Biot固结模型的混合间断Galerkin方法的预条件处理
Preconditioning of a hybridizable discontinuous Galerkin method for Biot's consolidation model
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中文总结 AI 辅助
本文针对Biot固结模型四场形式的HDG离散，提出参数鲁棒预条件子，并证明其约化形式在静态凝聚后仍保持参数鲁棒性，通过二维和三维数值实验验证。
中文摘要 AI 辅助
我们为Biot固结模型四场形式的混合间断Galerkin（HDG）离散提出了一种参数鲁棒的预条件子。我们首先为完整离散确定了一个参数鲁棒的预条件子。然而，HDG方法允许静态凝聚。因此，我们应用我们先前工作[arXiv:2503.05918, 2025]中提出的框架，证明该预条件子的约化形式对于约化HDG离散也是参数鲁棒的。我们通过二维和三维的数值算例验证了该预条件子的参数鲁棒性。
英文摘要
We present a parameter-robust preconditioner for a hybridizable discontinuous Galerkin (HDG) discretization of a four-field formulation of Biot's consolidation model. We first determine a parameter-robust preconditioner for the full discretization. HDG methods, however, allow for static condensation. We therefore apply the framework presented in our previous work [arXiv:2503.05918, 2025] to show that a reduced form of the preconditioner is also parameter-robust for the reduced HDG discretization. We verify the parameter-robustness of the preconditioner through numerical examples in both two and three dimensions.
