Graduate Student / Postdoc Seminar

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Newton methods revisited, with application to non-Newtonian fluid dynamics

Speaker: Georg Stadler, Courant

Location: Warren Weaver Hall 1302

Date: Friday, April 8, 2022, 11:15 a.m.

Synopsis:

I will review basic properties of Newton's method for solving
nonlinear equations and eventually nonlinear systems of PDEs. For
difficult nonlinearities it can be beneficial to introduce additional
variables before deriving the Newton linearization. These variables
can then be eliminated analytically before solving the Newton system,
such that the computational cost per iteration is the same as for
standard Newton methods.  The resulting algorithms may yield favorable
convergence properties. After illustrating the ideas on a simple
example, I will show its application for the solution of flow problems
with visco-plastic constitutive relations. Such models are commonly
used in earth science models.  This is joint work with
Johann Rudi (Argonne) and Melody Shih (NYU).