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The purpose of this paper is to introduce a reverted way to design electrical machines. The authors present a work flow that systematically yields electrical machine geometries from given air gap fields.

The solution process exploits the inverse Cauchy problem. The desired air gap field is inserted to this as the Cauchy data, and the solution process is stabilized with the aid of linear algebra.

The results are verified by solving backwards the air gap fields in the standard way. They match well with the air gap fields inserted as an input to the system.

The paper reverts the standard design work flow of electrical motor by solving directly for a geometry that yields the desired air gap field. In addition, a stabilization strategy for the underlying Cauchy problem is introduced.

The paper addresses various ways of driving a magneto‐quasi‐static coupled field‐circuit problems, starting with the underlying assumptions of this problem class. It focuses on problem consistency, supporting both conceptual understanding, and translation into software.

The paper proceeds from a precisely defined problem class and analyze its consistency with homology theory.

Precise notion of “driving a problem,” extensive discussion of modeling assumptions and decisions, and classification and consistency analysis of various driving methods.

Helps modelers systematically pose consistent coupled field‐circuit problems. The computation of homology groups can be automated to help pose problems and detect consistency problems.

Starting from the basic underlying assumptions, the paper summarizes logically the application of homology to consistency analysis. The style is tutorial for modelers, with numerous particular cases.

The purpose of this paper is to study algebraic structures that underlie the geometric approaches. The structures and their properties are analyzed to address how to systematically pose a class of boundary value problems in a pair of interlocked complexes.

The work utilizes concepts of algebraic topology to have a solid framework for the analysis. The algebraic structures constitute a set of requirements and guidelines that are adhered to in the analysis.

A precise notion of “relative dual complex”, and certain necessary requirements for discrete Hodge‐operators are found.

The paper includes a set of prerequisites, especially for discrete Hodge‐operators. The prerequisites aid, for example, in verifying new computational methods and algorithms.

The paper gives an overall view of the algebraic structures and their role in the geometric approaches. The paper establishes a set of prerequisites that are inherent in the geometric approaches.

The authors aim to search for a practical and accurate way to get good loss estimates for coil filaments in electrical machines, for example transformers. At the moment including loss estimations into standard finite element computations is prohibitively expensive for large coils.

A low-dimensional function space for finite element method (FEM) is introduced on the filament-air interface and then extended into the filament to significantly reduce the number of unknowns per filament. Careful choice of these extensions enables good loss estimate accuracy. The result is a system matrix assembly block that can be used verbatim for all filaments, further reducing the cost. Both net current and voltage per length of the filament are readily available in the problem formulation.

The loss estimates from the developed model agree well with traditional FEM and the computation times are faster.

To produce accurate loss estimates in large coils, the low-dimensional function space is constricted on the filament boundaries. The proposed method enables electrical engineers to compute the ohmic losses of individual conductors.

Finite element‐based PDE solver software systems are typically method‐driven. The user has to supply the data in a particular form required by a numerical method. The method refuses to start if the data is in incorrect format, and breaks down if correctly formatted data is insufficient or inconsistent. However, software can be made more flexible with data‐driven approach. The decisions on existence and uniqueness of the solution, as well as the choice of suitable computing methods are based on the data. This calls for a new stage of data processing for a solver, which is not essentially an expert system. The questions are formalizable and their solution must be based on efficient and robust computational techniques. We present an elementary computational technique for automatic treatment of topological problems arising from potential theory, boundary condition inspection, and coupled problems. The approach is based on computing Smith normal form of the non‐oriented boundary operator matrices, whose elements are from the ring N mod 2, i.e. only 0s and 1s, instead of the integers. This approach obviates the problems of excessive computation time and risk of overflow in integer computations.