论文标题
双曲线偏微分方程中的近似移动点源
Approximating moving point sources in hyperbolic partial differential equations
论文作者
论文摘要
我们考虑通过有限差异离散的双曲线方程中的点源。如果源是静止的，则已证明适当的源离散化可以保留有限差异方法的准确性。但是，移动点源构成了两个固定案例中没有出现的两个挑战。首先，离散源不得激发以源速度传播的模式。其次，离散的源频谱幅度必须独立于源位置。我们得出一个符合这些要求的源离散化，并证明了数值解决方案的设计阶融合对于一维对流方程。数值实验表明在两个维度的声波方程中也表明设计顺序收敛。源离散化涵盖$ \ sqrt {n} $网格的订单，并适用于不触摸域边界的源轨迹。
We consider point sources in hyperbolic equations discretized by finite differences. If the source is stationary, appropriate source discretization has been shown to preserve the accuracy of the finite difference method. Moving point sources, however, pose two challenges that do not appear in the stationary case. First, the discrete source must not excite modes that propagate with the source velocity. Second, the discrete source spectrum amplitude must be independent of the source position. We derive a source discretization that meets these requirements and prove design-order convergence of the numerical solution for the one-dimensional advection equation. Numerical experiments indicate design-order convergence also for the acoustic wave equation in two dimensions. The source discretization covers on the order of $\sqrt{N}$ grid points on an $N$-point grid and is applicable for source trajectories that do not touch domain boundaries.
