Department of Aerospace Engineering, Texas A&M University, College Station, Texas 77843, USA.
Phys Rev E. 2017 Sep;96(3-1):033304. doi: 10.1103/PhysRevE.96.033304. Epub 2017 Sep 8.
Massively parallel simulations of transport equation systems call for a paradigm change in algorithm development to achieve efficient scalability. Traditional approaches require time synchronization of processing elements (PEs), which severely restricts scalability. Relaxing synchronization requirement introduces error and slows down convergence. In this paper, we propose and develop a novel "proxy equation" concept for a general transport equation that (i) tolerates asynchrony with minimal added error, (ii) preserves convergence order and thus, (iii) expected to scale efficiently on massively parallel machines. The central idea is to modify a priori the transport equation at the PE boundaries to offset asynchrony errors. Proof-of-concept computations are performed using a one-dimensional advection (convection) diffusion equation. The results demonstrate the promise and advantages of the present strategy.
大规模传输方程系统的并行模拟需要在算法开发方面进行范式转变，以实现高效的可扩展性。传统方法需要处理元素 (PE) 的时间同步，这严重限制了可扩展性。放宽同步要求会引入误差并减缓收敛速度。在本文中，我们提出并开发了一种用于一般传输方程的新型“代理方程”概念，该概念 (i) 可容忍异步，误差最小，(ii) 保持收敛阶数，因此，(iii) 有望在大规模并行机器上高效扩展。核心思想是在 PE 边界处对传输方程进行预先修正，以抵消异步误差。使用一维平流 (对流) 扩散方程进行了概念验证计算。结果表明了当前策略的优势和潜力。
