Keywords: parallel computation, PC cluster, load balancing, explicit algorithms, implicit algorithms.

Typical engineering design offices are equipped with several PC computers with different processor power, available memory and disk capacity. The computers are usually connected with fast Ethernet. The computing performance is relatively high with respect to the demands of design process involving CAD, structural analysis, etc. This makes the offices well equipped for high performance computing provided relevant parallel software is available. Although there may be different combinations of hardware and software forming a parallel computing environment it can be shown that the results (computational time, speedup, efficiency) achieved on such cluster are competitive to results obtained on special parallel computers, as IBM SP2, SGI Origin, etc. It is important to realize that from engineering point of view the scalability of the algorithm is not the only criterion to judge the efficiency of parallel application. In many case, the ability to analyze extremely large problems not solvable on individual machines is of primary interest.

What is the cluster? It is a group of personal computers connected by a fast network. Strictly speaking, elements of a "traditional" cluster have no monitor, no keyboard, no floppy etc. The connection is provided by fast switch. "Traditional" PC cluster is mostly home made supercomputer. Some clusters are made by professionals, e.g. AC3 Velocity cluster at Cornell University (sponsored by Dell, Intel and Microsoft), and have really power of supercomputer. In fact the biggest supercomputers from IBM are precisely designed clusters. Unfortunately, very expensive. In "traditional" cluster, all computers are identical. They usually have the same processor, the same memory and the same disks. Even the processors have the same size of cache memory. So the user can apply the same strategies and algorithms developed earlier for distributed computers of IBM SP class. However, this arrangement of cluster is not typical for engineering offices. For example, a typical civil engineering design office has several PCs (of different power) connected by fast Ethernet. In reality, during working hours the individual PCs are mostly used for CAD jobs and therefore working under MS Windows. However during the nights and weekends these computers are mostly doing nearly nothing. This type of computer network is now called P2P (peer-to-peer) environment. Typical computers in this environment are one or two processors PCs. Such clusters are not built specifically for supercomputing. This is only a side effect of the computer network which is necessary for engineering processes, mostly for design. The principal advantage is that this environment is here, so there is no necessity to invest more money. The price/performance is approaching zero in this case.

In this paper we are trying to evaluate the performance of different parallel platforms using some algorithms from the area of computational mechanics. It is surprising that the P2P performance is nearly the same as the performance of other parallel platforms. Of course, this is true just in case when the members of network are not running another jobs. Computer science people conclude that the performance of PC clusters is at least three times higher than the performance of UNIX workstations or supercomputers of equivalent price. The performance of P2P network is still significantly higher.

Some remarks to the components of PC cluster. Our experience shows that the optimal solution is to use next-to-top parts of available computer hardware. The very top components (the fastest processors, the biggest cache memory, high node SMP computers) are sold for unreasonable price and due to this fact price/performance ratio is going up. The power of P2P environment is not just in power of individual members but mainly in parallelization.

Another important aspect and advantage of PC clusters is the opportunity for reusage of older components in the cluster. Unlike the supercomputer it is possible to use individual old fashion computers, used by secretaries or students typing Word documents, at universities for next years. If such an old computer is not powerful enough for MS Windows than it is possible to use it with Star Office under Linux.

The important advantage in P2P technology is the very low risk. If you find that your new cluster extension is not perfect for your specific purpose, you can still use this new hardware as ordinary individual PC in frame of your institution.

What is still missing? The software. But as the development of appropriate software for this parallel technology is a priority in coming European research programme we can be optimistic and believe in rapid progress. What type of software is needed? Except of traditional engineering software for the analysis of complex structures with different types of non-linearity it is mainly this software

• simulation of material behaviour on the different scale levels,
• analysis of structures and materials with uncertainty in input data
  (probabilistic and fuzzy),
• optimization of structures and materials (preferably topology optimization).

The most of the problems from mentioned areas are very time and memory demanding. So they are good candidates for application of advanced parallel technologies.

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