论文标题
korteweg de Vries方程的结构保存降低订购建模
Structure-preserving reduced-order modelling of Korteweg de Vries equation
论文作者
论文摘要
针对汉密尔顿形式的Korteweg de Vries（KDV）方程开发了计算高效的，结构性的还原方法。 KDV方程在空间中通过有限差异而离散。普通微分方程（ODE）的偏斜分量系统与线性隐式Kahan的方法集成在一起，该方法可在大约保留Hamiltonian。我们已经使用正确的正交分解（POD）表明，全阶模型（FOM）的哈密顿结构由还原阶模型（ROM）保留。 KDV方程的二次非线性项可以通过使用张力方法有效地评估，从而显然将FOM和ROM的离线在线成本分开。一维KDV方程，耦合的KDV方程和二维Zakharov-Kuznetzov等方程，证明了降低的解决方案，保留哈密顿，动量和质量的准确性，动量和质量以及ROM获得的计算加速度的准确性。
Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized in space by finite differences. The resulting skew-gradient system of ordinary differential equations (ODEs) is integrated with the linearly implicit Kahan's method, which preserves the Hamiltonian approximately. We have shown, using proper orthogonal decomposition (POD), the Hamiltonian structure of the full-order model (FOM) is preserved by the reduced-order model (ROM). The quadratic nonlinear terms of the KdV equation are evaluated efficiently by the use of tensorial methods, clearly separating the offline-online cost of the FOMs and ROMs. The accuracy of the reduced solutions, preservation of the Hamiltonian, momentum and mass, and computational speed-up gained by ROMs are demonstrated for the one-dimensional KdV equation, coupled KdV equations and two-dimensional Zakharov-Kuznetzov equation with soliton solutions
