Parallel simulation of Phase field equations through Spectral Deferred Corrections

Mr. Jan Gruenenwald
University of Wisconsin-Milwaukee
Graduate Student

Numerical solutions of partial differential equations (PDEs) are to this day a topic of great interest with applications in a plethora of scientific fields. The method of ‘Spectral Deferred Corrections’ (SDC) was developed and first referred to as such in 2000, but various advancements have since been made on the method. Using SDC, we can obtain approximations to the solution of an ordinary differential equation (obtained after discretizing the PDE in space) by placing Gauss-quadrature nodes in time and iteratively applying a corrector equation. This defense will go into how the method is derived, how it can be applied to so-called ‘Phasefield equations’, how it was implemented in C++ and how the method performed in select test-cases.

Committee Members:
Profs. Vinsent Larson (advisor), Peter Hinow, Dexuan Xie

Click here to view the event flyer.