论文标题
潮汐模型的预处理混合元素
Preconditioning mixed finite elements for tide models
论文作者
论文摘要
我们描述了一种可能在阻尼时进行线性化旋转浅水模型的完全离散的混合有限元方法。虽然曲柄 - 尼古尔森时间步变在没有阻力或强迫术语的情况下可以节省能量，并且不受类似CFL的稳定性条件的影响，但它需要在每个步骤中进行线性系统的反转。我们为这个代数系统开发加权标准的预处理，相对于系统中的物理和离散参数几乎是可靠的。使用FIREDRAKE的数值实验支持理论结果。
We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject to a CFL-like stability condition, it requires the inversion of a linear system at each step. We develop weighted-norm preconditioners for this algebraic system that are nearly robust with respect to the physical and discretization parameters in the system. Numerical experiments using Firedrake support the theoretical results.
