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Description:
Local and global forces are important quantities of interest in electrostatic and magnetostatic settings. They are important for the mechanical design or analysis of an electromechanical system and their computation via numerical simulations is thus a valuable tool. They are obtained through post-processing of the numerically computed fields and, generally speaking, can be obtained via either a volume-based or a boundary-based approach. For classical schemes based on the Maxwell Stress Tensor, the boundary-based computation yields lower convergence rates and total errors compared to the volume-based computations, especially for the case of non-smooth domains with sharp corners. When working with the boundary element method (BEM), the boundary data is obtained directly from the solvers, making it convenient to do a boundary-based computation of forces. Alas, it suffers from low convergence rates. Yet, it is not efficient to reconstruct the field solution inside the domain and use a volume-based computation in this case. This work is aimed at obtaining better boundary-based computation algorithms for electromagnetic forces. The central idea comes from the Virtual Work Principle which relates the change of field energy for a deformation of the geometric configuration to the work done by the force fields. These energy changes are tracked using the shape derivative of the field energy which yields the forces in the sense of a distribution over the space of velocity fields. The computation of the shape derivative can be done with a variational constraint using the adjoint method which provides another point of attack. By choosing a variational constraint in the volume, we recover the Maxwell Stress Tensor based formulas, but by choosing a boundary integral equation constraint we obtain novel expressions which resemble boundary integral operators and thus have certain smoothing properties, making them superior to the classical boundary based approaches. In this work we compute these boundary integral equation ...