A Parallel Approach of the Enhanced Craig–Bampton Method

The enhanced Craig–Bampton (ECB) method is a novel extension of the original Craig–Bampton (CB) method, which has been widely used for component mode synthesis (CMS). The ECB method, using residual modal compensation that is neglected in the CB method, provides dramatic accuracy improvement of reduced matrices without an increasing number of eigenbasis. However, it also needs additional computational requirements to treat the residual flexibility. In this paper, an efficient parallelization of the ECB method is presented to handle this issue and accelerate the applicability for large-scale structural vibration problems. A new ECB formulation within a substructuring strategy is derived to achieve better scalability. The parallel implementation is based on OpenMP parallel architecture. METIS graph partitioning and Linear Algebra Package (LAPACK) are used to automated algebraic partitioning and computational linear algebra, respectively. Numerical examples are presented to evaluate the accuracy, scalability, and capability of the proposed parallel ECB method. Consequently, based on this work, one can expect effective computation of the ECB method as well as accuracy improvement.

K-way Balanced Graph Partitioning for Parallel Computing

In modern computing, high-performance computing (HPC) and parallel computing require most of the decision-making in terms of distributing the payloads (input) uniformly across the available set of resources, majorly processors; the former deals with the hardware and its better utilization. In parallel computing, a larger, complex problem is broken down into multiple smaller calculations and executed simultaneously on several processors. The efficient use of resources (processors) plays a vital role in achieving the maximum throughput which necessitates uniform load distribution across available processors, i.e. load balancing. The load balancing in parallel computing is modeled as a graph partitioning problem. In the graph partitioning problem, the weighted nodes represent the computing cost at each node, and the weighted edges represent the communication cost between the connected nodes. The goal is to partition the graph G into k partitions such that: I) the sum of weights on the nodes is approximately equal for each partition, and, II) the sum of weights on the edges across different partitions is minimum. In this paper, a novel node-weighted and edge-weighted k-way balanced graph partitioning (NWEWBGP) algorithm of O(n x n) is proposed. The algorithm works for all relevant values of k, meets or improves on earlier algorithms in terms of balanced partitioning and lowest edge-cut. For evaluation and validation, the outcome is compared with the ground truth benchmarks.

Local Graph Edge Partitioning

Graph edge partitioning, which is essential for the efficiency of distributed graph computation systems, divides a graph into several balanced partitions within a given size to minimize the number of vertices to be cut. Existing graph partitioning models can be classified into two categories: offline and streaming graph partitioning models. The former requires global graph information during the partitioning, which is expensive in terms of time and memory for large-scale graphs. The latter creates partitions based solely on the received graph information. However, the streaming model may result in a lower partitioning quality compared with the offline model. Therefore, this study introduces a Local Graph Edge Partitioning model, which considers only the local information (i.e., a portion of a graph instead of the entire graph) during the partitioning. Considering only the local graph information is meaningful because acquiring complete information for large-scale graphs is expensive. Based on the Local Graph Edge Partitioning model, two local graph edge partitioning algorithms—Two-stage Local Partitioning and Adaptive Local Partitioning—are given. Experimental results obtained on 14 real-world graphs demonstrate that the proposed algorithms outperform rival algorithms in most tested cases. Furthermore, the proposed algorithms are proven to significantly improve the efficiency of the real graph computation system GraphX.

A GRAPH PARTITIONING TECHNIQUE TO OPTIMIZE THE PHYSICAL INTEGRATION OF FUNCTIONAL REQUIREMENTS FOR AXIOMATIC DESIGN

According to the concept of physical integration as understood in Axiomatic Design, design parameters of a product should be integrated into a single physical part or a few parts with the aim of reducing the information content, while still satisfying the independence of functional requirement. However, no specific method is suggested in the literature for determining the optimal degree of physical integration in a given design. This is particularly important with the current advancement in technologies such as additive manufacturing. As new manufacturing technologies allow physical elements to be integrated in new ways, new methods are needed to help designers optimize physical integration given the specific constraints and conflicts of each design. This study proposes an algorithm which uses graph partitioning to allow a designer to optimize the integration of functional requirements into a target number of parts, with the goal of minimizing the co-allocation of incompatible functional requirements in the same part. The operation and viability of the algorithm is demonstrated via two numerical examples and a practical example of designing a pencil.