论文标题
时间域弹性动力学的两级参数化模型降低方法
A Two-Level Parameterized Model-Order Reduction Approach for Time-Domain Elastodynamics
论文作者
论文摘要
我们为时间域弹性动力学的线性双曲线偏微分方程（PDE）提供了两级参数化模型级降低（PMOR）技术。为了近似频域PDE，我们利用端口减少的基本基本组件（PR-RBC）方法来开发（在离线阶段）减少子域的碱基；然后将后者组装（在在线阶段），以形成全球感兴趣的领域。 PR-RBC方法降低了参数空间的有效维度，还提供了拓扑和几何形状的灵活性。在在线阶段，对于每个查询，我们考虑一个给定的参数值和相关的全局域。在降低的第一级中，PR-RBC还原碱可用于在选定频率下近似频域溶液。在降低的第二层中，这些实例化的PR-RBC近似值用作强烈贪婪的方法中的替代真理解决方案，以识别减少的基础空间。然后将时间域弹性动力学的PDE投射到这个缩小的空间上。我们提供了一个数字示例来证明计算能力并评估所提出的两级方法的性能。
We present a two-level parameterized Model Order Reduction (pMOR) technique for the linear hyperbolic Partial Differential Equation (PDE) of time-domain elastodynamics. In order to approximate the frequency-domain PDE, we take advantage of the Port-Reduced Reduced-Basis Component (PR-RBC) method to develop (in the offline stage) reduced bases for subdomains; the latter are then assembled (in the online stage) to form the global domains of interest. The PR-RBC approach reduces the effective dimensionality of the parameter space and also provides flexibility in topology and geometry. In the online stage, for each query, we consider a given parameter value and associated global domain. In the first level of reduction, the PR-RBC reduced bases are used to approximate the frequency-domain solution at selected frequencies. In the second level of reduction, these instantiated PR-RBC approximations are used as surrogate truth solutions in a Strong Greedy approach to identify a reduced basis space; the PDE of time-domain elastodynamics is then projected on this reduced space. We provide a numerical example to demonstrate the computational capability and assess the performance of the proposed two-level approach.
