A basic heterogeneous parallel Red–Black successive over-relaxation (SOR) implement, the mono-color floating-point scheme, was developed on graphics processing units (GPU) with OpenCL platform. Designed in fine granularity, compact data structure, and stencil function, a concise mapping relationship was created to implicitly describe the complex rules for searching neighbor elements, which could avoid low utilization of GPU in the traditional scheme of Red–Black SOR. The new mono-color floating-point scheme was applied to build fast Semi-Implicit Method for Pressure Linked Equations (SIMPLE) solver with OpenCL and OpenMP on the heterogeneous parallel computing device. Compared with SIMPLE solver in the traditional Red–Black SOR scheme, the new scheme can achieve 1.7 to 1.8 faster accelerative performance on the same GPU. And this scheme can eliminate the complex searching module in mono-color logical scheme and behave better than the mono-color logical scheme by 20–30% acceleration. Numerical cases in double precision showed that SIMPLE solver on GPU with new scheme of Red–Black SOR could save up to 92% computing time compared with the serial solver on CPU.

中文翻译：

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异构并行红黑SOR技术及SIMPLE的数值研究

一种基本的异构并行红黑连续过松弛 (SOR) 实现，即单色浮点方案，是在具有 OpenCL 平台的图形处理单元 (GPU) 上开发的。细粒度、紧凑的数据结构和模板功能设计，创建简明的映射关系，隐式描述搜索邻居元素的复杂规则，避免传统红黑SOR方案中GPU利用率低的问题。应用新的单色浮点方案，在异构并行计算设备上使用 OpenCL 和 OpenMP 构建压力关联方程的快速半隐式求解器 (SIMPLE)。与传统 Red-Black SOR 方案中的 SIMPLE 求解器相比，新方案可以在同一 GPU 上实现 1.7 到 1.8 倍的加速性能。并且该方案可以消除单色逻辑方案中复杂的搜索模块，性能比单色逻辑方案好20-30%的加速。双精度下的数值案例表明，与CPU上的串行求解器相比，采用新的红黑SOR方案的GPU上的SIMPLE求解器可以节省高达92%的计算时间。