Special Lecture - 2/15, 12:00PM, Duncan Hall 3076
Timo Heister
Department of Mathematics
Texas A&M University
"Large Scale Computational Fluid Dynamics"
The numerical solution of incompressible flow problems on a massively parallel architecture requires a parallel discretization and a robust linear solver that are both scalable and efficient. Many important practical problems require the computational solution of complex fluid flow problems on large numbers of processors.
In this talk, I will present both, a preconditioner for the incompressible Navier Stokes equations based on Grad-Div stabilization, and a generic framework for adaptive, massively parallel finite element computations.
The preconditioner is based on the realization that Grad-Div stabilization, originally developed as a means to stabilize the discretization, also has a large influence on the algebraic properties of the discretized linear system similar to the classical augmented Lagrangian approach. This can be exploited in the approximation of the Schur complement.
In the second part of my talk I will discuss the motivations, algorithms, and data structures for a massively parallel finite element framework supporting adaptive mesh refinement. Implementation of such a framework is complex and often results in code tailored to specific problem domains, code without the ability to scale to a large number of machines, or often both. In contrast, the design presented here allows fast solution with good parallel scalability and retains the flexibility to solve all kinds of problems.
T. Heister, G. Rapin. Efficient Augmented Lagrangian-type Preconditioning for the Oseen Problem using Grad-Div Stabilization. Int. J. Numer. Meth. Fluids, 2013, 71: 118-134.
W. Bangerth, C. Burstedde, T. Heister, M. Kronbichler. Algorithms and Data Structures for Massively Parallel Generic Finite Element Codes. ACM Trans. Math. Softw., 2011. Volume 38(2).
W. Bangerth, T. Heister, G. Kanschat. deal.II Differential Equations Analysis Library, Technical Reference, 2013. http://www.dealii.org.