Two-way coupling of thin shell finite element magnetic models via an iterative subproblem method

Purpose The purpose of this paper is to deal with the correction of the inaccuracies near edges and corners arising from thin shell models by means of an iterative finite element subproblem method. Classical thin shell approximations of conducting and/or magnetic regions replace the thin regions with impedance-type transmission conditions across surfaces, which introduce errors in the computation of the field distribution and Joule losses near edges and corners. Design/methodology/approach In the proposed approach local corrections around edges and corners are coupled to the thin shell models in an iterative procedure (each subproblem being influenced by the others), allowing to combine the efficiency of the thin shell approach with the accuracy of the full modelling of edge and corner effects. Findings The method is based on a thin shell solution in a complete problem, where conductive thin regions have been extracted and replaced by surfaces but strongly neglect errors on computation of the field distribution and Joule losses near edges and corners. Research limitations/implications This model is only limited to thin shell models by means of an iterative finite element subproblem method. Originality/value The developed method is considered to couple subproblems in two-way coupling correction, where each solution is influenced by all the others. This means that an iterative procedure between the subproblems must be required to obtain an accurate (convergence) solution that defines as a series of corrections.

A Hybrid Forward–Backward Algorithm and Its Optimization Application

In this paper, we study a hybrid forward–backward algorithm for sparse reconstruction. Our algorithm involves descent, splitting and inertial ideas. Under suitable conditions on the algorithm parameters, we establish a strong convergence solution theorem in the framework of Hilbert spaces. Numerical experiments are also provided to illustrate the application in the field of signal processing.

Generalised Single-Passage Multi-Bladerow Method for Turbomachinery Forced Response

This paper describes the formulation and validation of a novel computational method for a quick and accurate assessment of multi-bladerow turbomachinery forced response using 3D, viscous, time-domain, unsteady aerodynamics. Phase-lagged boundary conditions are applied at the periodic boundaries and information is exchanged using a 0-thickness whole-annulus representation of the bladerow boundary. The proposed method is general in terms of rotor/stator blade numbers and preserves the accuracy of an equivalent multi-bladerow whole-annulus time-domain computation. The method is first validated on simple wave propagation cases for cylinders with known exact solutions. A turbine configuration is studied next, and results from the single-passage multi-bladerow method are checked against those from equivalent whole-annulus computations. The two sets of results are found to be in excellent agreement. The computational requirements of the two methods are compared and the advantages of the generalized single-passage method over its whole-annulus counterpart are highlighted in terms of CPU effort and memory storage. Implementation details, such as convergence, solution acceleration and the effect of non-reflecting boundary condition treatments at the inter-bladerow boundaries, are also discussed.

On Improved Approximate Solution of the Fredholm Integral Equation

A method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.