Colloquium

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 (LTL) 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 studied for the solution of large-scale flow problems with severely nonlinear constitutive laws arising in sea ice modeling.