Speaker
Timo Heister
(Clemson University)
Description
Multigrid methods are the only known approach to efficiently solve large
linear systems for solving PDEs by having runtime cost proportional to the
number of unknowns. Algebraic multigrid methods construct a hierarchy of
problems from the system matrix, while geometric multigrid methods use the
mesh hierarchy and system matrices from each level of this hierarchy.
While algebraic multigrid methods have been successful in the past and are
still the method of choice for large problems in deal.II, they have several
disadvantages over geometric multigrid methods when implemented in a
matrix-free version: First, scaling to more than a few thousand cores is
limited due to the large setup cost. Second, the low arithmetic intensity does
not lend itself to modern architectures. Third, implementation of
multithreading is difficult. Fourth, the matrices consume large amounts of
system memory.
Here we present the current status of adaptive, parallel, geometric multigrid
how it is implemented in deal.II. Several numerical tests demonstrate the
approach. Finally, we will close with future plans.
Primary author
Timo Heister
(Clemson University)
Co-authors
Guido Kanschat
(Heidelberg University)
Martin Kronbichler
(TU Munich)
Thomas Clevenger
(Clemson University)
