Saad

2008

Numerical Linear Algebra App

246

264

View full text Add to dashboard Cite

show abstract

“…All the slab structures have been fully relaxed with respect to atoms using the Broyden method. 34 Convergence was assumed when the absolute value of the atomic force on every atom was less than or equal to 25 x 10 -3 eV/Å. 14 and 10 k-points are used in the a and b periodic directions (described below) and 3, 2 and 1 k-points are used in the non-periodic direction for the 3, 5 and 7 unit-cell slab structures described below.…”

Section: A Density Functional Theory Calculationsmentioning

confidence: 99%

Size effects in NiTi from density functional theory calculations

Vishnu

Strachan

2012

Phys. Rev. B

View full text Add to dashboard Cite

We use density functional theory to characterize how size affects the relative stability of thin NiTi slabs of different crystal structures and its implication on the martensitic phase transition that governs shape memory. We calculate the surface energies of B2' phase (austenite), B19 (orthorhombic), B19' (martensite) and a body centered orthorhombic phase (BCO), the theoretically-predicted ground state. We find that (110) B2 surfaces with in-plane atomic displacements stabilize the austenite phase with respect to B19' and BCO, thus slabs with such orientations are predicted to exhibit a decrease in martensite transition temperature with decreasing thickness. Our calculations predict a critical thickness of 2 nm, below which the transition would not occur. The opposite trend is observed in slabs with atomic displacements along the surface normal: the phase transformation temperature increases with decreasing size.

show abstract

“…As a rule relatively big values (α = 0.3−0. [30]. The latter seems to be quite effective in situations of difficult convergence.…”

Section: Potential Mixingmentioning

confidence: 99%