Highly efficient and exact method for parallelization of grid-based algorithms and its implementation in DelPhi

• Published in: Journal of computational chemistry 2012-09, Vol.33 (24), p.1960-1966
• Main Authors: Li, Chuan, Li, Lin, Zhang, Jie, Alexov, Emil
• Format: Article
• Language: English
• Subjects: Algorithms; Analytical chemistry; Computational Biology - methods; DelPhi; Delphi method; electrostatics; Gauss-Seidel iteration; Molecular biology; Molecular structure; Nonlinear equations; Numerical analysis; Numerical Analysis, Computer-Assisted; parallel computing; Poisson-Boltzmann equation; Software; Static Electricity; Thermodynamics
• ISSN: 0192-8651; 1096-987X
• DOI: 10.1002/jcc.23033

The Gauss–Seidel (GS) method is a standard iterative numerical method widely used to solve a system of equations and, in general, is more efficient comparing to other iterative methods, such as the Jacobi method. However, standard implementation of the GS method restricts its utilization in parallel computing due to its requirement of using updated neighboring values (i.e., in current iteration) as soon as they are available. Here, we report an efficient and exact (not requiring assumptions) method to parallelize iterations and to reduce the computational time as a linear/nearly linear function of the number of processes or computing units. In contrast to other existing solutions, our method does not require any assumptions and is equally applicable for solving linear and nonlinear equations. This approach is implemented in the DelPhi program, which is a finite difference Poisson–Boltzmann equation solver to model electrostatics in molecular biology. This development makes the iterative procedure on obtaining the electrostatic potential distribution in the parallelized DelPhi several folds faster than that in the serial code. Further, we demonstrate the advantages of the new parallelized DelPhi by computing the electrostatic potential and the corresponding energies of large supramolecular structures. © 2012 Wiley Periodicals, Inc. Accurately solving the PoissonBoltzmann equation and calculating electrostatic potential and energies of biological macromolecules are highly desired for modeling biological molecules and nano‐objects immersed in water. Existing methods implemented in serial solvers are restricted to relatively small biomolecular systems due to high computational cost. In this article, we introduce a newly developed efficient parallelization algorithm, implemented in DelPhi, which uses cutting‐edge high performance computing techniques to accelerate calculations on large supramolecular structures without compromising accuracy.