发表机构
Ben-Gurion University of the Negev; Tel Aviv University（内盖夫本-古里安大学; 特拉维夫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出广义MAC紧致离散框架及弹性色散校正过程，用于求解弹性亥姆霍兹方程，实现二阶精度并显著降低色散误差，优于现有紧致格式。
AI 中文摘要
我们开发了一族用于弹性亥姆霍兹方程的紧致、色散校正的基于标记和网格（MAC）的有限差分离散格式。虽然色散校正对于标量亥姆霍兹问题已得到充分研究，但针对弹性问题的研究较少，且大多数采用非紧致模板。为此，我们引入了一个广义MAC（GMAC）框架，该框架能够对弹性亥姆霍兹方程进行紧致离散。我们证明了尽管GMAC是非对称的，但这种离散不会产生数值耗散，也不会出现剪切模式分离。对于某些权重，GMAC的极化误差低于标准MAC。我们还引入了一种弹性色散校正（EDC）过程，将实位移波数色散校正方法从声学问题扩展到弹性亥姆霍兹问题。我们证明并通过数值实验展示了GMAC具有二阶精度。此外，我们表明EDC显著降低了标准MAC的色散，并在某些GMAC实例中提供了额外的校正。色散分析表明，所得方法在色散精度上优于现有的紧致有限差分离散格式，并且与某些非紧致格式相比具有竞争力。我们给出了在轻度非均匀介质中相位对齐改善的数值证据。
英文摘要
We develop a family of compact, dispersion-corrected marker-and-cell (MAC)-based finite-difference discretizations for the elastic Helmholtz equation. While dispersion correction is well established for scalar Helmholtz problems, fewer approaches exist for the elastic problems, and most use non-compact stencils. To this end, we introduce a generalized MAC (GMAC) framework that enables compact discretization of the elastic Helmholtz equation. We prove that even though GMAC is non-symmetric, this discretization produces no numerical dissipation and no shear-mode separation. For certain weights, GMAC has lower polarization error than standard MAC. We also introduce an elastic dispersion correction (EDC) process, extending real-shifted-wavenumber dispersion correction methods from acoustic to elastic Helmholtz problems. We prove and demonstrate numerically that GMAC is second-order accurate. Furthermore, we show that EDC substantially reduces dispersion for standard MAC and can provide additional correction in some instances of GMAC. Dispersion analysis shows that the resulting method outperforms existing compact finite-difference discretizations in dispersion accuracy and is competitive with some non-compact schemes. We give numerical evidence for improved phase alignment in mildly heterogeneous media.
Comments28 pages, 8 figures
