Summary The isogeometric formulation of the boundary element method (IgA‐BEM) is investigated within the adaptivity framework. Suitable weighted quadrature rules to evaluate integrals appearing in the Galerkin BEM formulation of 2D Laplace model problems are introduced. The proposed quadrature schemes are based on a spline quasi‐interpolation (QI) operator and properly framed in the hierarchical setting. The local nature of the QI perfectly fits with hierarchical spline constructions and leads to an efficient and accurate numerical scheme. An automatic adaptive refinement strategy is driven by a residual‐based error estimator. Numerical examples show that the optimal convergence rate of the Galerkin solution is recovered by the proposed adaptive method.

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This paper presents a novel heuristic method for machine layout optimisation, developed in the course of an internal factory logistics optimisation project. The method is developed from a force-directed graph drawing algorithm, and integrates random permutations using simulated annealing to avoid local minima. The method was verified and validated with a discrete event simulation (DES) model of a furniture development factory consisting of 140 machines. The DES model was developed for manufacturing system analysis as well as design and testing of optimisation methods. The main optimisation goal was reduction of transport costs by minimising the total distance the products travel between the machines. The optimisation problem extends the quadratic assignment problem (QAP) by allowing arbitrary granularity of locations, facility sizes and fixed facilities. The resulting method can be used to solve a wider range of problems by altering the optimisation function or adding new feasibility conditions.

Two recently introduced quadrature schemes for weakly singular integrals [1] are investigated in the context of boundary integral equations arising in the isogeometric formulation of Galerkin Boundary Element Method (BEM). In the first scheme, the regular part of the integrand is approximated by a suitable quasi-interpolation spline. In the second scheme the regular part is approximated by a product of two spline functions. The two schemes are tested and compared against other standard and novel methods available in literature to evaluate different types of integrals arising in the Galerkin formulation. Numerical tests reveal that under reasonable assumptions the second scheme convergences with the optimal order in the Galerkin method, when performing h-refinement, even with a small amount of quadrature nodes. The quadrature schemes are validated also in numerical examples to solve 2D Laplace problems with Dirichlet boundary conditions.