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Summary: This paper presents a study of primal and dual Steklov‐Poincaré approaches for the identification of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We show that costless filtering of the solution is possible by postprocessing Ritz elements. Assessments are provided on a 3D mechanical problem. [ABSTRACT FROM AUTHOR]

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The article presents a mechanical engineering problem on the perturbation of an eigenvalue in the continuous spectrum of a waveguide with an asymmetric obstacle. The statement of the eigenvalue problem is provided, which has an obstacle closed set with a Lipschitz boundary. It looks at the solution of the limit problem, restricted to the upperwaveguide since the given problem is symmetric about the horizontal axis. Also illustrated is the augmented scattering matrix, the asymptotics of the augmented scattering matrix, and the search for an eigenvalue. A discussion for the conditions of the described theorem is included.

In this paper we use fuzzy set method to solve one of the important problems in mechanical engineering (the residual service life). The residual service life for rolling stock can change depending on it's using conditions. The Paper offer's a new method depending on fuzzy set method by using the material mechanical and chemical corrosion mathematical model. [ABSTRACT FROM AUTHOR]