Hwang Wonmuk, Gonzales James E, Brooks Bernard R
Department of Biomedical Engineering, Texas A&M University, College Station, Texas 77843, USA.
Department of Materials Science and Engineering, Texas A&M University, College Station, Texas 77843, USA.
J Chem Phys. 2025 Jun 14;162(22). doi: 10.1063/5.0264936.
We develop a highly parallelizable algorithm to calculate long-range electrostatic interactions named the Gauss-Legendre-Spherical-t (GLST) cubature method. Motivated by our recent spherical grid and treecode method, we utilize the Gauss-Legendre quadrature for integration over a finite range and spherical t-design for integration over a unit sphere. The resulting GLST cubature breaks the long-range interaction term into a sum of terms that can be calculated in parallel with minimal inter-processor communication. The simulation box is divided into cells that are grouped with a separate GLST cubature applied to each group, based on their distance from the atom or cell for which the long-range interaction is calculated. Periodic boundary conditions are handled at two levels: first by "wrapping-around" other cells about the cell under consideration, then by repeating the wrapped-around box over a pre-computed number of times to make the relative error of the calculated force meet the target accuracy. With its high granularity, tunable accuracy, and adaptability to different box geometries, the GLST method is suitable for the simulation of large systems on computer hardware where many cores or threads are available.
我们开发了一种高度可并行化的算法来计算长程静电相互作用，称为高斯 - 勒让德 - 球面 - t（GLST）求积法。受我们最近的球面网格和树码方法的启发，我们利用高斯 - 勒让德求积法在有限范围内进行积分，并利用球面t设计在单位球面上进行积分。由此产生的GLST求积法将长程相互作用项分解为一系列可以在处理器间通信最少的情况下并行计算的项。模拟盒被划分为多个单元，根据它们与计算长程相互作用的原子或单元的距离，将这些单元分组，并对每个组应用单独的GLST求积法。周期性边界条件在两个层面上处理：首先通过将其他单元“环绕”在正在考虑的单元周围，然后通过将环绕后的盒子重复预先计算的次数以使计算出的力的相对误差达到目标精度。由于其高粒度、可调精度以及对不同盒子几何形状的适应性，GLST方法适用于在具有许多内核或线程的计算机硬件上模拟大型系统。
