4 research outputs found
Computing the density of states for optical spectra by low-rank and QTT tensor approximation
In this paper, we introduce a new interpolation scheme to approximate the
density of states (DOS) for a class of rank-structured matrices with
application to the Tamm-Dancoff approximation (TDA) of the Bethe-Salpeter
equation (BSE). The presented approach for approximating the DOS is based on
two main techniques. First, we propose an economical method for calculating the
traces of parametric matrix resolvents at interpolation points by taking
advantage of the block-diagonal plus low-rank matrix structure described in [6,
3] for the BSE/TDA problem. Second, we show that a regularized or smoothed DOS
discretized on a fine grid of size can be accurately represented by a low
rank quantized tensor train (QTT) tensor that can be determined through a least
squares fitting procedure. The latter provides good approximation properties
for strictly oscillating DOS functions with multiple gaps, and requires
asymptotically much fewer () functional calls compared with the full
grid size . This approach allows us to overcome the computational
difficulties of the traditional schemes by avoiding both the need of stochastic
sampling and interpolation by problem independent functions like polynomials
etc. Numerical tests indicate that the QTT approach yields accurate recovery of
DOS associated with problems that contain relatively large spectral gaps. The
QTT tensor rank only weakly depends on the size of a molecular system which
paves the way for treating large-scale spectral problems.Comment: 26 pages, 25 figure
Solving the Bethe-Salpeter equation on massively parallel architectures
The last ten years have witnessed fast spreading of massively parallel
computing clusters, from leading supercomputing facilities down to the average
university computing center. Many companies in the private sector have
undergone a similar evolution. In this scenario, the seamless integration of
software and middleware libraries is a key ingredient to ensure portability of
scientific codes and guarantees them an extended lifetime. In this work, we
describe the integration of the ChASE library, a modern parallel eigensolver,
into an existing legacy code for the first-principles computation of optical
properties of materials via solution of the Bethe-Salpeter equation for the
optical polarization function. Our numerical tests show that, as a result of
integrating ChASE and parallelizing the reading routine, the code experiences a
remarkable speedup and greatly improved scaling behavior on both multi- and
many-core architectures. We demonstrate that such a modernized BSE code will,
by fully exploiting parallel computing architectures and file systems, enable
domain scientists to accurately study complex material systems that were not
accessible before.Comment: 17 Pages plus 7 pages of supplemental information, 6 figures and 3
tables. To be submitted to Computer Physics Communication
A structure preserving lanczos algorithm for computing the optical absorption spectrum
We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving the 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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A structure preserving lanczos algorithm for computing the optical absorption spectrum
We present a new structure preserving Lanczos algorithm for approximating the optical absorption spectrum in the context of solving the 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