论文标题
粘性塑料式海冰模型的强大而有效的原始双牛顿 - 克里洛夫求解器
Robust and efficient primal-dual Newton-Krylov solvers for viscous-plastic sea-ice models
论文作者
论文摘要
我们为粘稠的海冰模型提供了牛顿 - 克里洛夫求解器。这种构成关系通常在气候模型中用于描述海冰的材料特性。由于材料定律在动量方程中引入的强烈非线性，快速，健壮和可扩展的求解器的发展仍然是一个重大挑战。在本文中，我们提出了一种新颖的牛顿线性化新型牛顿线性化，以实现隐式离散的动量方程。与现有方法相比，它相对于网状细化而更快，更稳定，因此可以在高分辨率下进行数值收敛的海冰模拟。结合用于线性化系统的代数多族基于基本的Krylov方法，该方法包含较大的系数，所得的求解器尺度很好，可以并行使用。我们介绍了两个具有挑战性的测试问题的实验，并研究了求解器的性能，涉及多达840万个空间未知数的问题。
We present a Newton-Krylov solver for a viscous-plastic sea-ice model. This constitutive relation is commonly used in climate models to describe the material properties of sea ice. Due to the strong nonlinearity introduced by the material law in the momentum equation, the development of fast, robust and scalable solvers is still a substantial challenge. In this paper, we propose a novel primal-dual Newton linearization for the implicitly-in-time discretized momentum equation. Compared to existing methods, it converges faster and more robustly with respect to mesh refinement, and thus enables numerically converged sea-ice simulations at high resolutions. Combined with an algebraic multigrid-preconditioned Krylov method for the linearized systems, which contain strongly varying coefficients, the resulting solver scales well and can be used in parallel. We present experiments for two challenging test problems and study solver performance for problems with up to 8.4 million spatial unknowns.
