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Explicit high-order generalized-α methods for isogeometric analysis of structural dynamics
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-12-04 , DOI: 10.1016/j.cma.2021.114344
Pouria Behnoudfar 1 , Gabriele Loli 2 , Alessandro Reali 3 , Giancarlo Sangalli 2 , Victor M. Calo 4
Affiliation  

We propose a new family of high-order explicit generalized-α methods for hyperbolic problems with the feature of dissipation control. Our k-stage approach delivers 2k,kN accuracy order in time by solving k matrix systems explicitly and updating 2k variables at each time-step. The user can control the numerical dissipation in the discrete spectrum’s high-frequency regions by adjusting the method’s coefficients. We study the method’s spectral behaviour and show that the CFL condition is independent of the accuracy. The stability region remains invariant while increasing the number of stages, that is, the accuracy order. Next, we exploit efficient preconditioners for the isogeometric matrix to minimize the computational cost. These preconditioners use a diagonal-scaled Kronecker product of univariate parametric mass matrices; they have a robust performance with respect to the spline degree and the mesh size, and their decomposition structure implies that their application is faster than a matrix–vector product involving the fully-assembled mass matrix. Our high-order schemes require simple modifications of the available implementations of the generalized-α method. Finally, we present numerical examples demonstrating the methodology’s performance regarding single- and multi-patch IGA discretizations.



中文翻译:

用于结构动力学等几何分析的显式高阶广义α方法

我们提出了一个新的高阶显式广义家族α具有耗散控制特征的双曲线问题的方法。我们的-阶段方法提供 2,N 通过求解及时准确排序 矩阵系统明确和更新 2每个时间步的变量。用户可以通过调整方法的系数来控制离散谱高频区域的数值耗散。我们研究了该方法的光谱行为并表明 CFL 条件与精度无关。稳定区域保持不变,同时增加阶段数,即精度阶数。接下来,我们利用等几何矩阵的有效预处理器来最小化计算成本。这些预处理器使用单变量参数的对角线缩放Kronecker 乘积质量矩阵;它们在样条度数和网格尺寸方面具有稳健的性能,并且它们的分解结构意味着它们的应用比涉及完全组装质量矩阵的矩阵向量乘积更快。我们的高阶方案需要对通用的可用实现进行简单的修改——α方法。最后,我们展示了数值例子,展示了该方法在单和多面片 IGA 离散化方面的性能。

更新日期:2021-12-04
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