Applied Math Seminar: Operator Splitting Methods in Numerical Computations
3:15PM; Neill Hall 3W
Summary: In dealing with nonlinear PDEs, particularly those with discontinuous parameters, many difficulties arise. Exact solutions are sought like the ends of rainbows; at first they seem almost within reach, but as you draw nearer, they shrink away, and eventually you give up the chase in frustration. Numerical methods are a quick go-to, but with usual methods you end up playing games balancing stability against complexity, with several accuracy checks thrown in. This is where I found myself with my research last spring when I decided to investigate operator splitting methods. Since then I have explored a number of different approaches to operator splitting and have found several strengths, a few weaknesses, and a couple pots of gold along the way. This talk will give a general introduction to operator splitting methods, their effects on accuracy and stability, and some numerical results to evaluate their utility.