An Adaptive Meshless Method for Magnetic Field Computation

Increasing energy cost and advance in permanent magnet technology have provided the incentives to develop geometrically compact and energy-efficient electromagnetic (EM) actuators. Design of electromagnetic (EM) actuators often involves solving a magnetic field problem. This paper presents an adaptive meshless method (MLM) that inherits many advantages of the finite-element method (FEM) but needs no explicit mesh structure for design of EM actuators. Specifically, the paper offers a technique to estimate the distribution of numerical errors and a scheme that automatically inserts additional nodes to improve computational accuracy and efficiency. It gives several examples. The first three numerical examples, where exact solutions are available, provide a means to validate the adaptive MLM and evaluate its effectiveness against a regular MLM with a uniform node distribution. The other examples, where magnetic forces are computed from Lorenz´s law, illustrate the use of adaptive MLM for practical design of an EM actuator. The paper compares the computed forces against published experimental results.