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Domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) nonlinear model reduction
Computer Methods in Applied Mechanics and Engineering ( IF 7.2 ) Pub Date : 2021-06-23 , DOI: 10.1016/j.cma.2021.113997
Chi Hoang , Youngsoo Choi , Kevin Carlberg

A novel domain-decomposition least-squares Petrov–Galerkin (DD-LSPG) model-reduction method applicable to parameterized systems of nonlinear algebraic equations (e.g., arising from discretizing a parameterized partial-differential-equations problem) is proposed. In contrast with previous works, we adopt an algebraically non-overlapping decomposition strategy rather than a spatial-decomposition strategy, which facilitates application to different spatial-discretization schemes. Rather than constructing a low-dimensional subspace for the entire state space in a monolithic fashion, the methodology constructs separate subspaces for the different subdomains/components characterizing the original model. During the offline stage, the method constructs low-dimensional bases for the interior and interface of subdomains/components. During the online stage, the approach constructs an LSPG reduced-order model for each subdomain/component (equipped with hyper-reduction in the case of nonlinear operators), and enforces strong or weak compatibility on the ‘ports’ connecting them. We propose several different strategies for defining the ingredients characterizing the methodology: (i) four different ways to construct reduced bases on the interface/ports of subdomains, and (ii) different ways to enforce compatibility across connecting ports. In particular, we show that the appropriate compatibility-constraint strategy depends strongly on the basis choice. In addition, we derive a posteriori and a priori error bounds for the DD-LSPG solutions. Numerical results performed on nonlinear benchmark problems in heat transfer and fluid dynamics that employ both finite-element and finite-difference spatial discretizations demonstrate that the proposed method performs well in terms of both accuracy and (parallel) computational cost, with different choices of basis and compatibility constraints yielding different performance profiles.



中文翻译:

域分解最小二乘 Petrov-Galerkin (DD-LSPG) 非线性模型约简

提出了一种适用于非线性代数方程参数化系统的新型域分解最小二乘方 Petrov-Galerkin (DD-LSPG) 模型简化方法(例如,由于离散化参数化偏微分方程问题)。与之前的工作相比,我们采用代数非重叠分解策略而不是空间分解策略,这有助于应用于不同的空间离散化方案。而不是为整个状态空间构建一个低维子空间该方法以整体方式为表征原始模型的不同子域/组件构建单独的子空间。在离线阶段,该方法为子域/组件的内部和接口构建低维基础。在在线阶段,该方法为每个子域/组件构建一个 LSPG 降阶模型(在非线性算子的情况下配备超约简),并在连接它们的“端口”上强制执行强或弱兼容性。我们提出了几种不同的策略来定义表征该方法的成分:(i)在子域的接口/端口上构建简化基础的四种不同方法,以及(ii)在连接端口之间强制执行兼容性的不同方法。特别是,我们表明适当的兼容性约束策略在很大程度上取决于基础选择。此外,我们推导出DD-LSPG 解后验先验误差界限。在使用有限元和有限差分空间离散化的传热和流体动力学非线性基准问题上执行的数值结果表明,所提出的方法在精度和(并行)计算成本方面表现良好,具有不同的基础和兼容性约束产生不同的性能配置文件。

更新日期:2021-06-23
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