Достовірність комп’ютерних розв’язків при дослідженні  власних коливань

Alexandr Popov; Alexey Chystiakov

Alexandr Popov д. ф.-м. н., с. н. с., Інститут кібернетики ім. В.М. Глушкова НАН України, пр-т Академіка Глушкова, 40, 03187, Київ
Alexey Chystiakov к. ф.-м. н., с. н. с., Інститут кібернетики ім. В.М. Глушкова НАН України, пр-т Академіка Глушкова, 40, 03187, Київ

Abstract

The paper examines the reliability of the results of numerical modeling of natural oscillations of structures and buildings on computers with parallel organization of calculations. Based on the analysis of the finite element method for the discretization of problems about natural oscillations, methods of computer research of mathematical properties, solving and reliability research of the solutions of the partial generalized algebraic eigenvalue problem (AEP), which arises as a result of discretization, a posteriori estimates of errors of eigenvalues and eigenvectors of a generalized problem with symmetric matrices, one of which is positive definite, were obtained. Reasoned algorithms (which use a variable bit rate) for solving by subspace iteration method of a partial generalized AEP and a posteriori computer research of its solutions are proposed.

References

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Reliability of Computer Solutions in the Study of natural oscillations

Abstract

References