Solving Linear Systems of Equations with Block Skyscraper Structure

This paper proposes an efficient parallel algorithm for solving systems of linear algebraic equations (SLAE) using block skyscraper matrices, designed for execution on shared-memory computing systems. The algorithm is focused on achieving high performance and scalability, making it suitable for resource-intensive computational tasks. Special attention is given to optimizing computations and distributing the workload among processor cores to maximize acceleration. The study includes testing the proposed algorithm on nodes of a modern computational cluster by solving practical problems related to modeling the strength of building structures. The performance characteristics of the algorithm, including total execution time and acceleration coefficients depending on the number of processor cores used, have been analyzed. The impact of block sizes used in the calculations on computational performance has also been investigated. The experimental results demonstrate that the algorithm significantly reduces execution time as the number of processors increases and exhibits stable scalability on systems with a large number of cores. This highlights its applicability for solving complex engineering problems and modeling largescale systems. The proposed approach can be utilized in structural mechanics, applied physics, and other fields of engineering analysis requiring the processing of large data volumes. The conclusions of the study are valuable for further development of parallel programming methods and improving the efficiency of computational systems. Keywords: high-performance computing, system of linear algebraic equations, Cholesky method, sparse matrices, block skyscraper matrices, parallel algorithms, systems with shared memory.