Linear-scaling self-consistent field calculations based on divide-and-conquer method using resolution-of-identity approximation on graphical processing units

• Published in: Journal of computational chemistry 2015-01, Vol.36 (3), p.164-170
• Main Authors: Yoshikawa, Takeshi, Nakai, Hiromi
• Format: Article
• Language: English
• Subjects: Approximation; Central processing units; Cost reduction; CPUs; Libraries; Molecular chemistry; Numerical analysis
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.23782

Graphical processing units (GPUs) are emerging in computational chemistry to include Hartree−Fock (HF) methods and electron‐correlation theories. However, ab initio calculations of large molecules face technical difficulties such as slow memory access between central processing unit and GPU and other shortfalls of GPU memory. The divide‐and‐conquer (DC) method, which is a linear‐scaling scheme that divides a total system into several fragments, could avoid these bottlenecks by separately solving local equations in individual fragments. In addition, the resolution‐of‐the‐identity (RI) approximation enables an effective reduction in computational cost with respect to the GPU memory. The present study implemented the DC‐RI‐HF code on GPUs using math libraries, which guarantee compatibility with future development of the GPU architecture. Numerical applications confirmed that the present code using GPUs significantly accelerated the HF calculations while maintaining accuracy. © 2014 Wiley Periodicals, Inc. The graphical processing units (GPU) implementations were performed for accelerating the Hartree–Fock (HF) calculations by combining the linear‐scaling divide‐and‐conquer (DC) method with the effective resolution‐of‐the‐identity (RI) technique. The speedups of DC‐RI‐HF on GPU compared with standard HF increased with increasing molecular size because of the sparse density matrix and local diagonalization by the DC method.