#### Milestone Year

### 1972

#### Pioneering modern multi-scale computations

The fundamental laws governing physics and chemistry and many branches
of engineering are clearly defined, but when they are applied to solving
concrete practical and theoretical problems the required calculations
are often too costly to be carried out at any desired accuracy.
The common reason is the enormous gap between the fine (microscopic) scale
at which these laws are given and the much larger (macroscopic) scales
of the phenomena we wish to calculate.
To address this challenge, first in the specific context of fluid dynamic
problems, Weizmann Institute scientists devised in 1972 a new computational
approach in which separate calculations are conducted at many intermediate
scales (resolutions) of the problem, with various modes of transferring
information from one scale to another. This produced huge reductions in
the computer resources required to solve each flow problem.
The multi-scale (or "multigrid") methodology has subsequently been
generalized and extended to many other types of mathematical problems
and areas of application, influencing almost every aspect of
contemporary science and engineering. It also inspires current
developments of multi-level algorithms in computer science,
from large network analysis and data mining to machine vision,
learning and recognition.