Page 303 - The Combined Finite-Discrete Element Method

286 COMPUTATIONAL ASPECTS

This is in sharp contrast with, for instance, the PC home computer market. The price
of the latest generation of PC processors is reducing dramatically, fast approaching a
critical £10 level, and has the potential to go even lower. This is obviously because
of the massive quantities made, reducing development and capital costs to negligible
levels. In this environment £100,000 could soon be buying 10,000 processors, with the
potential of being enough money to buy 100,000 processors. £100,000 is a relatively
small amount of money with which at present day prices not much parallel hardware
could be bought. It is also a small amount in absolute terms, and many enterprises could
theoretically afford to invest this much in high performance computing every year. If
only 10 CPU critical jobs are run a year on such a machine, the capital cost would
be £10,000 per job. In many fields that require high performance computing this is not
a high price. These cheap, powerful, fast von Neumann architectures come with fast
mathematical libraries and incorporate fast inter-computer communications. World Wide
Web developments during the last decade have resulted in the speed of network cards
changing from 10 megabits per second to 100 megabits per second, and recently to over 3
gigabits per second. This has been fast recognised as a cheap opportunity to build massive
custom made distributed high performance computing clusters. The basic idea is not to
build a parallel machine, but to distribute the CPU and/or RAM intensive computing job
over different computers connected to a network. So, for instance, the visual part of an
application sits on one machine, the sound part is on another, frequently used data is
distributed over another couple of machines, and so on. There are a number of emerging
concepts that are related to distributed computing. These include fabric computing, on-
demand computing, organic IT, utility computing, grid computing, etc. In the context of
the combined finite-discrete element method, one could think of different aspects of the
combined finite-discrete element simulation residing on different machines connected to
anetwork.
However, a better approach is to divide a domain into sub-domains. For instance, if
discrete elements are all packed inside a box, as shown in Figure 9.5, the box can be
subdivided into five parts. Each part with all the discrete elements in it is then loaded
as a separate problem on its own PC. These five sub-domains share the boundaries of
the sub-domains. These are not real boundaries, and discrete elements are free to move

Sub-domain Sub-domain Sub-domain Sub-domain Sub-domain
allocated to allocated to allocated to allocated to allocated to
PC-1 PC-2 PC-3 PC-4 PC-5

Figure 9.5 A typical combined finite-discrete element domain divided into sub-domains for dis-
tributed computing purposes.