发表机构
University of Bergen（卑尔根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出频域Biot--Allard方程的双场公式，通过速度-压力率表示恢复斜伴随结构，实现稳定迭代分裂，并验证了数值方法的鲁棒性，为多孔介质波动建模提供高效框架。
AI 中文摘要
我们提出了一个频域形式的Biot动态多孔弹性方程，该方程包含频率相关的耗散（Biot--Allard），适用于具有记忆效应的各向异性、非均匀介质。两种等价的二场表示——位移-压力和速度-压力率公式——使得稳定的迭代分裂成为可能。虽然耦合算子通常在有限频率下缺乏伴随或斜伴随关系，但速度-压力率表示在准静态极限下恢复了斜伴随结构。我们证明了耦合算子的连续性和对角块的强制性，这对于L-稳定分裂方案的收敛性至关重要。频域设置消除了卷积记忆项，通过复值参数纳入衰减和色散，并将时间相关问题简化为适合并行计算和多频反演的一族椭圆边值问题。一致Galerkin有限元离散保持了块结构，数值实验确认了鲁棒性并捕获了频率相关的衰减。为了说明离散化无关性，我们包含了一个使用伪谱方法的大规模波动模拟。这项工作为复杂多孔介质中的波动现象建模提供了一个严谨且高效的框架。
英文摘要
We present a frequency-domain formulation of Biot's dynamic poroelastic equations with frequency-dependent dissipation (Biot--Allard) for anisotropic, heterogeneous media with memory effects. Two equivalent two-field representations--a displacement-pressure and a velocity-pressure-rate formulation--enable stabilized iterative splitting. While coupling operators generally lack an adjoint or skew-adjoint relationship at finite frequencies, the velocity--pressure-rate representation restores a skew-adjoint structure in the quasi-static limit. We prove continuity of the coupling operators and coercivity of the diagonal blocks, essential for convergence of the L-stabilized splitting scheme. The frequency-domain setting eliminates convolutional memory terms, incorporates attenuation and dispersion via complex-valued parameters, and reduces the time-dependent problem to a family of elliptic boundary-value problems suited for parallel computation and multi-frequency inversion. A conforming Galerkin finite element discretization preserves block structure, and numerical experiments confirm robustness and capture frequency-dependent attenuation. To illustrate discretization independence, we include a large-scale wave simulation using a pseudo-spectral method. This work provides a rigorous and efficient framework for modeling wave phenomena in complex porous media.
