Integral equations in electromagnetics

Abstract

Algorithms for the numerical solution of continuum electromagnetic field problems are based either on differential or integral formulations. The most common approach, at least for low frequency problems, has been the former, using the finite element method. The paper examines the special advantages of integral equations over differential equations, explores some of the difficulties involved and suggests that, in the context of more advanced problems, i.e. optimization and moving systems, the integral equation approach may be particularly effective.

Modeling of Magneto-Mechanical Coupling Using Magnetic Volume Integral and Mechanical Finite-Element Methods

“…In this case, the integral formulations of the magnetostatic field problems are particularly advantageous for the numerical solution of open boundary problems which include magnetic materials. Indeed only the active regions containing these materials need to be discretized [4]. Therefore, a volume integral method is used to solve the magnetostatic problem.…”

Topological optimization in 3D-magnetostatics: development of adjoint methods using the equations of magnetic moments

“…The main interest in this approach based on MMM is to avoid the need to mesh the air. Note that, there exist some other numerical modelization approaches like FEM-BEM (Calzadilla, 2023; Wautischer et al , 2022), volume integral methods (VIM) (Trowbridge, 1996; Le-Van et al , 2015; Han et al , 1994) or FEM-MMP (Smajic et al , 2015) which also does not need to mesh the air. In this work, we choose to work with MMM because it is one of the most popular numerical methods in electrical engineering and it focuses on the optimization unknowns.…”

Application of the virtual work principle to compute magnetic forces with a volume integral method

“…A classical method to numerically solve such problems is the finite element one (FEM), but for devices with a huge volume of free space compared with the active structure or with a high size ratio between the geometric objects, problems of accuracy and convergence to the solution can be present [1]. In such case, integral methods are attractive alternatives [2].…”