Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation
Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation
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DOI：
10.1142/s0218396x03001912
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发表时间：
2003-06
影响因子：
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通讯作者：
O. Cessenat;B. Després
中科院分区：
文献类型：
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作者：
O. Cessenat;B. Després
本文讨论用超弱变分法求解Helmholtz方程和时谐麦克斯韦方程。该方法，从区域分解技术发出，在于在分区的域划分成子域与使用自适应的接口条件。比区域分解更进一步，我们使问题退化为界面问题。新公式与弱公式等价。离散化过程是一个Galerkin。一个可能的优势UWVF适用于波动方程是，我们使用的物理方法，包括在近似的解决方案与平面波。该配方允许使用一个非常大的网格相比，频率，相反的有限元法时，适用于时间谐波方程。此外，收敛性分析表明，该方法是一个高阶的：阶的发展作为自由度的数量的平方根。
This article deals with the use of the Ultra Weak Variational Formulation to solve Helmholtz equation and time harmonic Maxwell equations. The method, issued from domain decomposition techniques, lies in partitioning the domain into subdomains with the use of adapted interface conditions. Going further than in domain decomposition, we make so that the problem degenerates into an interface problem only. The new formulation is equivalent to the weak formulation. The discretization process is a Galerkin one. A possible advantage of the UWVF applied to wave equations is that we use the physical approach that consists in approximating the solution with plane waves. The formulation allows to use a very large mesh as compared to the frequency, on the contrary to the Finite Element Method when applied to time harmonic equations. Furthermore, the convergence analysis shows the method is a high order one: the order evolves as the square root of the number of degrees of freedom.