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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.

This paper aims to develop a parallel fast neighbor search method and communication strategy for particle-based methods with adaptive smoothing-length on distributed-memory computing systems.

With a multi-resolution-based hierarchical data structure, the parallel neighbor search method is developed to detect and construct ghost buffer particles, i.e. neighboring particles on remote processor nodes. To migrate ghost buffer particles among processor nodes, an undirected graph is established to characterize the sparse data communication relation and is dynamically recomposed. By the introduction of an edge coloring algorithm from graph theory, the complex sparse data exchange can be accomplished within optimized frequency. For each communication substep, only efficient nonblocking point-to-point communication is involved.

Two demonstration scenarios are considered: fluid dynamics based on smoothed-particle hydrodynamics with adaptive smoothing-length and a recently proposed physics-motivated partitioning method [Fu et al., JCP 341 (2017): 447-473]. Several new concepts are introduced to recast the partitioning method into a parallel version. A set of numerical experiments is conducted to demonstrate the performance and potential of the proposed parallel algorithms.

The proposed methods are simple to implement in large-scale parallel environment and can handle particle simulations with arbitrarily varying smoothing-lengths. The implemented smoothed-particle hydrodynamics solver has good parallel performance, suggesting the potential for other scientific applications.

The design of a cellular manufacturing system requires that a machine population be partitioned into machine groups called manufacturing cells. A new graph partitioning heuristic is proposed to solve the manufacturing cell formation problem (MCFP). In the proposed heuristic, The MCFP is represented by a graph whose node set represents the machine cluster and edge set represents the machine‐pair association weights. A graph partitioning approach is used to form the manufacturing cells. This approach offers improved design flexibility by allowing a variety of design parameters to be controlled during cell formation. The effectiveness of the heuristic is demonstrated by comparing it to two MCFP published solution methods using several problems from the literature.

The purpose of this paper is to introduce a general equation for eigensolution. Eigenvalues and eigenvectors of graphs have many applications in combinatorial optimization and structural mechanics. Some important applications of graph products consist of nodal ordering and graph partitioning for structuring the structural matrices and finite element subdomaining, respectively.

In the existing methods for the eigensolution of Laplacian matrices, members have been added to the model of a graph product such that for its Laplacian matrix an algebraic relation between blocks become possible. These methods are categorized as topological approaches. Here, using concepts of linear algebra a general algebraic method is developed.

A new algebraic method is introduced for calculating the eigenvalues of Laplacian matrices in graph products.

The present method provides a simple tool for calculating the eigenvalues of the Laplacian matrices without using the configurational model and merely by using the Laplacian matrices. The developed formula for calculating the eigenvalues contains approximate terms which can be managed by the analyst.

In this paper a new method is proposed for finite element domain decomposition. A weighted incidence graph is first constructed for the finite element model. A spectral partitioning heuristic is then applied to the graph using the second and the third eigenvalues of the Laplacian matrix of the graph, to partition it into three subgraphs and correspondingly trisect the finite element model.

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.

Virtual assembly process plays an important role in assembly design of complex product and is typically time- and resource-intensive. This paper aims to investigate a dynamic assembly simplification approach in order to demonstrate and interact with virtual assembly process of complex product in real time.

The proposed approach regards the virtual assembly process of complex product as an incremental growth process of dynamic assembly. During the growth process, the current-assembled-state assembly model is simplified with appearance preserved by detecting and removing its invisible features, and the to-be-assembled components are simplified with assembly features preserved using conjugated subgraphs matching method based on an improved subgraph isomorphism algorithm.

The dynamic assembly simplification approach is applied successfully to reduce the complexity of computer aided design models during the virtual assembly process and it is proved by several cases.

A new assembly features definition is proposed based on the notion of “conjugation” to assist the assembly features recognition, which is a main step of the dynamic assembly simplification and has been translated into conjugated subgraphs matching problem. And an improved subgraph isomorphism algorithm is presented to address this problem.

The NP‐complete problem of optimally placing tuples on a hierarchy of secondary storage devices is considered using a heuristic approach. From load specification details captured at database design time, those tuples associated with queries which merit tailored, “set‐in‐concrete”, physical access paths are placed using a two‐level graph partitioning algorithm. Experiments are reported with the pages and cylinders as the two hierarchical levels of storage for a centralised database, but the technique is applicable to an n‐Ievel storage hierarchy—as up to the “different sites” level for distributed databases. The results show up to 39% improvement over single‐level partitioning algorithms for the database considered.

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 purpose of this paper is to find a global method for the limited K‐partitioning of hypergraphs representing optimal design problems in complex machine systems.

To represent some real design considerations, a new concept of semi‐free hypergraphs is proposed and a method to apply semi‐free hypergraphs to the decomposition of complex design problems based on optimal models is also suggested. On this basis, the limited K‐partitioning problem of semi‐free hypergraphs and its partitioning objective for the optimal design of complex machines is presented. A global method based on genetic algorithms, GALKP, for the limited K‐partitioning of semi‐free hypergraphs is also proposed. Finally, a case study is presented in detail.

Semi‐free hypergraphs are a more powerful tool to map a complex engineering design problem. The decomposition of complex design problems may be converted to a limited K‐partitioning problem of semi‐free hypergraphs. The algorithm presented in this paper for the limited K‐partitioning of semi‐free hypergraphs is fast, effective, and powerful.

The traditional methods based on hypergraphs have some limitations while applied to the decomposition of some complex problems such as the design of large‐scale machine systems. The proposed method is helpful to solve similar engineering design problems.

The paper illustrates a faster and more effective method to implement the decomposition of large‐scale optimal design problems in complex machine systems.

This paper shows a new way to solve the complex engineering design problems based on semi‐free hypergraphs and its K‐partitioning method.