A note on the numerical solution of the wave equation with piecewise smooth coefficients
A note on the numerical solution of the wave equation with piecewise smooth coefficients
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DOI：
10.1090/s0025-5718-1984-0736442-3
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发表时间：
1984-05
影响因子：
2
通讯作者：
David L. Brown
中科院分区：
文献类型：
--
作者：
David L. Brown
本文考虑了波动方程初值问题的数值解，当方程系数为分段光滑时。这个问题模拟了线性波在介质中的传播，其中介质的属性在界面处不连续地变化。收敛差分近似可以被发现，不需要明确的规格的边界条件在接口中的介质，因此是简单的程序。虽然这种差分近似通常只能被预期为一阶精度，但是如果微分方程中的系数是平滑的，则数值相速度具有与差分近似相同的精度。这是证明了一维的情况下，并证明了在两个空间维度中的接口是不对齐的计算网格的例子数值。
The numerical solution of the initial value problem for the wave equation is considered for the case when the equation coefficients are piecewise smooth. This problem models linear wave propagation in a medium in which the properties of the medium change discontinuously at interfaces. Convergent difference approximations can be found that do not require the explicit specification of the boundary conditions at interfaces in the medium and hence are simple to program. Although such difference approximations typically can only be expected to be first-order accurate, the numerical phase velocity has the same accuracy as the difference approximation would if the coefficients in the differential equation were smoooth. This is proved for the one-dimensional case and demonstrated numerically for an example in two space dimensions in which the interface is not aligned with the computational mesh.