An adaptive degrees-of-freedom finite-element method for transient magnetic field analysis

A novel adaptive degrees-of-freedom (DoFs) finite-element method (FEM) for the numerical computation of transient magnetic fields is presented. The proposed adaptive FEM incorporates functions of both mesh refinement and mesh coarsening. The mesh refinement procedure is implemented using the longest edge bisection algorithm, whereas for the coarsening procedure, a novel DoFs constraining algorithm is proposed to replace conventional algorithms which explicitly eliminate the unnecessary nodes which have sufficiently small estimated errors. This process avoids solution interpolation errors due to the changes from a fine mesh to a coarse mesh. It can also be implemented readily in element analysis level. The slave-master technique is adopted to eliminate the constrained DoFs in the linear system conveniently to result in coarsening of the underlying finite element space and hence it has the same effect as mesh coarsening. Implementation details of the algorithm are presented and numerical examples using the proposed method are tested to validate the algorithm and showcase its effectiveness in transient magnetic field computation of engineering problems.