Page 299 - The Combined Finite-Discrete Element Method

282 COMPUTATIONAL ASPECTS

This is a very large sum indeed to pay to run a single combined finite-discrete element
job. The problem that such a job could solve would, for instance, involve rock blasting
of a total volume of
10·10·10 = 1000 m 3 (9.4)

discretised to the resolution of 1 mm (which would give a reasonable accuracy). The mar-
ket value of all the rock would probably not exceed £10,000. Coarser discretisation to
1 cm resolution (with a greatly reduced accuracy and micromechanical processes associ-
ated with fines mostly neglected) would result in the total amount of rock being simulated
equal to, say
40·50·500 = 1000,000 m 3 (9.5)

and a probable market value of the rock £10,000,000, which is still much less than the
cost of a computer simulation of such a problem.
Grand challenge combined finite-discrete element simulations are clearly beyond the
CPU and RAM limits of present day computers, and at present day RAM and CPU prices
are not affordable for most practical engineering, industrial and scientific applications.
However, it is worth mentioning that even a one billion system seemed impossible five
years ago. A one million system was beyond the limits of most available hardware in the
early 1990s, while even a one hundred thousand system was beyond limits of the most
powerful and most expensive computers in the early 1980s. It is only 25 years since those
early days. If Moore’s law is to continue in the future, the next 25 years may even bring
systems comprising a quadrillion of discrete elements. This is illustrated by an imaginary
scenario of the market price of a single processor of performance of a modern workstation
being reduced to 1 penny. An array of

1000·1000·1000 = 1000,000,000 processors (9.6)

would cost £10,000,000. Say that each processor can handle 1,000,000 discrete element
system in one day. A grid of such processors, if communication between processors
is neglected, would handle a one thousand trillion (one quadrillion) particle system in
24 hours. This is equivalent to a cube of rock 1000 by 1000 by 1000 m comprising
discrete elements of an average size of 1 cm. The probable value of such a cube of rock
would be £10 billion. Assuming that the computer is outdated after two years, and that
computer capacity is used 100%, the cost of computer simulations would be

10,000,000
= £1370 (9.7)
2·365
This is negligible in comparison to the probable market price of the rock. This clearly
demonstrates that there is no need to be pessimistic about grand challenge combined finite-
discrete element simulations. On the contrary, one has to look forward to the day when
these will become small-scale combined finite-discrete element simulations because of
the massive CPU power available. A pile of rock is a relatively low technology problem.
However, there is a whole class of similar discontinua problems that will require grand
challenge combined finite-discrete element simulations. That such simulations will become
possible is beyond doubt; the only question is whether the suitable hardware will become