Keywords: 3D structural analysis, high performance computing techniques, numerical libraries, direct and iterative solvers, grid computing, globus toolkit.

Structural analysis is one of the most time consuming stage in the design cycle of a building, where lots of different alternatives must be analysed with the purpose to find the cheapest, most functional and safest structural solution. Traditionally, structural applications have carried out different simplifications, especially when simulating large buildings or in 3D dynamic solutions, in order to reduce the computational and memory requirements. The employment of High Performance Computing (HPC) techniques allows tackling efficiently this problem.

In this way, this paper presents a MPI-based application for the 3D structural linear analysis of buildings, where all its phases have been parallelised. Having in mind that the large sparse symmetric linear system is the crucial problem, the following parallel public domain numerical libraries have been tested: WSMP [1], MUMPS [2] and PETSc [3]. WSMP and MUMPS employ parallel Multifrontal Cholesky factorization, whereas PETSc is composed of parallel iterative solvers and preconditioners. Two large dimension buildings (about 330,000 and 600,000 degrees of freedom) have been chosen to compare the results when using different libraries. The MUMPS library, together with QAMD ordering algorithm, has demonstrated to be the fastest and most scalable solver. As an example, the approximation based on MUMPS spends 16.9 seconds, using 8 processors, on the whole structural analysis of the larger building. Since coefficient matrices are very ill-conditioned, iterative methods are much slower than direct methods, although they present better efficiencies when increasing the number of PCs. Simulations have been run on a cluster of 8 Pentium Xeon@2GHz biprocessors (1 GB RAM), connected by a SCI network. The HPC-based application performs 3D realistic structural analysis of large buildings, providing with comprehensive results in reasonable response times.

However, in most of the cases, a studio for architecture and design does not own a parallel structural application nor advanced computational resources like clusters of PCs or supercomputers, mainly owing to factors like the high cost of purchase and maintenance or physical space needed. Habitually, simulations are performed in standard PCs which limit the size of the problems to be treated. In these cases, Grid Computing technology [4] is applicable, taking advantage of not owned, geographically distributed resources in the network, without having to make new investments in computers.

Therefore, a Grid application service, that makes use of the parallel software mentioned, has been implemented in this paper, which provides with a tool for solving remotely structural problems. Moreover, the integration of HPC and Grid strategies, performing parallel executions on remote multiprocessors, enables to test at the same time a greater number of different alternatives in the design stage, increasing productivity, which redounds in benefit of other factors like safety, cost, design time, etc. In order to create the Grid infrastructure, the Globus Toolkit 2.4 middleware [5] has been employed. Starting from a set for different structural alternatives and a group of heterogeneous machines distributed throughout Internet, the Grid system developed performs the necessary work to analyse all of them by running the application on the available resources. The Grid system consists in three main parts: the scheduler, the resource selector and the retrieval processes. For each structure in the repository, the scheduler module asks the resource selector for a machine to run the parallel application. This resource selector queries the number of free processors of the computational resources available in the Grid. The system deals with a desirable minimum and maximum number of processors to execute the application, in order to increase productivity and ensure executions with some minimum requirements. Once the first host with enough number of free processors is chosen, the scheduler sends it the input files and the structure is simulated. Finally, the scheduler module starts a retrieval process that recovers results once the task has finished. If any part of the process fails, the scheduler will analyse it later.

As a conclusion, small and medium-sized enterprises can now easily increase its productivity and business volume. Since Grid Computing enables efficient resource usage when a high coordinated computational power is demanded, the system developed can be very useful to analyse very large and singular buildings, and moreover in a time-consuming 3D and realistic dynamic structural analysis.

1

Gupta, A., "WSMP: Watson Sparse Matrix Package Part I - Direct Solution of Symmetric Sparse Systems", IBM Research Rpt RC 21886(98462), IBM, 2000.

2

Amestoy, P., Duff, I., L'Excellent, J.-Y., Koster. J., "MUltifrontal Massive Parallel Solver (MUMPS Version 4.3) Users' Guide, 2003".

3

Balay, S., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M., Curfman, L., McInnes, Smith. B.F., Zhang, H., "PETSc Users Manual, Technical Report ANL-95/11 - Revision 2.1.6", Argonne National Laboratory, 2003.

4

Foster, I., Kesselman, C., Tuecke, S., "The Anatomy of the Grid: Enabling Scalable Virtual Organizations", Intl. J. High Performance Computing Applications, 15(3), 200, 2001. doi:10.1177/109434200101500302

5

Ferreira, L., Berstis, V., "Introduction to Grid Computing with Globus", IBM Redbooks Paper", IBM, 2002.

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