论文标题
基于内核的无网状保守盖金方法，用于求解哈密顿波程
A kernel-based meshless conservative Galerkin method for solving Hamiltonian wave equations
论文作者
论文摘要
我们提出了一种无网状的保守盖尔金方法，用于解决哈密顿波方程。我们首先使用galerkin型公式中的径向基础函数在空间中离散方程。与传统的RBF Galerkin方法不同，该方法直接使用其弱形式的非线性函数，我们的方法采用适当的投影算子来构建Galerkin方程，该方程将被证明可以保存全球能量。此外，我们为提出的离散化提供了完整的错误分析。我们通过二阶平均向量场方案进一步得出完全离散的解决方案。我们证明，完全离散的解决方案准确保留了离散的能量。最后，我们提供了一些数值示例，以证明准确性和节能。
We propose a meshless conservative Galerkin method for solving Hamiltonian wave equations. We first discretize the equation in space using radial basis functions in a Galerkin-type formulation. Differ from the traditional RBF Galerkin method that directly uses nonlinear functions in its weak form, our method employs appropriate projection operators in the construction of the Galerkin equation, which will be shown to conserve global energies. Moreover, we provide a complete error analysis to the proposed discretization. We further derive the fully discretized solution by a second order average vector field scheme. We prove that the fully discretized solution preserved the discretized energy exactly. Finally, we provide some numerical examples to demonstrate the accuracy and the energy conservation.
