Study Results
The new SLEPc solvers were benchmarked using dense matrices of various sizes (up to 103,680 rows) on both a local CPU cluster and the Leonardo Booster GPU cluster. The results show up to a 10× speed-up over previous methods. On CPU, computing 100 eigentriples of a 36,288-sized matrix took less than 10 minutes using 32 cores. On GPU, the largest tested matrices were solved within a few minutes using 32 GPUs. The solvers also demonstrated good strong scaling up to 128 GPUs. While polynomial filters were not competitive for a small number of eigenvalues, they may be advantageous in spectrum slicing contexts. The LOBPCG variant outperformed Lanczos by up to 1.75× when configured with optimal parameters.
More details can be found in two manuscripts which are presently under review:
[1] P. Milev et al. “Performances in solving the Bethe-Salpeter equation with the Yambo code”, arXiv 2504.10096 (2025)
[2] F. Alvarruiz, B. Mellado-Pinto, J. Roman, “Variants of thick-restart Lanczos for the Bethe-Salpeter eigenvalue problem”, arXiv 2503.20920 (2025)
Benefits
The project has resulted in an efficient eigensolver for pseudo-Hermitian matrices, now available as part of the SLEPc library and already in use through its integration into the Yambo code. The new solver significantly improves computational efficiency by reducing memory usage by a factor of two and accelerating time to solution by up to an order of magnitude, depending on the system size.
These improvements make it feasible to study larger and more complex systems, particularly those that were previously beyond reach due to computational constraints. Relevant application cases include systems with low-energy poles relative to the electronic gap, such as materials close to excitonic insulator transitions or magnetic systems with magnonic excitations, as well as isolated systems like molecules or point defects, and lower-dimensional materials such as two-dimensional materials or one-dimensional structures like carbon nanotubes.
Beyond its use in Yambo, the solver has potential for broader adoption in other ab initio simulation codes, including BerkeleyGW, GPAW, Exc, VASP, and abinit. Its structure-preserving design and integration into SLEPc ensure long-term availability and usability across a wide range of applications in materials science and computational physics
Partners
| The Universitat Politècnica de València (UPV), based in Spain, served as the project coordinator and led the development of the new algorithms within the SLEPc library. UPV is a public technical university with a strong tradition in scientific computing and parallel processing. The work was headed by Professor José E. Roman, a senior academic in the Department of Computer Science and principal developer of the SLEPc library. His research group has over 25 years of experience in high-performance computing, numerical methods, and scientific software engineering. The team at UPV was responsible for algorithm design, implementation, and small-scale benchmarking of the solvers within modern HPC environments. |
| The Consiglio Nazionale delle Ricerche (CNR), through the Istituto di Struttura della Materia (ISM) in Italy, contributed its deep domain knowledge in materials science and ab initio simulation methods. Led by Dr. Davide Sangalli, the CNR team provided expertise in many-body physics and the practical application of the Bethe-Salpeter Equation for modeling excitonic effects in advanced materials. CNR is also one of the lead institutions behind the Yambo code, a widely used software package for excited-state simulations. Within the project, CNR focused on integrating the new solvers into Yambo and evaluating their performance on relevant physical systems. |
Team
- Davide Sangalli
- Marco D’Alessandro
- Petru Milev
- Jose E. Roman
- Fernando Alvarruiz
- Enrique Ramos
- Blanca Mellado-Pinto
Contact
Name: Prof. José E. Roman
Institution: Universitat Politècnica de València, Spain
Email Address: jroman@dsic.upv.es