Modelling of impulse loading in high-temperature superconductors. Assessment of accuracy and performance of computational techniques.

Purpose – The aim of this paper is to access performance of existing computational techniques to model strongly non-linear field diffusion problems. Design/methodology/approach – Multidimensional application of a finite volume front-fixing method to various front-type problems with moving boundaries and non-linear material properties is discussed. Advantages and implementation problems of the technique are highlighted by comparing the front-fixing method with computations using fixed grids. Particular attention is focused on conservation properties of the algorithm and accurate solutions close to the moving boundaries. The algorithm is tested using analytical solutions of diffusion problems with cylindrical symmetry with both spatial and temporal accuracy analysed. Findings – Several advantages are identified in using a front-fixing method for modelling of impulse phenomena in high-temperature superconductors (HTS), namely high accuracy can be obtained with a small number of grid points, and standard numerical methods for convection problems with diffusion can be utilised. Approximately, first order of spatial accuracy is found for all methods (stationary or mobile grids) for 2D problems with impulse events. Nevertheless, errors resulting from a front-fixing technique are much smaller in comparison with fixed grids. Fractional steps method is proved to be an effective algorithm for solving the equations obtained. A symmetrisation procedure has to be introduced to eliminate a directional bias for a standard asymmetric split in diffusion processes. Originality/value – This paper for the first time compares in detail advantages and implementation complications of a front-fixing method when applied to the front-type field diffusion problems common to HTS. Particular attention is paid to accurate solutions in the region close to the moving front where rapid changes in material properties are responsible for large computational errors. Keywords - Modelling, Numerical analysis, Diffusion, High temperatures, Superconductors Paper type - Research pape

Critical evaluation of numerical techniques for highly non-linear field diffusion modelling

Various numerical techniques have been applied to multidimensional field diffusion problems with front-type behaviour, moving boundaries and non-linear material properties. Advantages and implementation challenges of the methods are discussed with special attention paid to conservation properties of the algorithm and achieving accurate solutions close to the moving boundaries. The techniques are evaluated using analytical solutions of diffusion problems with cylindrical symmetry

Exploration versus Exploitation Using Kriging Surrogate Modelling in Electromagnetic Design

This paper discusses the use of kriging surrogate modelling in multiobjective design optimisation in electromagnetics. The importance of achieving appropriate balance between exploration and exploitation is emphasised when searching for the global optimum. It is argued that this approach will yield a procedure to solve time consuming electromagnetic design problems efficiently and will also assist the decision making process to achieve a robust design of practical devices considering tolerances and uncertainties

Numerical investigation of fano resonances in metamaterials with electric asymmetry

The excitation of high quality factor asymmetric Fano-type resonances on a double layer metafilm structure is investigated through numerical simulation. The paper demonstrates that it is possible to design simple structures capable to sustain a very high quality factor resonance by reducing their radiation losses. An equivalent circuit formed by two linearly coupled resonant RLC circuits is extracted in an attempt to explain the observed Fano resonance through classical circuit theory

Considerations of uncertainty in robust optimisation of electromagnetic devices

Due to unavoidable uncertainties related to material properties and manufacturing processes, the robustness of the optimal solution must be considered when designing electromagnetic devices. In this paper, the worst-case optimisation (WCO) and the worst-vertex-based WCO are proposed to evaluate the robustness of both performance and constraints under uncertainty. To reduce computing times when searching for the robust solution a predicted objective function is used, obtained with the help of a kriging algorithm which explores the searching space using the concept of rewards. Finally, to avoid some of the shortcomings of WCO, the concept of average performance evaluation is developed