The Carl F. Gauss Minerva Center for
Scientific Computation
Achi Brandt, Director
The Elaine & Bram Goldsmith Professor of
Applied Mathematics
The Gauss Center was officially inaugurated in the fall of 1993, thanks to a generous endowment
from the Ministry for Science and Technology (BMFT) of the Federal Republic of Germany, through
the joint committee for GermanIsraeli cooperation (Minerva). Its objective is to act as a catalyst
for the development of new fundamental computational approaches in physics, chemistry, applied
mathematics and engineering, introducing, in particular, advanced multiscale (multiresolution)
and parallelprocessing methods. The Gauss Center interacts with many fields of application,
contributing to the transfer of algorithmic ideas back and forth among widely varying types of
problems. It offers workshops, short courses, temporary supervision and graduate studies for fulltime students, guest students, and visiting scientists.
The Gauss Minerva Center's
technical report series is available for downloading. So is also a detailed
survey paper
of all the current projects, briefly listed below.
Current Projects:

New topefficiency multigrid methods for steadystate fluid dynamics at all Mach and
Reynolds numbers, and other nonelliptic stationary PDE systems.

Multilevel approaches to timedependent partialdifferential equations, emphasizing
applications to oceanic and atmospheric flows.

Grid adaptation techniques for bounded and unbounded domains, exploiting multigrid structures and resulting in a oneshot solveradaptor.

Direct multigrid solvers for inverse problems, including system identification
(e.g., impedance tomography) and data assimilation (in atmospheric
simulations).

Optimal control: Feedback control via very fast updating of openloop solutions, based
on their multiscale representations.

General and highly accurate algebraic coarsening schemes (e.g. for algebraic
multigrid).

Topefficiency multilevel algorithms for highly indefinite (e.g., standing wave)
problems, with ray (geometricaloptics) equations at the limit of very coarse grids.

Multigrid solvers for the Dirac equations arising in quantum field theory.
 Compact multiresolution representation of the inverse matrix of a discretized
differential operator; fast updating of the inverse matrix and of the value of the
determinant upon changing an arbitrary term in the matrix itself; with application
to the QCD fermionic interaction.

Collective multiscale representation and fast calculation of many eigenfunctions of a
differential operator, e.g., the Schrodinger operator in electronicstructures
calculations. Fast expansion in terms of the eigenfunctions of a general differential
operator.

Multiscale MonteCarlo algorithms for eliminating both the critical slowing down and
the volume factor in increasingly advanced models of statistical physics, including
nonequilibrium models.

Multigrid MonteCarlo approaches for solving the highdimensional (severalparticle)
Schrodinger equation by realtime path integrals.

Introducing multiscale computations to manyparticle (macromolecule or
manysmallmolecule) calculations, including fast
evaluation of forces, fast convergence to local and global ground states, fast
Monte Carlo simulations and large time steps, with applications to molecular
mechanics; a new approach to molecular dynamics, based on stochastic implicit time
steps.

Multigrid methods for integral transforms and integrodifferential equations,
on adaptable grids, with applications to tribology.

Multiscale methods for the fast evaluation and inversion of the Radon transform
and other lineintegral transforms; applications to medical tomography (CT, MRI,
PET and SPECT) and airplane and satellite radar reconstruction.

Multiscale algorithms for early vision tasks such as surface reconstruction,
edge and fiber detection, segmentation, and meaningful picture coarsening.

Rigorous quantitative theory for predicting the performance of multigrid solvers.
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