Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes (≲4000), performance of traditional dense diagonalization algorithms on modern GPUs is underwhelming compared to the peak performance of these devices. This motivates the exploration of alternative algorithms better suited to these types of architectures. We newly derive, and present in detail, an existing Chebyshev expansion algorithm [Liang et al., J. Chem. Phys. 119, 4117–4125 (2003)] whose number of required matrix multiplications scales with the square root of the number of terms in the expansion. Focusing on dense matrices of modest size, our implementation on GPUs results in large speed ups when compared to diagonalization. Additionally, we improve upon this existing method by capitalizing on the inherent task parallelism and concurrency in the algorithm. This improvement is implemented on GPUs by using CUDA and HIP streams via the MAGMA library and leads to a significant speed up over the serial-only approach for smaller (≲1000) matrix sizes. Finally, we apply our technique to a model system with a high density of states around the Fermi level, which typically presents significant challenges.
Skip Nav Destination
A fast, dense Chebyshev solver for electronic structure on GPUs
Article navigation
14 September 2023
Rapid Communication|
September 11 2023
A fast, dense Chebyshev solver for electronic structure on GPUs
Joshua Finkelstein
;
Joshua Finkelstein
a)
(Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft, Writing – review & editing)
1
Theoretical Division, Los Alamos National Laboratory
, Los Alamos, New Mexico 87545, USA
a)Author to whom correspondence should be addressed: jdf@lanl.gov
Search for other works by this author on:
Christian F. A. Negre;
Christian F. A. Negre
b)
(Formal analysis, Funding acquisition, Validation, Writing – original draft, Writing – review & editing)
1
Theoretical Division, Los Alamos National Laboratory
, Los Alamos, New Mexico 87545, USA
Search for other works by this author on:
Jean-Luc Fattebert
Jean-Luc Fattebert
c)
(Conceptualization, Formal analysis, Investigation, Methodology, Software, Supervision, Writing – original draft, Writing – review & editing)
2
Computational Sciences and Engineering Division, Oak Ridge National Laboratory
, Oak Ridge, Tennessee 37830, USA
Search for other works by this author on:
a)Author to whom correspondence should be addressed: jdf@lanl.gov
b)
Electronic mail: cnegre@lanl.gov
c)
Electronic mail: fattebertj@ornl.gov
J. Chem. Phys. 159, 101101 (2023)
Article history
Received:
June 21 2023
Accepted:
August 14 2023
Citation
Joshua Finkelstein, Christian F. A. Negre, Jean-Luc Fattebert; A fast, dense Chebyshev solver for electronic structure on GPUs. J. Chem. Phys. 14 September 2023; 159 (10): 101101. https://doi.org/10.1063/5.0164255
Download citation file:
Sign in
Don't already have an account? Register
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Sign in via your Institution
Sign in via your InstitutionPay-Per-View Access
$40.00
260
Views
Citing articles via
Related Content
Porting fragmentation methods to GPUs using an OpenMP API: Offloading the resolution-of-the-identity second-order Møller–Plesset perturbation method
J. Chem. Phys. (April 2023)
Deterministic GPU Boltzmann solver
AIP Conference Proceedings (December 2014)
Multi-GPU kinetic solvers using MPI and CUDA
AIP Conference Proceedings (December 2014)
GPU accelerated kinetic solvers for rarefied gas dynamics
AIP Conference Proceedings (November 2012)
High-performance computing on GPUs for resistivity logging of oil and gas wells
AIP Conference Proceedings (October 2017)