The article addresses the solution of systems of linear algebraic equations arising in static and steady-state vibration problems solved by the finite element method. A block-sparse matrix format based on the CSR (Compressed Sparse Row) format is presented, along with its GPU implementation using CUDA. A stabilized biconjugate gradient method is implemented and applied to model problems of varying dimensions; a comparison with a reference implementation in MATLAB is also conducted.

Keywords: sparse matrices, finite element method, block matrices, GPU, parallel computing, systems of linear algebraic equations, biconjugate gradient method

The article describes the main problems of circuit simulation. The problem of solving ill-conditioned systems of linear algebraic equations (SLAE) of large dimension. The modified algorithm is a linear algebraic solutions. Described a hybrid evolutionary algorithm for solving linear systems based on the proposed modified method. The results of the pilot study and comparison of the algorithm with the algorithms based on the traditional methods for solving linear algebraic equation, which confirm the advantages of the hybrid evolutionary algorithm.

Keywords: Genetic operators, evolutionary algorithm, the system of linear algebraic equations, computer-aided design.