STRING-WAVE DIRECT PARALLEL SOLVER FOR SPARSE SYSTEM OF LINEAR EQUATIONS
The article discusses a parallel algorithm for solving systems of linear algebraic equations for symmetric sparse matrices, which allows you to split a large task into many small subtasks, thereby both increasing performance and reducing memory consumption. It is based on a method of simultaneous calculation of intermediate values during matrix decomposition while maintaining load balancing on processors so that when the final result of the left parts of the decomposition is obtained, the right parts of the decomposition do not depend on them. This approach allows the initial stiffness matrix to be represented as a product of a large number of simple matrices and solve a system of linear algebraic equations in the form of a sequence of solutions by substitution. To reduce the filling of sparse decomposition matrices, an approximate minimum degree method was used, which, in addition to being one of the most efficient and fastest existing at the moment, allows the developed algorithm to distribute the load of calculations more evenly. The developed method is implemented in NTC APM software products for systems with shared memory, but it can also be implemented for systems with distributed memory.
Likhosherstnyy A.Yu., Velikaya Ya.G. String-Wave Direct Parallel Solver for Sparse System of Linear Equations // Research result. Information technologies. – T.10, №3, 2025. – P. 72-79. DOI: 10.18413/2518-1092-2025-10-3-0-7
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