GRID technology for structural analysis

Abstract

This paper presents a High Performance Computing-based application for 3D structural analysis of buildings. Since the solution of a large linear system of sparse equations supposes the most time-consuming phase, several public domain parallel numerical libraries, with state-of-the-art capabilities, have been tested. The parallel application developed allows reducing the analysis time and simulating larger structures. Nevertheless, structural engineers rarely have available high cost parallel machines. Thus, a Grid Structural Analysis service, that integrates the parallel application, has been implemented, taking advantage of computers geographically distributed in Internet. This service makes it possible to simulate in a realistic way, and concurrently, a high number of different structural alternatives of large dimension buildings during their design stage, without considering structural simplifications or investing in expensive computers.

Introduction

Structural analysis plays a relevant role during the design stage of a building. The current trend of erecting more complex and larger buildings is giving place to structural systems which analysis implies solving algebraic problems with several hundreds of thousands of unknowns, consequently requiring greater accuracy and speed [1].

When designing structures, security must be assured for persons and goods, therefore accuracy in this kind of simulations is a key factor and precise methods of analysis have to be applied. Traditionally, structural applications have carried out different simplifications, especially in 3D dynamic analysis, aiming to reduce computational and memory requirements. These simplifications, although perfectly satisfactory when used on simple structures, have been found inadequate when applied to complex structures.

On the other hand, the requirement of speed is imposed by the need of having comprehensive information about the structure during the design cycle, so that any structural modification can be considered before the structure enters into the production stage. Furthermore, in order to achieve the most adequate design, a large number of different structural solutions may have to be analysed rapidly before a particular configuration is selected for detailed study. In the preliminary stage, the structural engineer is concerned mainly with several designs of the building. Moreover, each design could be composed of various materials (concrete, steel, etc.), with different member sizes or even different loads applied which could occur during the lifetime of the structure.

Therefore, structural analysis is one of the most time consuming stages in the design cycle of a building. High Performance Computing (HPC) technology provides powerful numerical and programming tools to manage efficiently large scientific and technical problems. These techniques enable reducing the computing time of a simulation, obtaining comprehensive results in very reasonable response times. The impact of the advances in computer technology on structural analysis and design is described in [2], [3], [4].

Multiple papers can be found in literature related to parallel structural analysis. Besides, it is well known that the performance of a system of linear equation solver is crucial of the overall efficiency of the simulation of large-scale linear structural problems. In this way, several works can be cited where parallel iterative and direct methods have been applied, in an attempt to find out the most appropriate procedure.

Storaasli et al. developed a parallel-vector Cholesky-based method for the solution of large-scale structural problems [5]. It exploited the parallel and vectors capabilities of Cray supercomputers. The implementation employs a variable-band storage scheme. Baddourah et al. presented algorithms for massively-parallel computers for the most computationally intensive tasks involved in structural analysis, such as generation and assembly of system matrices and solution of systems of equations [6]. Qin and Nguyen implemented a Cholesky-based parallel-vector equation solver for distributed memory computers [7]. A summary of general-purpose, highly-efficient algorithms, for parallel-vector supercomputers, for solution of linear systems, generation and assembly of element matrices, and so on are collected in [8].

Employing the message-passing paradigm, Farhat and Roux [9] presented parallel skyline direct methods and domain decomposition based iterative solvers. They tried promoting the use of parallel computers in the structural engineering community and encouraging professional software developers to port their current technology to commercially available multiprocessors. Soegiarso and Adeli [10] presented parallel-vector algorithms for assembly of structure stiffness matrix and solution of the resulting simultaneous linear equations using Cholesky decomposition and preconditioned Conjugate Gradient method. Performance results were shown for shared-memory CRAY supercomputers. Suarjana compared the efficiency of the preconditioned Conjugate Gradient method and the LDLT factorization, both serially implemented, for solving a sparse system of linear equations in large-scale structural analysis with both single and multiple load cases [11].

Moretti et al. presented a set of tools (geometry modeling, mesh generation, domain partitioning, object-oriented finite element analysis and visualisation of results) that composed an integrated parallel environment for 2D linear structural analysis [12]. A parallel version of the preconditioned Conjugate Gradient method was employed as linear equation system solver. In [13], a sequential multifrontal solver was developed by combining the multifrontal scheme with graph partitioners and mesh-mapping schemes. Large-scale structural analysis problems were solved using the developed solver and excellent performance were shown.

Adeli and Kumar used modified versions of direct solvers in the preconditioning phase of iterative solvers creating hybrid approaches for distributed memory multiprocessors [14]. Farhat et al., advocated geometric an algebraic multigrid and preconditioned Conjugate Gradient methods by multilevel domain decomposition for large dimension structures [15].

Sotelino presented a survey of parallel algorithms that are of interest to structural engineering [16]. Such algorithms include parallel solvers for linear systems of equations, techniques for the parallelization of the finite element method, and concurrent time-stepping algorithms for the solution of the motion equations arising in structural dynamic problems. Adeli reviewed the research papers published on parallel processing, supercomputing and distributed computing in analysis, optimisation an control of structures [17].

Romero et al. developed a parallel software for 3D nonlinear analysis of reinforced concrete buildings, both for shared and distributed memory systems [18]. Finally, Bhadwaj et al. presented Salinas, a MPI-based C++ scalable software application for the finite element static and dynamic parallel analysis of complex structural systems [19].

Parallel computing-based applications, and others which make use of special devices, specific network topologies, etc., are not fully useful for people who work in studios for architecture and design. These users do not own advanced computational resources (like clusters of PCs or supercomputers), mainly owing to factors like the high cost of purchase and maintenance or the physical space needed. Even more, the acquisition of new specific software to solve structural problems brings up two main problems: on the one hand, high investments are required from the beginning, with some additional cost for the maintenance and future updates; on the other hand, commercial software presents some requirements like operating system dependencies, etc.

This paper describes an innovative approach for using HPC techniques together with Grid technology in a application devoted to structural analysis of buildings. The advantages of both technologies are combined to allow the designer to solve large problems in less time in an easy manner. The Grid application (see Fig. 1) is an advanced tool for simulating remotely structural systems, detaching the user from aspects such as availability of computational resources or updates of the needed software. Therefore, the HPC application is offered as a service, taking up the necessity of acquiring specific software which in some cases could be unprofitable.

Augenbroe discussed new trends in the light of the challenges that the building simulation discipline faces, where Internet represents the natural environment for distributed simulation [20]. In this way, it may ultimately be appropriate to enforce a formal agreement between design team and building simulation experts, concerning the model assumptions that underlie a delivered design analysis. As an example of the advances of Grid Computing technologies in engineering, Yang et al. has designed a web-based platform for the simulation of seismic ground response and liquefaction effects [21], where the analysis is carried out remotely. According to Yang et al., the use of Internet provide an open environment for efficient collaboration to develop large-scale software. Therefore, this kind of distributed applications will continue to grow and become an important medium for civil and structural engineering simulations.

Anyway, the most important effort about the application of Grid Computing to structural engineering is being carried out by the NEES (Network for Earthquake Engineering Simulation) Consortium.¹ It is devoted to reduce the impact of earthquake and tsunami disasters in the man–human infrastructures. NEESgrid, the system integration component of the NEES project, links earthquake researchers across the US with leading-edge computing and research equipment, allowing collaborative teams to plan, perform, and publish their experiments. The integrated computational resources, data repositories and software tools made available by NEESgrid enable earthquake simulation providing an environment for researchers to develop increasingly complex, comprehensive, and accurate models of how structures respond to earthquake loadings [22].

The remaining paper is structured as follows: First, Section 2 describes an HPC application developed for 3D static structural analysis of buildings, which needs a Beowulf platform, and where the stiffness method has been parallelized. Then, a brief introduction to the public domain parallel numerical libraries that have been employed to solve the large systems of linear equations is also given in this section. Next, Section 3 presents an overview of Grid Computing. The Grid prototype for the analysis of large 3D structural systems is also introduced in this section. Performance of the parallel application, when computing two large buildings, and the Grid demonstrator are shown in Section 4. Finally, conclusions and further work are presented in Section 5.