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Explicit higher-order accurate isogeometric collocation methods for structural dynamics

机译：结构动力学的显式高阶精确等几何配点方法

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The objective of the present work is to develop efficient, higher-order space- and time-accurate, methods for structural dynamics. To this end, we present a family of explicit isogeometric collocation methods for structural dynamics that are obtained from predictor-multicorrector schemes. These methods are very similar in structure to explicit finite-difference time-domain methods, and in particular, they exhibit similar levels of computational cost, ease of implementation, and ease of parallelization. However, unlike finite difference methods, they are easily extended to non-trivial geometries of engineering interest. To examine the spectral properties of the explicit isogeometric collocation methods, we first provide a semi-discrete interpretation of the classical predictor-multicorrector method. This allows us to characterize the spatial and modal accuracy of the isogeometric collocation predictor- multicorrector method, irrespective of the considered time-integration scheme, as well as the critical time step size for a particular explicit time-integration scheme. For pure Dirichlet problems, we demonstrate that it is possible to obtain a second-order-in-space scheme with one corrector pass, a fourth-order-in-space scheme with two corrector passes, and a fifth-order-in-space scheme with three corrector passes. For pure Neumann and mixed Dirichlet-Neumann problems, we demonstrate that it is possible to obtain a second-order-in-space scheme with one corrector pass and a third-order-in-space scheme with two corrector passes, and we observe that fourth-order-in-space accuracy may be obtained pre-asymptotically with three corrector passes. We then present secondorder-in-time, fourth-order-in-time, and fifth-order-in-time fully discrete predictor-multicorrector algorithms that result from the application of explicit Runge-Kutta methods to the semi-discrete isogeometric collocation predictor-multicorrector method. We confirm the accuracy of the family of explicit isogeometric collocation methods using a suite of numerical examples. (C) 2018 Elsevier B.V. All rights reserved.
机译：本工作的目的是开发有效的，高阶的空间和时间精确的结构动力学方法。为此，我们提出了一系列用于结构动力学的显式等几何线配置方法，这些方法是从预测器-多校正器方案中获得的。这些方法在结构上与显式有限差分时域方法非常相似，特别是它们具有相似的计算成本，易于实现和易于并行化的水平。但是，与有限差分方法不同，它们很容易扩展到工程感兴趣的非平凡几何形状。为了检查显式等几何配点方法的光谱特性，我们首先提供经典预测器-多重校正器方法的半离散解释。这使我们能够表征等几何搭配预测器-多重校正器方法的空间和模态精度，而不考虑所考虑的时间积分方案以及特定显式时间积分方案的关键时间步长。对于纯狄利克雷问题，我们证明可以通过一个校正器遍历获得一个空间二阶方案，通过两个校正器遍历获得一个空间四阶方案，并且在空间上获得一个五阶空间带有三个校正器通行证的方案。对于纯Neumann问题和混合Dirichlet-Neumann问题，我们证明有可能获得一个校正因子通道的二阶空间方案和两个校正因子通道的三阶空间方案，并且观察到可以使用三个校正器预渐近地获得空间四阶精度。然后，我们介绍第二次时间，第四次时间和第五次时间完全离散的预测器-多重校正器算法，这些算法是通过将显式Runge-Kutta方法应用于半离散等几何搭配预测器得到的-multicorrector方法。我们使用一组数值示例来确认一系列显式等几何配置方法的准确性。 （C）2018 Elsevier B.V.保留所有权利。

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