This work provides a complete analysis of eddy current problems, ranging from a proof of unique solvability to the analysis of a multiharmonic discretization technique.For proving existence and uniqueness, we use a Schur complement approach in order to combine the structurally different results for conducting and non-conducting regions.For solving the time-dependent problem, we take advantage of the periodicity of the solution. Since the sources usually are alternating current, we propose a truncated Fourier series expansion, i.e. a so-called multiharmonic ansatz, instead of a costly time-stepping scheme. Moreover, we suggest to introduce a regularization parameter for the numerical solution, what ensures unique solvability not only in the factor space of divergence-free functions, but in the whole space H(curl). Finally, we provide estimates for the errors that are due to the truncated Fourier series, the spatial discretization and the regularization parameter.

This work deals with all aspects of the numerical simulation of nonlinear time-periodic eddy current problems, ranging from the description of the nonlinearity to an efficient solution procedure. Due to the periodicity of the solution, we suggest a truncated Fourier series expansion, i.e. a so-called multiharmonic ansatz, instead of a costly time-stepping scheme. Linearization is done by a Newton iteration, where the preconditioning of the linearized problems is a special issue: Since the matrices are non-symmetric, we need a special adaptation of a multigrid preconditioner to our problem. Eddy current problems comprise another difficulty that complicates the numerical simulation, namely the formation of extremely thin boundary layers. This challenge is handled by means of adaptive mesh refinement.

With the increasing number of created and deployed prediction models and the complexity of machine learning workflows we require so called model management systems to support data scientists in their tasks. In this work we describe our technological concept for such a model management system. This concept includes versioned storage of data, support for different machine learning algorithms, fine tuning of models, subsequent deployment of models and monitoring of model performance after deployment. We describe this concept with a close focus on model lifecycle requirements stemming from our industry application cases, but generalize key features that are relevant for all applications of machine learning.

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