Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

Vecharynski, Eugene; Brabec, Jiří; Shao, Meiyue; Govind, Niranjan; Yang, Chao

doi:10.1016/j.cpc.2017.07.017

Cited by 16 publications

(16 citation statements)

References 32 publications

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“…A C-neutral vector is a vector v ∈ C 2n which satisfies v H Cnv = 0. 4 A similar behavior has been observed in[36] when solving the linear response eigenvalue problem. 5 http://www.nersc.gov/users/computational-systems/edison/…”

supporting

confidence: 64%

A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum

Shao¹,

Jornada²,

Lin³

et al. 2018

SIAM J. Matrix Anal. & Appl.

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We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving full Bethe-Salpeter equation without Tamm-Dancoff approximation. The new algorithm is based on a structure preserving Lanczos procedure, which exploits the special block structure of Bethe-Salpeter Hamiltonian matrices. A recently developed technique of generalized averaged Gauss quadrature is incorporated to accelerate the convergence. We also establish the connection between our structure preserving Lanczos procedure with several existing Lanczos procedures developed in different contexts. Numerical examples are presented to demonstrate the effectiveness of our Lanczos algorithm.

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supporting

confidence: 64%

A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum

Shao¹,

Jornada²,

Lin³

et al. 2018

SIAM J. Matrix Anal. & Appl.

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“…Specifically, we adopt the Locally Optimal Block Preconditioned Gradient (LOBPCG) algorithm [17] as our eigensolver. The LOBPCG algorithm and its variants have been used to solve eigenvalue problems arising from a number of applications, including material science [6,15,20,37] and machine learning [18,19,24]. The use of a block iterative method allows us to improve the memory access pattern of the computation and make use of approximations to several eigenvectors at the same time.…”

Section: Introductionmentioning

confidence: 99%

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

Shao

Aktulga

Yang

et al. 2018

Computer Physics Communications

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We describe a number of recently developed techniques for improving the performance of large-scale nuclear configuration interaction calculations on high performance parallel computers. We show the benefit of using a preconditioned block iterative method to replace the Lanczos algorithm that has traditionally been used to perform this type of computation. The rapid convergence of the block iterative method is achieved by a proper choice of starting guesses of the eigenvectors and the construction of an effective preconditioner. These acceleration techniques take advantage of special structure of the nuclear configuration interaction problem which we discuss in detail. The use of a block method also allows us to improve the concurrency of the computation, and take advantage of the memory hierarchy of modern microprocessors to increase the arithmetic intensity of the computation relative to data movement. We also discuss implementation details that are critical to achieving high performance on massively parallel multi-core supercomputers, and demonstrate that the new block iterative solver is two to three times faster than the Lanczos based algorithm for problems of moderate sizes on a Cray XC30 system.

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“…The Davidson algorithms 76,77 form a family of subspace-iterative diagonalization schemes that are extensively used in large-scale quantum chemistry applications. 78,79 These methods allow rapid computation of a selected numbers of eigenvalues of large matrices, while reducing memory requirements when compared to other methods.…”

Section: E Iterative Matrix-free Eigensolvers For the Bsementioning

confidence: 99%

Excited-state electronic structure of molecules using many-body Green’s functions: Quasiparticles and electron–hole excitations with VOTCA-XTP

Tirimbó

Sundaram

Çaylak

et al. 2020

The Journal of Chemical Physics

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We present the open-source VOTCA-XTP software for the calculation of the excited-state electronic structure of molecules using many-body Green's functions theory in the GW approximation with the Bethe-Salpeter Equation (BSE). This work provides a summary of the underlying theory and discusses details of its implementation based on Gaussian orbitals, including, i.a., resolution-of-identity techniques, different approaches to the frequency integration of the self-energy or acceleration by offloading compute-intensive matrix operations using GPUs in a hybrid OpenMP/Cuda scheme. A distinctive feature of VOTCA-XTP is the capability to couple the calculation of electronic excitations to a classical polarizable environment on atomistic level in a coupled quantum-and molecular-mechanics (QM/MM) scheme, where a complex morphology can be imported from Molecular Dynamics simulations. The capabilities and limitations of the GW -BSE implementation are illustrated with two examples. First, we study the dependence of optically active electron-hole excitations in a series of diketopyrrolopyrrole-based oligomers on molecular-architecture modifications and the number of repeat units. Second, we use the GW -BSE/MM setup to investigate the effect of polarization on localized and intermolecular charge-transfer excited states in morphologies of low-donor content rubrenefullerene mixtures. These showcases demonstrate that our implementation currently allows to treat systems with up to 2500 basis functions on regular shared-memory workstations, providing accurate descriptions of quasiparticle and coupled electron-hole excited states of various character on an equal footing.

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Efficient block preconditioned eigensolvers for linear response time-dependent density functional theory

Cited by 16 publications

References 32 publications

A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum

A Structure Preserving Lanczos Algorithm for Computing the Optical Absorption Spectrum

Accelerating nuclear configuration interaction calculations through a preconditioned block iterative eigensolver

Excited-state electronic structure of molecules using many-body Green’s functions: Quasiparticles and electron–hole excitations with VOTCA-XTP

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