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Numerical Parallel Scalability of the Shifted Boundary Method


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A new embedded finite element method has been developed, named "Shifted Boundary Method'' (or SBM). This new approach overcomes the difficulty on matrix conditioning and algorithmic stability that the occurrence of small cut cells produced in standard embedded methods. This works without creating complicated data structures and keeps limited computational complexity to a minimum. The key feature of the SBM is the idea of shifting the location where boundary conditions are applied from the true to the surrogate boundary, and to appropriately modify the shifted boundary conditions in order to preserve optimal convergence rates of the numerical solution. This process yields a method that is simple, robust, and efficient. One aspect is the analysis of performance of the SBM in the context of parallel computing architectures. It was expected from previous experience that the SBM would show good overall parallel scalability. The setup phase is parallel in nature, since it requires the computation of the three-dimensional intersections and distances between the computational grid and the geometric shapes to be simulated. A few open questions remained on the preconditioning of the algebraic system of equations associated with the SBM in large-scale computations. The PI purchased a high-performance computing cluster and test the hypotheses mentioned above. The PI studied the scalability of the SBM in an engineering application in the realm of additive manufacturing and related applications. The computational outcomes have shown that the SBM maintains good scalability up to the largest problems attempted, on the order of 20 million elements. Problems of this size are about the largest computational grids that fit on the purchased computing cluster, and the typical size for applied engineering applications. The cluster was successfully installed and deployed. We tested the proposed algorithms and their scalability was shown on computational grids up to 20-25 million elements.



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