An adaptive Newton multigrid method for a model of marine ice sheets
An adaptive Newton multigrid method for a model of marine ice sheets
复制标题
DOI：
10.1016/j.jcp.2013.06.032
复制
发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
G. Jouvet;Carsten Gräser
中科院分区：
文献类型：
--
作者：
G. Jouvet;Carsten Gräser
在本文中，我们考虑一个模型的时间演变的三维海洋冰盖。该模型结合了冰变形的浅冰近似（SIA），基底滑动的浅陆架近似（SSA）和质量守恒原理。在每一个时间步，我们解决一个标量拉普拉斯最小化类型的问题与障碍（SIA），一个矢量的p-Laplace最小化类型的问题（SSA）和运输方程（质量守恒）。这两个最小化问题使用截断非光滑牛顿多重网格法求解，而输运方程则使用顶点中心有限体积法求解。我们的方法相结合的启发式网格自适应细化过程，以面对大梯度的解决方案，预计冰盖和冰架之间。作为应用程序，我们提出了一些模拟的海洋冰盖模型相互比较项目MISMIP（2D和3D），并验证我们的结果对解析解（2D）和其他参与者的模型结果（3D）。进一步的数值结果表明，我们的牛顿多重网格方法的收敛是不敏感的局部细化，使我们的整体自适应策略充分有效。
In this paper, we consider a model for the time evolution of three-dimensional marine ice sheets. This model combines the Shallow Ice Approximation (SIA) for the ice deformation, the Shallow Shelf Approximation (SSA) for the basal sliding, and the mass conservation principle. At each time step, we solve a scalarp-Laplace minimization-type problem with obstacle (SIA), a vectorialp-Laplace minimization-type problem (SSA) and a transport equation (mass conservation). The two minimization problems are solved using a truncated nonsmooth Newton multigrid method while the transport equation is solved using a vertex-centred finite volume method. Our approach is combined to an heuristic mesh adaptive refinement procedure to face the large gradients of the solution that are expected between the ice sheet and the ice shelf. As applications, we present some simulations of the Marine Ice Sheet Model Intercomparison Project MISMIP (2D and 3D) and validate our results against an analytic solution (2D) and other participant model results (3D). Further numerical results show that the convergence of our Newton multigrid method is insensitive to local refinements making our overall adaptive strategy fully efficient.