Mitigating the nonlinearity in PDEs, with application to continuous sea ice models

Speaker: Georg Stadler (NYU)

Date: 11/14/23

Abstract: I will argue that nonlinearity in PDE systems can be mitigated through lifting the systems to a higher-dimensional space. After reviewing basic properties of Newton’s method for solving nonlinear equations, I will detail the proposed lift-transform-linearize approach and show that the resulting Newton-type algorithms may yield favorable convergence properties. I will illustrate the ideas first on simple examples, and show connections to primal-dual interior point methods and mixed finite element methods. The resulting solvers will be illustrated for the solution of a large-scale flow problems with severely nonlinear constitutive law arising in the most commonly used continuous sea ice model.