負載平衡下的自適應網格精緻化流體模擬

Abstract

自適應網格精緻化(Adaptive Mesh Refinement, AMR)是一個當計算誤差變大時，將網格動態調配得更細密以達到更高精確度的一個模擬方法。為了獲得更大的效能及速率，本實驗室發展出一個以高速圖形計算核心(Graphic Processing Units, GPU)加速運算，且各台平行電腦負責相同且固定大小物理空間的AMR平行程式GAMER(GPU-accelerated, Adaptive-MEsh-Refinement code)。但使用GAMER時，不同的模擬條件卻可能令各台電腦的運算量負載不平衡(load imbalance)，造成總體計算效能降低。本論文利用空間填充曲線(Space-filling Curve, SC)來規劃，重新定義每台電腦所應負責的區域，達到各台平行電腦的負載平衡，且各台電腦負責區域內的相鄰網格因SC而有空間性緊密相關的特性，降低網路溝通造成的損耗，提供比以往AMR平行模擬更高的效能。

Adaptive Mesh Refinement (AMR) is an idea of saving computing resources. In many cases, the most important flow features occupy only small regions in the computational domain. AMR can recursively refine grids when errors grow and remove the fine grids when coarser grids provide enough accuracy. GAMER (GPU-accelerated, Adaptive-MEsh-Refinement code) is a parallel AMR program using Graphic Processing Units (GPU). Simulations using GAMER can frequently create problems that reduce the computational performance due to load imbalance. In this thesis, I use Space-filling Curve (SC) which has high locality in any neighborhood to redistribute the computational loads in each node in a parallel cluster. It makes loads balanced in parallel computation and offers better performance than otherwise.