The fast calculation of magnetic field using the local refinement method

The speed of the Finite Element Method (FEM) is an obstacle to the fast calculation of magnetic fields. A fast Local Refinement Method (LRM) using the first-order FEM is presented for quickly tracking the magnetic field changes while electromagnetic models have small changes made to their shape. This method resolves the potentials in the local mesh or submesh extracted from the whole mesh, with a boundary condition that is calculated by the initial solution based on the whole mesh. Instead of being re-meshed in the local area, the extracted submesh is coarsened and reshaped by the LRM to speed up the calculation time by sharply decreasing the time used for building the S matrix and solving the matrix equation Ax = b. The new potentials in the submesh are, with an acceptable error, embedded back into the whole problem to update the magnetic fields which provide designers or users with a fast visual feedback to their adjustment.