Abstract The governing equations of the flow of an oldroyd-B fluid is discretized using the finite element method. To overcome the convective nature of the momentum equation, the Galerkin/Least-Squares Finite Element Method (GLS/FEM) method is used while the Discrete Elastic-Viscous Stress-Splitting (DEVSS) method is used to overcome the instability due to the absence of diffusion in the constitutive equations. The discretized equations are implemented on a hybrid system between the Graphics Processing Unit (GPU) architecture using Compute-Unified-Device-Architecture (CUDA) and a multi-core CPU. The implementation is applied successfully to simulate the blood flow in abdominal aortic aneurysm. To accelerate application performance on the GPU several optimized approaches are adopted. The most significant approach is the coloring technique that is used to assemble the global matrix. Numerical experiments show that the hybrid CPU-GPU implementation has a 26 time speedup over the multi-core CPU implementations.

中文翻译：

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图形处理单元 (GPU) 架构上 oldroyd-B 流体流动方程的稳定变分公式

摘要 用有限元方法离散了oldroyd-B流体流动的控制方程。为了克服动量方程的对流性质，使用伽辽金/最小二乘有限元方法 (GLS/FEM) 方法，而使用离散弹性粘性应力分裂 (DEVSS) 方法来克服由于缺少的不稳定性本构方程中的扩散。离散方程在使用统一计算设备架构 (CUDA) 的图形处理单元 (GPU) 架构和多核 CPU 之间的混合系统上实现。该实现已成功应用于模拟腹主动脉瘤的血流。为了加速 GPU 上的应用程序性能，采用了多种优化方法。最重要的方法是用于组装全局矩阵的着色技术。数值实验表明，混合 CPU-GPU 实现比多核 CPU 实现有 26 倍的加速。