Parallel Solution of Dynamic Elasticity Problems

An algorithm for parallel solution of the dynamic problems of the elasticity theory for axisymmetric objects as a three-dimensional problem of the elasticity theory has been proposed. The semidiscrete approximations reduce the problem to the solution of the Cauchy problem for a system of linear differential equations of the second order. The elements of the matrix are determined with the help of the semi-analytical finite element method (FEM) using the Fourier series analytical expansion by trigonometric functions of the angle coordinate and numerical expansion of isoparametric approximations on serendipity quadrilaterals in the meridional section. The Cauchy problem is solved by decomposing the solution into eigenfunctions, which we find using the subspace iterations method. The method has been parallelized with domain decomposition and message passing interface (MPI), and the parallelized method has been scaled to over 20 processors with high parallel performance. The numerical examples have demonstrated the performance of the proposed algorithm. The numerical results indicate that the method is very accurate and its parallelizations are efficient for both types of problems.