Mathematics Colloquium - Pavel Solin
This event is in the past.
Detroit, MI 48202
Speaker: Professor Pavel Solin, University of Nevada at Reno
Title: Solution of Time-Dependent Multiphysics Coupled Problems
with Adaptive hp-FEM and hp-DG Methods
Abstract: When using advanced computational methods such as hp-FEM and hp-DG for multiphysics coupled problems, the design of mathematical methods and the design of the software platform for their implementation are tightly connected both ways. In particular, good software design makes it possible to develop better mathematical methods. We will present several novel techniques for higher-order adaptive FEM and DG methods and show how they can be combined elegantly in an object-oriented software design. This software architecture was created in the framework of a NEUP project sponsored by the U.S. Department of Energy. Using this approach, we will show how to combine various physical fields and equations in multiphysics PDE systems, use different meshes to approximate specific behavior of each field, split the spatial and temporal discretization to eliminate interference between spatial discretizations and time integration methods, and to combine hp-FEM and hp-DG in a monolithic way for problems where only some of the quantities need to be discretized via DG. We will also show the importance of controlled-accuracy time integration based on adaptive implicit higher-order time-integration methods.