This article presents methods for correct decomposition for high performance computations related to large sets of graphs. These computations contain large number of calls of sequential, recursive algorithm for NP-complete problem - proper edge coloring of graph. Decomposition of this computational problem is not trivial, since the number of recursions in various parts of the computation is different and causes a high load and time imbalance. We designed, implemented and experimentally verified a new decomposition method that significantly reduces the computational time for a large set of graphs (up to 404 million graphs). This method ensures the same duration of computational time for partial subtasks and thus eliminates the need to wait for synchronization of parallel computations.

This work focuses on the issue of a high performance computing education based on systems such as grid, cloud, HPC cluster or systems with hybrid environments. The goal is based on the analysis of the High Performance Computing Strategic Research Agenda in Europe and the published findings in USA in context of needs for education and training specifically in HPC and Compute Intensive Science. In order to bridge the gap between the need for HPC proficient staff we have prepared the model of education and training strategy for the HPC ecosystem. We created undergraduate courses for bachelor and master study program and for research program. The work specifies the course of running tasks on high performance computing cluster with support of e-learning. The courses in research program are realized in environment of high performance computing cluster which is part of the Slovak infrastructure of high performance computing.

The article extends the performance that can be achieved with the setup for the design of higher-order proportional-integral-derivative (HO PID) controllers using ultra-local integrator-plus-dead-time (IPDT) models. The previously derived reference family of controllers, referred to as 1PID, is complemented by a new family of 2PIDs corresponding to the double integrator plus dead time (DIPDT) model. The individual members of the 1PID and 2PID families are derived using the multiple real dominant pole method (MRDP) and normalized by the parameters of the ultra-local models used. The degree of the considered controller derivatives m ∈ [1, 6] significantly outperforms most of the known methods for PID control design, which mainly use m ≤ 1 and only exceptionally consider the cases with m > 1. Therefore, the obtained results are even comparable to the HO controllers created by approximating fractional-order PID controllers. To implement the mth-order derivative, binomial low-pass filters of order n ≥ m are used in the controllers, specified by an equivalent filter delay added to the process. The traditional controllers with two degrees of freedom, for the separate design of setpoint and disturbance responses, are extended by two additional degrees of freedom provided by m and n, allowing to modify the speed of the transients together with their shapes and the closed-loop robustness. The choice of 1PIDs and 2PIDs brings another degree of freedom related to the process model used. The multiple controller parameters are set by a new modification of the Performance Portrait Method (PPM), which makes it possible to shape the closed-loop responses by specifying tolerances for deviations of step responses from their ideal shape in the time domain. The illustrative examples, which deal with two stable higher-order processes and an unstable system, show the possibility of a multiple increase in performance compared to previously known methods. They show that HO-2PID controllers are inherently better suited for processes characterized by multiple dominant time constants. The novel design opens the door to wider use of HO controllers enabled by embedded control and programmable device technology, and allows the development of new HO controllers tuned by parallel computation.

The performance portrait method (PPM) can be characterized as a systematized digitalized version of the trial and error method—probably the most popular and very often used method of engineering work. Its digitization required the expansion of performance measures used to evaluate the step responses of dynamic systems. Based on process modeling, PPM also contributed to the classification of models describing linear and non-linear dynamic processes so that they approximate their dynamics using the smallest possible number of numerical parameters. From most bio-inspired procedures of artificial intelligence and optimization used for the design of automatic controllers, PPM is distinguished by the possibility of repeated application of once generated performance portraits (PPs). These represent information about the process obtained by evaluating the performance of setpoint and disturbance step responses for all relevant values of the determining loop parameters organized into a grid. It can be supported by the implementation of parallel calculations with optimized decomposition in the high-performance computing (HPC) cloud. The wide applicability of PPM ranges from verification of analytically calculated optimal settings achieved by various approaches to controller design, to the analysis as well as optimal and robust setting of controllers for processes where other known control design methods fail. One such situation is illustrated by an example of predictive integrating (PrI) controller design for processes with a dominant time-delayed sensor dynamics, representing a counterpart of proportional-integrating (PI) controllers, the most frequently used solutions in practice. PrI controllers can be considered as a generalization of the disturbance–response feedback—the oldest known method for the design of dead-time compensators by Reswick. In applications with dominant dead-time and loop time constants located in the feedback (sensors), as those, e.g., met in magnetoencephalography (MEG), it makes it possible to significantly improve the control performance. PPM shows that, despite the absence of effective analytical control design methods for such situations, it is possible to obtain high-quality optimal solutions for processes that require working with uncertain models specified by interval parameters, while achieving invariance to changes in uncertain parameters.

This paper analyses basic concept of elastic cluster as a hybrid solution of high-performance computing tasks for computing grid and cloud. The analysis is focused on the context of managing resources and tasks in the elastic cluster. In this work design, model and implementation of scheduling algorithm is described. The scheduling algorithm is based on particle swarm optimization (PSO) and hill climbing (HC) optimization and it is appropriate combination of good features the both methods. The algorithm is implemented on HPC cluster into the resource manager Torque. There is included methodology of measurement and evaluation of the algorithm. The paper presents methods of verifying behaviour of algorithm for different tasks requirements, which are typical for grid or elastic cluster. We compare suitability of the proposed algorithm with known solutions. On the base of analysed results is confirmed that proposed algorithm better satisfies specific criteria of elastic cluster.