Том: 15888 , Год издания: 2025

In this paper we consider the problem of numerical solution of the boundary value problem of the theory of elasticity in static formulation in a rectangle with arbitrary boundary conditions. For this purpose, we use the approach of splitting in the direction of the Laplace operator based on its spectral decomposition, which is similar to the discrete Fourier transform but does not require periodicity of the boundary conditions. A fast matrix-to-vector multiplication algorithm is proposed using an effciently software-implemented matrix multiplication algorithm. Numerical experiments are performed to show the effectiveness of the proposed method with the ability to solve the elasticity problem on a mesh of 10⁹ nodes on systems with 128G RAM.