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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

This paper outlines a dynamic domain decomposition‐based parallel strategy for combined finite/discrete element analysis of multi‐fracturing solids and discrete systems. Attention is focused on the parallelised interaction detection between discrete objects. Two graph representation models for discrete objects in contact are proposed which lay the foundation of the current development. In addition, a load imbalance detection and re‐balancing scheme is also suggested to enhance the parallel performance. Finally, numerical examples are provided to illustrate the parallel performance achieved with the current implementation.

Some issues related to effective parallel implementation of the combined finite‐discrete element approach on PC clusters are discussed. Attention is focused on the interprocessor communications. Three communication schemes suitable for different problems are presented. The worker‐to‐manager scheme is simple to implement. The neighbour‐to‐neighbour scheme is sophisticated with regard to programming, and requires extra memory space, but has good overall performance for larger problems. The mixed worker‐manager scheme can balance the difficulty in programming and the overall communication performance. The effects of subdomain buffer zone on communications are also demonstrated by numerical examples.

The purpose of this paper is to present the implementation of a balanced domain decomposition approach for the numerical simulation of large electro-quasistatic (EQS) systems in biology. The numerical scheme is analyzed and first applications are discussed.

The scheme is based on a finite element discretization of the individual domains obtained by decomposition and a physically consistent inter-domain coupling realized via Robin boundary conditions. The proposed algorithms can efficiently be implemented on a highly parallelized computing grid.

The feasibility and applicability of the method is proven. Further, a couple of technical details are found that increase the efficiency of the method.

The presented method offers an enhanced geometrical flexibility and extensibility to simulate larger cell systems with higher model resolution compared to other methods presented in the literature. The presented analysis provides an understanding of the balanced coupling scheme for large EQS systems.

Taking into account the long‐term influences of the non‐linear behavior of the material as well as the large deformation and contact conditions, the limiting factors of the computer simulation are the computer runtime and the memory requirement during solution of seismic response analysis for immersed tunnel. This research aims to overcome these problems.

This research deals with parallel explicit finite element simulation with domain decomposition for seismic response analysis of immersed tunnel, which is the non‐linear and time‐dependent behavior of complex structures in engineering. A domain decomposition method based on parallel contact algorithm and dynamic‐explicit time integration procedure are used, and the latter is used for the solution of the semi‐discrete equations of motion, which is very suited for parallel processing. Using the high performance computer SGI Onyx3800, the seismic response analysis of the immersed tunnel in Shanghai is processed with more than 1.2 million nodes and more than 1 million elements in final finite element model.

The results show numerical scalability of this algorithm and reveal the dangerous joints in this immersed tunnel under Tangshan seismic acceleration, and it could also provide references for the antiseismic design of the immersed tunnel.

With the increasing demands in the scale, accuracy and speed of numerical simulation in geotechnical engineering, parallel computing has its great application in this area. This paper fulfils an identified method need, and it is believed more and more research work will be devoted to this research field in the near future.

A general philosophy is presented in which all the modules within the computational cycle are parallelised and executed on parallel computer hardware, thereby avoiding the creation of computational bottlenecks. In particular, unstructured mesh generation with adaptation, computational fluid dynamics and computational electromagnetic solvers and the visualisation of grid and solution data are all performed in parallel. In addition, all these modules are embedded within a parallel problem solving environment. This paper will provide an overview of these developments. In particular, details of the parallel mesh generator, which has been used to generate meshes in excess of 100 million elements, will be given. A brief overview will be presented of the approach used to parallelise the solvers and how large data sets are interrogated and visualised on distributed computer platforms. Details of the parallel adaptation algorithm will be presented. These parallel component modules are linked using CORBA communication to provide an integrated parallel approach for large scale simulations. Several examples are given of the approach applied to the simulation of large aerospace calculations in the field of aerodynamics and electromagnetics.

This paper aims to consider a multiscale electromagnetic wave problem for a housing with a ventilation grill. Using the standard finite element method to discretise the apertures leads to an unduly large number of unknowns. An efficient approach to simulate the multiple scales is introduced. The aim is to significantly reduce the computational costs.

A domain decomposition technique with upscaling is applied to cope with the different scales. The idea is to split the domain of computation into an exterior domain and multiple non-overlapping sub-domains. Each sub-domain represents a single aperture and uses the same finite element mesh. The identical mesh of the sub-domains is efficiently exploited by the hybrid discontinuous Galerkin method and a Schur complement which facilitates the transition from fine meshes in the sub-domains to a coarse mesh in the exterior domain. A coarse skeleton grid is used on the interface between the exterior domain and the individual sub-domains to avoid large dense blocks in the finite element discretisation matrix.

Applying a Schur complement to the identical discretisation of the sub-domains leads to a method that scales very well with respect to the number of apertures.

The error compared to the standard finite element method is negligible and the computational costs are significantly reduced.

A fully parallel algorithm for the solution of a finite element system using a MIMD (multiple‐instruction multiple‐data architecture) parallel computer is presented. The formulation includes a simple domain decomposer that automatically divides a finite element mesh into a list of subdomains to guarantee the load balancing. Furthermore, each subdomain is assigned to a processor of a parallel computer and treated as a sub‐finite element system with information exchanged through the interface between two adjacent subdomains. With this new algorithm, these sub‐finite element systems are solved fully parallelly as independent finite element systems, not only the computations of the interior nodes but also the computations of the interface nodes can be executed parallelly. Also, the inherently sequential Gauss‐Seidel and SOR schemes are altered into fully parallel iterative schemes. An implementation of this new scheme on an iPSC/2 D5 Hypercube Concurrent Computer reached an efficiency of more than 100% when compared with the sequential SOR scheme.

The present work is concerned with three‐dimensional finite element analysis of the hollow section extrusion process using a porthole die. The effects of related design parameters are discussed through the finite element simulation for extrusion of a triply‐connected rectangular tubular section. For economic computation, mismatching refinement, an efficient domain decomposition method with different mesh density for each subdomain is implemented. In order to obtain the uniform flow at the outlet, design parameters such as the hole size and the hole position are investigated and compared through the numerical analysis. Comparing the velocity distribution with that of the original design, it is concluded that the design modification enables more uniform flow characteristics. The analysis results are then successfully reflected on the industrial porthole die design.

The purpose of this paper is to develop and test an implicit scheme, accurate to the second order, for solving full Navier‐Stokes equations for three dimensional problems, using parallel algorithm.

Parallel solution to the 3‐D incompressible full Navier‐Stokes equations is presented, based on two fractional steps in time and finite element in space. The accuracy of the scheme is second order in both time and space domains. Large time‐step sizes, with Courant‐Friedrichs‐Lewy (CFL) numbers much larger than unity, are taken since the momentum equation is solved implicitly. A fourth order artificial viscosity term is added. In order to stabilize the numerical solution, fourth order artificial viscosity term is used for high Reynolds number flows. The domain decomposition technique is implemented for parallel solution to the problem with matching and non‐overlapping sub‐domains. It is aimed to study both a 3D free and mixed convection problems using the developed scheme. The segregate solution for temperature field is calibrated by a 3‐D free convection problem. Then the flow case where the forced convection is one order of magnitude higher than the free convection is studied.

It is observed that the long time solution to the flow field shows oscillatory behaviour as the Reynolds number of the flow doubled while keeping the ratio of the forced to free convection fixed. The solution using a parallel algorithm gives satisfactory results, in terms of computation time and accuracy, for the natural convection problem in cubic cavity, and, the forced cooling of a room with chilled ceiling having a parabolic geometry as presented at the end. It is observed that doubling the Reynolds number, while keeping all the parameters unchanged, varies the flow behaviour completely.

A code previously developed and published by the author only solved momentum equation and studied the velocity field. In this study, full Navier Stokes equation is solved and the code is calibrated with a well‐known 3D free‐convection for two different Rayleigh number cases and then 3D mixed convection problem is studied for two cases. Re=2000 case results, solved both by the scheme in this study and by commercial code, presented an interesting physics of the problem. For Re=2000 case, continuous cooling of the room is not possible. Doubling the Reynolds number, raising it from 1000 to 2000, while keeping all the parameters unchanged, varies the flow behaviour completely.