In this paper, we propose a hybrid parallel programming approach for a numerical solution of a two-dimensional acoustic wave equation using an implicit difference scheme for a single computer. The calculations are carried out in an implicit finite difference scheme. First, we transform the differential equation into an implicit finite-difference equation and then using the alternating direction implicit (ADI) method, we split the equation into two sub-equations. Using the cyclic reduction algorithm, we calculate an approximate solution. Finally, we change this algorithm to parallelize on graphics processing unit (GPU), GPU + Open Multi-Processing (OpenMP), and Hybrid (GPU + OpenMP + message passing interface (MPI)) computing platforms. The special focus is on improving the performance of the parallel algorithms to calculate the acceleration based on the execution time. We show that the code that runs on the hybrid approach gives the expected results by comparing our results to those obtained by running the same simulation on a classical processor core, Compute Unified Device Architecture (CUDA), and CUDA + OpenMP implementations.

This study presents a combined numerical and experimental analysis of heat and mass transfer in mare’s milk during vacuum sublimation drying, which is a process essential for producing high-quality powdered products. The numerical model was developed using two-dimensional simulations and validated against experimental data obtained for varying sample thicknesses (3 mm, 5 mm, and 7 mm). Results demonstrated a strong agreement between the model and experimental temperature data, with a coefficient of determination ($R^2$) of 95% during the sublimation process. The findings revealed that thinner samples (3 mm) exhibited a 20% faster drying rate than thicker samples (7 mm), highlighting the critical role of sample thickness in sublimation dynamics. Additionally, the effects of heat flux distribution and mass loss due to sublimation were analyzed to understand the drying dynamics. This study highlights the importance of optimizing process parameters such as chamber pressure, shelf temperature, and sample thickness to enhance drying efficiency and reduce processing time. The findings provide valuable insights for scaling vacuum sublimation drying of mare’s milk for industrial applications.

In this paper, we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media. The stability analysis of the scheme using the von Neumann stability method has been studied. We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps. Developed parallel code using Compute Unified Device Architecture (CUDA) technology and tested on domains of various sizes. Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit (CPU). The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.

This paper presents a numerical realization of the Navier-Stokes equations in irregular domains using the fictitious domain method with a continuation along with the lowest coefficient. To solve numerous connected issues in irregular regions, the fictitious domain method is broadly used. The advantage of the fictitious domain method is that the problem is solved not in the original complex domain, but in a few other, easier domains. Using the method, computation is done easily for a sufficiently wide class of problems with arbitrary computational domains. The problem is solved using two methods. The primary method is based on the development of a distinct issue in variables of the stream function and the vortex velocity using the pressure uniqueness condition. The second method is to understand the expressed issue by the fictitious domain method with a continuation by lower coefficients. Using the fictitious domain method, a computational algorithm is constructed based on the explicit finite difference schemes. The finite difference scheme is stable and has high computational accuracy and it gives the possibility to parallelize. Temperature distributions and stream functions are presented as numerical results. A parallel algorithm has been developed using Open Multi-Processing (hereinafter OpenMP) and Message Passing Interface (hereinafter MPI) technologies. Within the parallel approach, we used OpenMP technology for parallel calculation of vorticity and stream work, and for calculating temperature we applied MPI technology. The performance analysis on our parallel code shows favorable strong and weak scalability. The test results show that the code running in the parallel approach gives the expected results by comparing our results with those obtained while running the same simulation on the central processing unit (CPU)

The article discusses methods for processing unstructured data using an analytical platform. The authors analyze existing methods and technologies used to implement data processing and propose new approaches to solving this problem. The possibilities of using analytical platforms to solve the problem of processing source data are considered. The purpose of the article is to explore the possibilities of data import, partial preprocessing, missing data recovery, anomaly removal, spectral processing and noise removal. The authors explored how analytics platforms can function without a data warehouse, obtaining information from any other sources, but the most optimal way is to use them together, and how big data and unstructured data can be processed using an analytics platform. The authors solved a specific problem related to processing problems and proposed ways to solve them using an analytical platform. Particular attention is paid to a complete set of mechanisms that allows you to obtain information from any data source, carry out the entire processing cycle and display the results. Overall, the paper represents an important contribution to the development of raw data processing technologies. The authors plan to continue research in the field of processing big unstructured data.

The study aims to accurately predict the presence of heart disease using machine learning models. The research evaluates and compares the performance of five algorithms - Logistic Regression, Support Vector Machine (SVM), Decision Tree, Random Forest, and Gradient Boosting - on a dataset containing clinical features of patients. The primary research question is to identify which algorithm demonstrates the best predictive performance for heart disease diagnosis. The study used a dataset of 270 patients with 13 clinical features. The data was preprocessed, and target variables were converted into binary values for classification. The dataset was split into training and test sets in a 70-30 ratio. Five machine learning models were trained and evaluated using metrics such as accuracy, precision, recall, F1-score, and ROC-AUC. Confusion matrices were analyzed to gain additional insights into model performance. Logistic Regression and Random Forest showed the best results among all models, with an accuracy of 86.4 and 80.2%, respectively. The Logistic Regression showed a ROC-AUC score of 0.844, while the Random Forest showed a score of 0.88. The confusion matrices revealed the strengths and weaknesses of each model in terms of forecasting. Logistic Regression and Random Forest were identified as the most reliable models for predicting heart disease in this dataset. Future work will explore hyperparameter tuning and ensemble methods to further enhance model performance, providing valuable insights for early diagnosis and treatment of cardiovascular diseases.