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Proper Generalized Decomposition with time adaptive space separation for transient wave propagation problems in separable domains

机译:适当的广义分解在可分离域中的瞬态波传播问题的时间自适应空间分离

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Transient wave propagation problems may involve rich discretizations, both in space and in time, leading to computationally expensive simulations, even for simple spatial domains. The Proper Generalized Decomposition (PGD) is an attractive model order reduction technique to address this issue, especially when the spatial domain is separable. In this work, we propose a space separation with a time adaptive number of modes to efficiently capture transient wave propagation in separable domains. We combine standard time integration schemes with this original space separated representation for empowering standard procedures. The numerical behavior of the proposed method is explored through several 2D wave propagation problems involving radial waves, propagation on long time analyses, and wave conversions. We show that the PGD solution approximates its standard finite element solution counterpart with acceptable accuracy, while reducing the storage needs and the computation time (CPU time). Numerical results show that the CPU time per time step linearly increases when refining the mesh, even with implicit time integration schemes, which is not the case with standard procedures. (C) 2021 Elsevier B.V. All rights reserved.
机译:瞬态波传播问题可能涉及空间和时间内的丰富离散化,从而导致计算昂贵的模拟,即使是简单的空间域。适当的广义分解(PGD)是一种有吸引力的模型顺序减少技术来解决这个问题,尤其是当空间域是可分离的时。在这项工作中,我们提出了一种空间分离,具有时间自适应模式,以有效地捕获可分离域中的瞬态波传播。我们将标准时间集成方案与此原始空间分开表示组合起来,以赋予标准程序权力。通过涉及径向波的若干2D波传播问题探索所提出的方法的数值行为,长时间分析和波转换的传播。我们表明PGD解决方案近似于其标准有限元解决方案对应于可接受的精度,同时降低存储需求和计算时间(CPU时间)。数值结果表明,即使具有隐式时间集成方案,在改装网格时,每次时间步长的CPU时间线性地增加,这不是标准过程的情况。 (c)2021 elestvier b.v.保留所有权利。

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