Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns.

Parallelized Element-by-Element Solver for Structural Analysis of Flexible Pipes Using Finite Macroelements

Due to the number of layers and their respective geometrical complexities, finite element analyzes of flexible pipes usually require large-scale schemes, with a high number of elements and degrees-of-freedom. If proper precautions are not taken, such as suitable algorithms and numerical methods, the computational costs of these analyzes may become unfeasible to the current computational standards. Finite macroelements are finite elements formulated for the solution of a specific problem considering and taking advantage of its particularities, such as geometry patterns, in order to obtain computational advantages, as reduced number of degrees-of-freedom and ease of problem description. The element-by-element method (EBE) also fits very well in this context, since it is characterized by the elimination of the global stiffness matrix and its memory consumption grows linearly with the number of elements, besides being highly parallelizable. Over the last decades, several works regarding the EBE method were published in the literature, but none of them directly applied to flexible pipes. Due to the contact elements between the layers, problems with flexible pipes are usually characterized by very large matrix-bandwidth, making the implementation of EBE method more challenging, so that its efficiency and scalability are not compromised. Therefore, this work presents a parallelized implementation of an element-by-element architecture for structural analysis of flexible pipes using finite macroelements, consisting of an extension of a previous work from the same authors. New synchronization algorithms were developed, with scalability improvements, the methodology was extended to other finite macroelements and comparisons were made with a well-stablished FEM software, with significant gains in simulation time and memory consumption.