Applications of Anderson Acceleration to Algorithms for Newtonian and Non-Newtonian Fluid Simulation

Dr. Leo Rebholz
Dr. Leo Rebholz

Abstract: After reviewing recent theoretical results for Anderson acceleration (AA), we consider its application to solving incompressible Navier-Stokes (NS) equations and regularized Bingham equations. For NS, the classical penalty method is considered, which typically will only work with very small penalty (but very small penalty causes issues with iterative solvers, making it not practical for large scale use). For regularized Bingham, we consider a Picard type iteration that has trouble converging for small regularization parameter. We show that both of these methods can be cast as fixed-point iterations that fall into the AA theory framework, which allows for improved convergence rates to be proven. Moreover, numerical results reveal that with AA, the classical penalty method is very effective even with O(1) penalty parameter and regularized Bingham Picard iteration is dramatically improved and nearly robust with respect to the regularization parameter.

 Speaker’s Bio: Leo Rebholz is a Professor of Mathematical Sciences at Clemson University, with research interests in numerical analysis, partial differential equations, computational fluid dynamics, turbulence, numerical linear algebra, model reduction, data assimilation, and nonlinear solvers. He received his PhD in mathematics from the University of Pittsburgh (Pitt) in 2006, studying numerical analysis under the direction of Professor William Layton. After Pitt, he spent two years as a Senior Mathematician at Bechtel Bettis Atomic Power Laboratory, working on dynamical system model reduction. In 2008, he began a tenure track job at Clemson 
University and has been there ever since. He has published three books, over 100 journal articles, and has advised nine PhD students.

Last Updated: November 3, 2021 - 7:57 am