 
Summary: Colloquium
Jaap van der Vegt
Optimization of Multigrid Algorithms for Higher Order
Accurate Discontinuous Galerkin Discretizations
Thursday 26 January, Citadel T300 , 15:4516:30
Multigrid algorithms provide some of the most efficient methods
for the solution of large systems of (non)linear algebraic equations.
These equations can originate from numerical discretizations of par
tial differential equations, but also from many other sources. Multi
grid performance is, however, quite sensitive to the details of the al
gorithm. New classes of problems frequently require a detailed math
ematical analysis before excellent convergence rates are obtained.
In this presentation, first a brief outline will be given of multigrid
algorithms and the analysis of their performance using discrete Fourier multilevel analysis.
Next, we will discuss the novel hpMultigrid as Smoother algorithm, which was developed
for higher order accurate discontinuous Galerkin finite element discretizations of advection
dominated flow problems.
Using multilevel analysis the operator norm and spectral radius of the multigrid error
transformation operator can be computed. Searching for multigrid smoother coefficients
that minimize the spectral radius of the error transformation operator then optimizes
