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The governing equations of the flow of an oldroyd-B fluid are discretized using the finite element method. To overcome the convective nature of the momentum equation, the Galerkin/Least-Squares Finite Element Method (GLS/FEM) 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 …