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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.

The cell‐based method of domain decomposition was first introduced for complex 3D geometries. To further assess the method, the aim is to carry out flow simulation in rectangular ducts to compare the known analytical solutions.

The method is not based on equal subvolumes but on equal numbers of active cells. The variables of the simulation are stored in ordered 1D arrays to replace the conventional 3D arrays, and the domain decomposition of the complex 3D problems therefore becomes 1D. Finally, the 3D results can be recovered using a coordinate matrix. Through the flow simulation in the rectangular ducts how the algorithm of the domain decompositions works was illustrated clearly, and the numerical solution was compared with the exact solutions.

The cell‐based method can find the subdomain interfaces successfully. The parallelization based on the algorithm does not cause additional errors. The numerical results agree well with the exact solutions. Furthermore, the results of the parallelization show again that domains of 3D geometries can be decomposed automatically without inducing load imbalances.

Although, the approach is illustrated with lattice Boltzmann method, it is also applicable to other numerical methods in fluid dynamics and molecular dynamics.

Unlike the existing methods, the cell‐based method performs the load balance first based on the total number of fluid cells and then decomposes the domain into a number of groups (or subdomains). Thus, the task of the cell‐based method is to recover the interface rather than to balance the load as in the traditional methods. This work has examined the celled‐based method for the flow in rectangular ducts. The benchmark test confirms that the cell‐based domain decomposition is reliable and convenient in comparison with the well‐known exact solutions.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

The numerical simulation of metal forming processes approximated by means of finite element techniques, require large computational effort, which contradicts the need of interactivity for industrial applications. This work analyses the computational efficiency of algorithms combining elastoplasticity with finite deformation and contact mechanics, and in particular, the optimum solution of the linear systems to be solved through the incremental‐iterative schemes associated with non linear implicit analysis. A method based on domain decomposition techniques especially adapted to contact problems is presented, as well as the improved performance obtained in the application to hot rolling simulation, as a consequence of bandwidth reduction and the differentiated treatment of subdomains along the non linear analysis.

The purpose of this paper is to present a methodology of hybrid parallelization applied to the discrete element method that combines message-passing interface and OpenMP to improve computational performance. The scheme is based on mapping procedures based on Hilbert space-filling curves (HSFC).

The methodology uses domain decomposition strategies to distribute the computation of large-scale models in a cluster. It also partitions the workload of each subdomain among threads. This additional procedure aims to reach higher computational performance by adjusting the usage of message-passing artefacts and threads. The main objective is to reduce the communication among processes. The work division by threads employs HSFC in order to improve data locality and to avoid related overheads. Numerical simulations presented in this work permit to evaluate the proposed method in terms of parallel performance for models that contain up to 3.2 million particles.

Distinct partitioning algorithms were used in order to evaluate the local decomposition scheme, including the recursive coordinate bisection method and a topological scheme based on METIS. The results show that the hybrid implementations reach better computational performance than those based on message passing only, including a good control of load balancing among threads. Case studies present good scalability and parallel efficiencies.

The proposed approach defines a configurable execution environment for numerical models and introduces a combined scheme that improves data locality and iterative workload balancing.

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.

It is important to investigate large‐scale numerical analyses of electromagnetic fields in design processes of electromagnetic machines. Thus, faster solvers for eddy current analyses are necessary. Parallel computation methods for linear solvers in electromagnetic field analyses have been investigated. These methods have gained importance due to the diffusion of PC clusters and multi‐core CPUs in recent years.

This paper discuses linear solvers for the finite element method in eddy current analyses on parallel computers. The preconditioned conjugate gradient method with overlapping domain decomposition is treated. Some techniques treated to improve the convergence was investigated.

The numerical results show that the overlapping effect results in good convergence in eddy current analyses.

The preconditioned conjugate gradient method with overlapping domain decomposition has been treated. The numerical results show that the overlapping method works more efficiently for eddy current analyses. Moreover, this method enables large‐scale analyses on popular computers such as PC clusters.

This paper aims to present a domain decomposition method to overcome the challenges posed by multi-domain, multi-scale high frequency problems.

A hybrid finite element and boundary integral procedure is also presented that allows for domains to employ different solution methods in different subdomains.

By decomposing large electromagnetic regions into smaller domains, the finite element method can cope with the simulation of electrically large problems.

Real life examples demonstrate the accuracy and efficiency of the new method.

The Robin transmission condition (RTC) is applied to link the domains and preserve field continuity on interfaces.

The finite volume method for radiative heat transfer calculations has been parallelized using two strategies, the angular domain decomposition and the spatial domain decomposition. In the first case each processor performs the calculations for the whole domain and for a subset of control angles, while in the second case each processor deals with all the control angles but only treats a spatial subdomain. The method is applied to three‐dimensional rectangular enclosures containing a grey emitting‐absorbing medium. The results obtained show that the number of iterations required to achieve convergence is independent of the number of processors in the angular decomposition strategy, but increases with the number of processors in the domain decomposition method. As a consequence, higher parallel efficiencies are obtained in the first case. The influence of the angular discretization, grid size and absorption coefficient of the medium on the parallel performance is also investigated.

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.