Weizmann Institute of Science

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 German-Israeli 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 multi-scale (multi-resolution) and parallel-processing 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 full-time 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:

  1. New top-efficiency multigrid methods for steady-state fluid dynamics at all Mach and Reynolds numbers, and other non-elliptic stationary PDE systems.

  2. Multilevel approaches to time-dependent partial-differential equations, emphasizing applications to oceanic and atmospheric flows.

  3. Grid adaptation techniques for bounded and unbounded domains, exploiting multigrid structures and resulting in a one-shot solver-adaptor.

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

  5. Optimal control: Feedback control via very fast updating of open-loop solutions, based on their multiscale representations.

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

  7. Top-efficiency multilevel algorithms for highly indefinite (e.g., standing wave) problems, with ray (geometrical-optics) equations at the limit of very coarse grids.

  8. Multigrid solvers for the Dirac equations arising in quantum field theory.

  9. 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.

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

  11. Multiscale Monte-Carlo algorithms for eliminating both the critical slowing down and the volume factor in increasingly advanced models of statistical physics, including non-equilibrium models.

  12. Multigrid Monte-Carlo approaches for solving the high-dimensional (several-particle) Schrodinger equation by real-time path integrals.

  13. Introducing multiscale computations to many-particle (macromolecule or many-small-molecule) 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.

  14. Multigrid methods for integral transforms and integro-differential equations, on adaptable grids, with applications to tribology.

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

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

  17. Rigorous quantitative theory for predicting the performance of multigrid solvers.

* * Prof. Brandt's home page * * Scientific Center's home page * * Faculty of Mathematics home page

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