Andrea Brugnoli , Ramy Rashad , Yi Zhang , Stefano Stramigioli
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引用次数: 0
摘要
在本文中,我们将Hodge Laplacian [Awanou et al.(2023)[16]]的杂化框架扩展到描述线性波传播现象的port- hamilton系统。为此,引入了一种双场混合伽辽金离散化方法,其中一个变量是通过拟合有限元空间逼近的,而另一个变量是完全局部的。然后将混合公式进行杂化以得到一个等效公式,该公式可以在离散时间内使用静态凝聚过程更有效地求解。由于最终系统只包含一个变量的全局耦合迹,因此由于杂交所实现的尺寸减小比霍奇拉普拉斯所获得的尺寸减小更大。对三维波和麦克斯韦方程组的数值实验表明了该方法的收敛性和杂化后的尺寸减小。
Finite element hybridization of port-Hamiltonian systems
In this contribution, we extend the hybridization framework for the Hodge Laplacian [Awanou et al. (2023) [16]] to port-Hamiltonian systems describing linear wave propagation phenomena. To this aim, a dual field mixed Galerkin discretization is introduced, in which one variable is approximated via conforming finite element spaces, whereas the second is completely local. The mixed formulation is then hybridized to obtain an equivalent formulation that can be more efficiently solved using a static condensation procedure in discrete time. The size reduction achieved thanks to the hybridization is greater than the one obtained for the Hodge Laplacian as the final system only contains the globally coupled traces of one variable. Numerical experiments on the 3D wave and Maxwell equations illustrate the convergence of the method and the size reduction achieved by the hybridization.
期刊介绍:
Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results.
In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.