A fast, dense Chebyshev solver for electronic structure on GPUs

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Materials Science

Background:

• Traditional dense diagonalization algorithms show underwhelming performance on modern GPUs for quantum chemistry calculations involving modest matrix sizes.
• The computation of the density matrix is a critical step in quantum chemistry, often relying on matrix diagonalization.

Purpose of the Study:

• To explore and enhance alternative algorithms for density matrix computation on GPUs.
• To improve the performance of existing Chebyshev expansion algorithms for large-scale quantum chemistry simulations.

Main Methods:

• Implementation of an existing Chebyshev expansion algorithm with a square root scaling of matrix multiplications.
• GPU acceleration using CUDA and HIP streams via the MAGMA library to exploit task parallelism.
• Application of the improved method to a model system with a high density of states.

Main Results:

• The GPU-implemented Chebyshev expansion algorithm achieves significant speedups compared to traditional diagonalization for modest-sized dense matrices.
• Exploiting task parallelism and concurrency resulted in further speed improvements for smaller matrix sizes (≲1000).
• The technique was successfully applied to a challenging model system with a high density of states.

Conclusions:

• The enhanced Chebyshev expansion algorithm offers a more efficient approach for density matrix computation on GPUs in quantum chemistry.
• GPU acceleration and parallelization strategies are crucial for overcoming performance bottlenecks in computational chemistry.
• This method shows promise for tackling complex systems with high densities of states, advancing computational materials science.