论文标题
使用能量稳定的有限差异具有弱执行边界和界面条件
Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
论文作者
论文摘要
逐个求和（SBP）有限差方法具有二阶波方程的几种理想特性。它们结合了窄模式有限差算子的计算效率与曲线多嵌段网格上可证明的稳定性。虽然存在几种针对边界和界面条件的技术，但同时通过近似项（SATS）的弱施加也许是最灵活的技术。尽管SBP方法已多次应用于弹性波方程，但文献中尚未介绍用于一般各向异性弹性波方程的SBP-SAT方法。我们通过得出能源稳定的自动化联合会SBP-SAT方法来填补这一空白，以用于曲线多块网格上的一般各向异性材料。这些方法基于完全兼容的SBP操作员。尽管本文着重于经典的SBP有限差异操作员，但提出的边界和接口处理是一般的，并且适用于满足SBP属性的一系列方法。我们使用制造溶液的方法证明了一组完全兼容的SBP-SAT方案的稳定性和准确性。我们还展示了新方法在山区弹性动力的披肩和地震成像中的实用性。
Summation-by-parts (SBP) finite difference methods have several desirable properties for second-order wave equations. They combine the computational efficiency of narrow-stencil finite difference operators with provable stability on curvilinear multiblock grids. While several techniques for boundary and interface conditions exist, weak imposition via simultaneous approximation terms (SATs) is perhaps the most flexible one. Although SBP methods have been applied to elastic wave equations many times, an SBP-SAT method for general anisotropic elastic wave equations has not yet been presented in the literature. We fill this gap by deriving energy-stable self-adjoint SBP-SAT methods for general anisotropic materials on curvilinear multiblock grids. The methods are based on fully compatible SBP operators. Although this paper focuses on classical SBP finite difference operators, the presented boundary and interface treatments are general and apply to a range of methods that satisfy an SBP property. We demonstrate the stability and accuracy properties of a particular set of fully compatible SBP-SAT schemes using the method of manufactured solutions. We also demonstrate the utility of the new method in elastodynamic cloaking and seismic imaging in mountainous regions.
