Error control schemes for adaptive time integration of magnetodynamic systems with variable spatial mesh resolution

Abstract

Purpose

A combination of both time step adaptivity and spatial mesh adaptivity is presented for transient magneto‐quasistatic fields.

Design/methodology/approach

Error controlled time step adaptivity is achieved using an implicit integration scheme and the spatial mesh resolution is adapted in each time step in order to effectively resolve the appearing and disappearing local transient saturation effects and eddy current layers. Two spatial refinement strategies are considered, the red‐green refinement leading to a regular mesh and the red refinement leading to an irregular mesh. Numerical results for 2d nonlinear magneto‐dynamic problems are presented.

Findings

An algorithm is proposed which computes the solution of a transient magnetostatic problem given a user prescribed error tolerance for the time stepping and the spatial refinement. The red refinement leading to irregular meshes requires projection techniques in the iterative conjugate gradient solver. However, the algorithm with red‐green refinement turns out to perform faster since the projection is too expensive.

Originality/value

The combination of error controlled time stepping and spatial adaptivity is firstly established in electromagnetic field computation.

Citation

Wimmer, G., Steinmetz, T. and Clemens, M. (2007), "Error control schemes for adaptive time integration of magnetodynamic systems with variable spatial mesh resolution", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 26 No. 3, pp. 758-772. https://doi.org/10.1108/03321640710751208