Page 298 - The Combined Finite-Discrete Element Method

GRAND CHALLENGE COMBINED FINITE-DISCRETE ELEMENT SIMULATIONS 281

variable at address 2, third variable at address 3, nth variable at address n. The address
of an individual variable is in essence a number pointing to where this variable is in the
array. If this number is, say, a 32-bit number, the total number of different variables is
given by
n = 2 32 = 4.29 billion (9.1)

Exact implementation of the virtual memory concept varies from operating system to
operating system, and can be different on different workstations. Irrespective of these
different implementations, it is evident from equation (9.1) that there is a limit to the size
of problem that can be handled with a 4 byte address. The problem of RAM space can
be resolved in two ways:

• Implementation of parallel, distributed or grid computing options, with both RAM
and CPU requirements being distributed to different processors or different computers.
With a distributed option comprising a 1000 workstation cluster, the above limit would
increase by 1000 times. The same applies to parallel or grid computing options.
• The 64 bit address increases the above RAM limit by 4.29 billion times, making virtual
RAM space almost unlimited for all practical purposes of very large scale combined
finite-discrete element simulations.

9.3 GRAND CHALLENGE COMBINED FINITE-DISCRETE
ELEMENT SIMULATIONS

Some combined finite-discrete element problems may require over one hundred billion
discrete elements. Some may even require over one trillion or even a quadrillion of
discrete elements. Combined finite-discrete element simulations of this type are beyond
the power of present day affordable desktop workstations. Thus they are termed ‘grand
challenge combined finite-discrete element simulations’.
Grand challenge combined finite-discrete element simulations are grand in terms of
both CPU and RAM requirements. If a one million discrete element combined finite-
discrete element problem takes 24 hours of CPU on present day workstations, a typical
one trillion combined finite-discrete element simulation would probably take 1,000,000
workstation-days, which translates into

1,000,000
= 2740 years (9.2)
365

It is evident that either massive parallelisation or massive distributed computing are at
present the only options. The distributed computing option would probably require a
cluster of 30,000 present day affordable workstations for a year. At present day costs,
assuming that a workstation is outdated after two years, the cost of such a job would be

30,000·2000
= £30,000,000 (9.3)
2