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.

Adaptivity in Space and Time for Magnetoquasistatics

“…Recently, first investigations for space and time adaptive MQS solvers have been made in [42] where first-order approximations in time and space are considered and in [41] where higher-order embedded SDIRK-methods are used for first-order spatial discretizations. In [31] a new variable step-size one-step Rosenbrock methods R0S3PL is coupled with lowest-order edge elements to solve linear MQS problems.…”