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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.

An algorithm for domain partitioning with iterative load balancing is presented. A recursive graph labeling scheme is used to distribute elements among subdomains at each iteration. Both graph distance information and information about neighbor vertices are employed during the labeling process. Element quantities for balanced subdomains are predicted, solving the algebraic load balancing problem after each iteration. The same graph labeling scheme with slight modifications is applied to node renumbering inside subdomains. The proposed algorithm is especially suitable for load balancing when a direct method is used for subdomain condensation and the evaluation of cost function is time consuming. Several examples of optimized partitioning of irregular and regular meshes show that load balancing can be achieved with one to three iterations.

Balancing and dual domain decomposition methods (DDMs) comprise a family of efficient high performance solution approaches for a large number of problems in computational mechanics. Such DDMs are used in practice on parallel computing environments with the number of generated subdomains being generally larger than the number of available processors. This paper presents an effective heuristic technique for organizing the subdomains into subdomain clusters, in order to assign each cluster to a processor. This task is handled by the proposed approach as a graph partitioning optimization problem using the publicly available software METIS. The objective of the optimization process is to minimize the communication requirements of the DDMs under the constraint of producing balanced processor workloads. This constraint optimization procedure for treating the subdomain cluster generation task leads to increased computational efficiencies for balancing and dual DDMs.

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 a methodology for parallel simulation that employs the discrete element method (DEM) and improves the cache performance using Hilbert space filling curves (HSFC).

The methodology is well suited for large-scale engineering simulations and considers modelling restrictions due to memory limitations related to the problem size. An algorithm based on mapping indexes, which does not use excessive additional memory, is adopted to enable the contact search procedure for highly scattered domains. The parallel solution strategy uses the recursive coordinate bisection method in the dynamical load balancing procedure. The proposed memory access control aims to improve the data locality of a dynamic set of particles. The numerical simulations presented here contain up to 7.8 millions of particles, considering a visco-elastic model of contact and a rolling friction assumption.

A real landslide is adopted as reference to evaluate the numerical approach. Three-dimensional simulations are compared in terms of the deposition pattern of the Shum Wan Road landslide. The results show that the methodology permits the simulation of models with a good control of load balancing and memory access. The improvement in cache performance significantly reduces the processing time for large-scale models.

The proposed approach allows the application of DEM in several practical engineering problems of large scale. It also introduces the use of HSFC in the optimization of memory access for DEM simulations.

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.

Describes a new finite element scheme for the large‐scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible‐ incompressible Galerkin least‐squares (GLS) space‐time variational formulation. Three‐ dimensional unstructured meshes are employed, with piecewise‐constant temporal interpolation, local time‐stepping for steady flows, and linear continuous spatial interpolation in all the variables. The scheme incorporates automatic adaptive mesh refinement, with a choice of various error indicators. It is implemented on a distributed‐memory parallel computer, and includes an automatic load‐balancing procedure. Demonstrates the ability to solve both compressible and incompressible viscous flow problems using the parallel adaptive framework via numerical examples. These include Mach 3 flow over a flat plate, and a divergence‐free buoyancy‐driven flow in a cavity. The latter is a model for the steady melt flow in a Czochralski crystal growth process.

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.

Domain decomposition of finite element models (FEM) for parallel computing are often performed using graph theory and algebraic graph theory. This paper aims to present a new method for such decomposition, where a combination of algebraic graph theory and differential equations is employed.

In the present method, a combination of graph theory and differential equations is employed. The proposed method transforms the eigenvalue problem involved in decomposing FEM by the algebraic graph method, into a specific initial value problem of an ordinary differential equation.

The transformation of this paper enables many advanced numerical methods for ordinary differential equations to be used in the computation of the eigenproblems.

Combining two different tools, namely algebraic graph theory and differential equations, results in an efficient and accurate method for decomposing the FEM which is a combinatorial optimization problem. Examples are included to illustrate the efficiency of the present method.

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.