Stable and accurate second-order formulation of the shifted wave equation
Stable and accurate second-order formulation of the shifted wave equation
复制标题
稳定且准确的位移波动方程二阶公式
DOI：
10.4208/cicp.2009.08.135
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发表时间：
2009
影响因子：
3.7
通讯作者：
Florencia Parisi
中科院分区：
文献类型：
--
作者：
K. Mattsson;Florencia Parisi
本文导出了一维二阶位移波方程的高阶有限差分近似。该域离散使用完全兼容的求和部分运营商和边界条件施加使用惩罚方法，导致完全显式的时间积分。这种离散化产生严格稳定和有效的计划。通过一维数值模拟验证了分析的正确性。目前的研究是第一步，对严格稳定的模拟二阶制定爱因斯坦方程在三维空间。AMS科目分类：35L05、35L20、65N06、65N12、83C05
High order finite difference approximations are derived for a onedimensional model of the shifted wave equation written in second-order form. The domain is discretized using fully compatible summation by parts operators and the boundary conditions are imposed using a penalty method, leading to fully explicit time integration. This discretization yields a strictly stable and efficient scheme. The analysis is verified by numerical simulations in one-dimension. The present study is the first step towards a strictly stable simulation of the second-order formulation of Einstein’s equations in three spatial dimensions. AMS subject classifications: 35L05, 35L20, 65N06, 65N12, 83C05