Assessment of OpenMP Master–Slave Implementations for Selected Irregular Parallel Applications

The paper investigates various implementations of a master–slave paradigm using the popular OpenMP API and relative performance of the former using modern multi-core workstation CPUs. It is assumed that a master partitions available input into a batch of predefined number of data chunks which are then processed in parallel by a set of slaves and the procedure is repeated until all input data has been processed. The paper experimentally assesses performance of six implementations using OpenMP locks, the tasking construct, dynamically partitioned for loop, without and with overlapping merging results and data generation, using the gcc compiler. Two distinct parallel applications are tested, each using the six aforementioned implementations, on two systems representing desktop and worstation environments: one with Intel i7-7700 3.60GHz Kaby Lake CPU and eight logical processors and the other with two Intel Xeon E5-2620 v4 2.10GHz Broadwell CPUs and 32 logical processors. From the application point of view, irregular adaptive quadrature numerical integration, as well as finding a region of interest within an irregular image is tested. Various compute intensities are investigated through setting various computing accuracy per subrange and number of image passes, respectively. Results allow programmers to assess which solution and configuration settings such as the numbers of threads and thread affinities shall be preferred.

Assessment of an isogeometric approach with Catmull–Clark subdivision surfaces using the Laplace–Beltrami problems

An isogeometric approach for solving the Laplace–Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull–Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace–Beltrami equation requires only $$C^0$$ C 0 continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull–Clark subdivision surfaces. Catmull–Clark subdivision bases are used to discretise both the geometry and the physical field. A fitting method generates control meshes to approximate any given geometry with Catmull–Clark subdivision surfaces. The performance of the Catmull–Clark subdivision method is compared to the conventional finite element method. Subdivision surfaces without extraordinary vertices show the optimal convergence rate. However, extraordinary vertices introduce error, which decreases the convergence rate. A comparative study shows the effect of the number and valences of the extraordinary vertices on accuracy and convergence. An adaptive quadrature scheme is shown to reduce the error.

Local Versus Global Decisions in Bayesian Automatic Adaptive Quadrature

The paper reports new significant enhancement of the robustness and effectiveness of the Bayesian automatic adaptive quadrature over macroscopic integration ranges. The implementation of a classical m-panel rule (CC-32, Clenshaw-Curtis quadrature of algebraic degree of precision m = 32) is thought again. It involves new global and local decisions blocks which, on the one side, provide sharp diagnostics redirecting the advancement to the solution and, on the other side, take advantage of the progress in the available hardware to accelerate and to increase the accuracy of the computations. Where the decision power of CC-32 is exhausted, identification and precise characterization of the features of the integrand profile which prevent quick convergence are obtained by means of three-point Simpson rules spanned at triplets of successive CC-32 knots. This local complementary investigation tool provides scale insensitive diagnostics concerning the occurrence of integrand irregularities and prevents the activation of inappropriate decision blocks which would result in fake outputs.