# Acceleration of Linear Finite-Difference Poisson-Boltzmann Methods on Graphics Processing Units

## TL;DR

This paper demonstrates how GPU acceleration, especially with Jacobi-preconditioned conjugate gradient solvers, significantly speeds up linear finite-difference Poisson-Boltzmann computations in biomolecular modeling.

## Contribution

It introduces GPU-optimized implementations of linear PBE solvers, analyzing their performance and efficiency with various preconditioners and matrix formats.

## Key findings

- Jacobi-preconditioned CG on GPU outperforms CPU solvers
- Diagonal matrix format yields best efficiency for finite-difference systems
- Single precision GPU computations maintain good numerical accuracy

## Abstract

Electrostatic interactions play crucial roles in biophysical processes such as protein folding and molecular recognition. Poisson-Boltzmann equation (PBE)-based models have emerged as widely used in modeling these important processes. Though great efforts have been put into developing efficient PBE numerical models, challenges still remain due to the high dimensionality of typical biomolecular systems. In this study, we implemented and analyzed commonly used linear PBE solvers for the ever-improving graphics processing units (GPU) for biomolecular simulations, including both standard and preconditioned conjugate gradient (CG) solvers with several alternative preconditioners. Our implementation utilizes standard Nvidia CUDA libraries cuSPARSE, cuBLAS, and CUSP. Extensive tests show that good numerical accuracy can be achieved given that the single precision is often used for numerical applications on GPU platforms. The optimal GPU performance was observed with the Jacobi-preconditioned CG solver, with a significant speedup over standard CG solver on CPU in our diversified test cases. Our analysis further shows that different matrix storage formats also considerably affect the efficiency of different linear PBE solvers on GPU, with the diagonal format best suited for our standard finite-difference linear systems. Further efficiency may be possible with matrix-free operations and integrated grid stencil setup specifically tailored for the banded matrices in PBE-specific linear systems.

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Source: https://tomesphere.com/paper/1704.02745