论文标题
窗户时空最小二乘彼得罗夫 - 盖尔金方法，用于降低非线性模型订单
Windowed space-time least-squares Petrov-Galerkin method for nonlinear model order reduction
论文作者
论文摘要
这项工作介绍了窗户时空最小二乘彼得罗夫 - 盖尔金方法（WST-LSPG），用于降低非线性参数化动态系统。 WST-LSPG是时空最小二乘petrov-galerkin方法（ST-LSPG）的概括。 ST-LSPG的主要缺点是，它需要在整个全球时域中求解具有时空基础的密集时空系统，这对于大规模应用可能是不可行的。 Instead of using a temporally-global space-time trial subspace and minimizing the discrete-in-time full-order model (FOM) residual over an entire time domain, the proposed WST-LSPG approach addresses this weakness by (1) dividing the time simulation into time windows, (2) devising a unique low-dimensional space-time trial subspace for each window, and (3) minimizing the discrete-in-time space-time residual of the dynamical system over each window.该公式会产生一个问题，即在每个窗口内限制耦合，但在整个窗口之间进行顺序。为了启用以相对较少数量的基础向量为特征的高保真试验子空间，这项工作提出了使用每个窗口的张量分解来构建时空碱基。 WST-LSPG配备了高还原技术，以进一步降低计算成本。一维汉堡方程的数值实验和二维可压缩的Navier-Stokes方程的流量超过NACA 0012机翼，这表明WST-LSPG在准确性和计算增益方面优于ST-LSPG。
This work presents the windowed space-time least-squares Petrov-Galerkin method (WST-LSPG) for model reduction of nonlinear parameterized dynamical systems. WST-LSPG is a generalization of the space-time least-squares Petrov-Galerkin method (ST-LSPG). The main drawback of ST-LSPG is that it requires solving a dense space-time system with a space-time basis that is calculated over the entire global time domain, which can be unfeasible for large-scale applications. Instead of using a temporally-global space-time trial subspace and minimizing the discrete-in-time full-order model (FOM) residual over an entire time domain, the proposed WST-LSPG approach addresses this weakness by (1) dividing the time simulation into time windows, (2) devising a unique low-dimensional space-time trial subspace for each window, and (3) minimizing the discrete-in-time space-time residual of the dynamical system over each window. This formulation yields a problem with coupling confined within each window, but sequential across the windows. To enable high-fidelity trial subspaces characterized by a relatively minimal number of basis vectors, this work proposes constructing space-time bases using tensor decompositions for each window. WST-LSPG is equipped with hyper-reduction techniques to further reduce the computational cost. Numerical experiments for the one-dimensional Burgers' equation and the two-dimensional compressible Navier-Stokes equations for flow over a NACA 0012 airfoil demonstrate that WST-LSPG is superior to ST-LSPG in terms of accuracy and computational gain.
