The second article in the series presents the application of the Smoothed Particle Hydrodynamics (SPH) method to modelling of batch crystallisation in stirred tanks. A methodology to integrate the population balance equations (PBE) in parallel and independently from the Navier-Stokes equations is demonstrated. The benefits of the proposed methodology in terms of computational requirements, accuracy and availability of the crystal size distribution are discussed. The specific formulation of the SPH equations where the resulting system of ordinary differential equations is solved using the weighted contributions rather than numerically by solving a linear system of equations allows for massive parallelisation and a very loose coupling of the population balance and the fluid dynamics. It has been demonstrated, that the population balance equations can be solved on a Shared Memory Architecture (SMA) system using the OpenMP interface while the fluid dynamics equations being computed independently on a General Purpose Graphics Processing Unit (GPGPU) using the NVidia CUDA technology. This way, a significant portion of the computational overhead due to the large number of additional transport equations resulting from the discretisation of the population balance was removed: the SPH simulation coupled with 200 population balance equations was only 40% slower compared to SPH-only simulation. Two methods for the solution of population balance equations that preserve full crystal size distribution were implemented: discretised population balance (DPB) and method of characteristics (MOCH). The DPB equations are solved using the high-resolution finite-volume method with flux limiter and the effect of a large number of different flux limiters have been investigated. Both methods were validated using the case studies from the literature where an analytical solution can be derived. The developed models were applied to a numerical solution of coupled computational fluid dynamics and population balance equations to model a batch crystallization process. The effect of the hydrodynamics on the local temperature/supersaturation and the resulting crystal size distribution was captured and compared to the ideal mixing case. The simulation results from the DPB and MOCH methods were compared in terms of computational requirements and accuracy and MOCH selected as computationally more efficient and accurate.

The performance of lattice-Boltzmann solver implementations usually depends mainly on memory access patterns. Achieving high performance requires then complex code which handles careful data placement and ordering of memory transactions. In this work, we analyse the performance of an implementation based on a new approach called the data-oriented language, which allows the combining of complex memory access patterns with simple source code. As a use case, we present and provide the source code of a solver for D2Q9 lattice and show its performance on GTX Titan Xp GPU for dense and sparse geometries up to 4096 2 nodes. The obtained results are promising, around 1000 lines of code allowed us to achieve performance in the range of 0.6 to 0.7 of maximum theoretical memory bandwidth (over 2.5 and 5.0 GLUPS for double and single precision, respectively) for meshes of size above 1024 2 nodes, which is close to the current state-of-the-art. However, we also observed relatively high and sometimes difficult to predict overheads, especially for sparse data structures. The additional issue was also a rather long compilation, which extended the time of short simulations, and a lack of access to low-level optimisation mechanisms.

In Chuanming Zong’s program to attack Hadwiger’s covering conjecture, which is a longstanding open problem from Convex and Discrete Geometry, it is essential to estimate covering functionals of convex bodies effectively. Recently, He et al. [J. Optim. Theory Appl. 2023, 196, 1036–1055.] and Yu et al. [Mathematics, 2023, 11, 2000] provided two deterministic global optimization algorithms having high computational complexity for this purpose. Since satisfactory estimations of covering functionals will be sufficient in Zong’s program, we propose a stochastic global optimization algorithm based on CUDA and provide an error estimation for the algorithm. The accuracy of our algorithm is tested by comparing numerical and exact values of covering functionals of convex bodies including the Euclidean unit disc, the three-dimensional Euclidean unit ball, the regular tetrahedron, and the regular octahedron. We also present estimations of covering functionals for the regular dodecahedron and the regular icosahedron.

One of the non-linear phenomena that affect high bandwidth and long reach communication systems is the non-linear phenomenon called four-wave mixing (FWM). Unfortunately, the simulation of such systems aiming to obtain their design parameter limitations require more time as the number of channels increases. In this paper, we propose a new high-performance computational model to obtain optimal design parameters in a multi san Dense Wavelength Division Multiplexing (DWDM) system, limited by FWM and the intrinsic Amplified Spontaneous Emission (ASE) noise of optical amplifiers employed in each segment. The simulation in this work provides a complete optical design characterization and compares the efficiency and speed improvement of the proposed parallelization model versus a previous sequential model. Additionally, an analysis of the computational complexity of parallel model is presented, where two parallel implementations are used. First, Open Multi−Processing (OpenMP), based on the use of a central, multi-core processing unit is used and secondly the Compute Unified Device Arquitecture (CUDA), which is based on the use of graphics processing unit. Results show that parallelism improves to up to 40 times the performance of the simulation when nested parallelization with CUDA is used, over de sequential method and up to 6 times compared with the implementation with OpenMP using 12 processors. Within our parallel implementation, it is possible to simulate with an increased number of channels, that was unpractical in the sequential simulation.

With the development of engineering technology, engineering has higher requirements for the accuracy and the scale of simulation calculation. The computational efficiency of traditional se-rial program can not meet the requirements of engineering。Therefore, reducing the calcula-tion time of temperature control simulation program has important engineering significance for real-time simulation of temperature field and stress field, and then adopting more reasona-ble temperature control and crack prevention measures. GPU parallel computing is introduced into the temperature control simulation program of massive concrete to solve this problem and the optimization is carried out. Considering factors such as GPU clock rate, number of cores, parallel overhead and Parallel Region, The improved GPU parallel algorithm analysis indicator formula is proposed. It makes up for the shortcomings of traditional formula that focus only on time. According to this formula, when there are enough threads, the parallel effect is limited by the size of the parallel domain, and when the parallel domain is large enough, the efficiency is limited by the parallel overhead and the clock rate. This paper studies the optimal Kernel execu-tion configuration. Shared Memory is utilized to improve memory access efficiency by 155%. After solving the problem of bank conflicts, an accelerate rate of 437.5x was realized in the sub-routine of the matrix transpose of the solver. The asynchronous parallel of data access and logi-cal operation is realized on GPU by using CUDA Stream , which can overlap part of the data access time. On the basis of GPU parallelism, asynchronous parallelism can double the compu-ting efficiency. Compared with the serial program, the accelerate rate of inner product matrix multiplication of the GPU asynchronous parallel program is 61.42x. This study further proposed a theoretical formula of data access overlap rate to guide the selection of the number of CUDA streams to achieve the optimal computing conditions. The GPU parallel program compiled and optimized by CUDA Fortran platform can effectively improve the computational efficiency of the simulation program for concrete temperature control, and better serve for engineering computing.

This study explores the integration of Artificial Intelligence (AI) and collaborative robotics in industrial surface finishing, focusing on feature detection on object reflective surfaces using neural networks in computationally constrained environments. Central to this investigation is the utilization of cameras considered as sensors that can capture detailed images of reflective surfaces. These images are then analyzed by a custom neural network, demonstrating the feasibility of feature detection with non-powerful computers. The public dataset for recognizing light reflection defects, available in the SPADD repository, supports this approach. Employing open-source tools like Darknet YOLOv3 and Yolo\_mark, this method proves particularly advantageous for small and medium-sized enterprises (SMEs) due to its low cost and maintenance requirements. This research highlights the challenges of AI and collaborative robotics in industrial applications, especially in adapting to varying conditions and the need for continuous training with new data coming from several sensors. Looking ahead, plans are in place to integrate this system with cobot-assisted polishing tasks, using cameras to enhance manufacturing efficiency and quality. This work contributes to the broader understanding of practical applications of AI in industrial automation, surface finishing processes, and the effective use of sensor technology.