Efficient Transient Magnetic Field Computation Using Adaptive Dual-order Finite-element Method

An adaptive dual-order finite element method (FEM) for efficient transient magnetic field analysis is presented. For each time step being simulated, the proposed adaptive FEM uses both first order and second order finite element basis functions to dynamically adjust the orders of finite elements of the problem region, aiming at using less computational resources to achieve better solution accuracy. To reduce the order of basis functions for sub-regions where the solution variation is smooth, a degrees-of-freedom (DoFs) constraining algorithm is investigated to eliminate unnecessary DoFs. This method can avoid solution interpolation errors between different meshes and it can also be implemented readily in the element matrix analysis and further global matrix assembly. Numerical examples computed using the proposed method are presented to validate the algorithm and showcase its effectiveness in transient magnetic field analysis.