Numerical simulation of repetitive transcranial magnetic stimulation by the smoothed finite element method

This paper presents a series of smoothed finite element methods (SFEM) for repetitive transcranial magnetic stimulation (rTMS) based on the quasi-static electromagnetic equations. The problem domain is first discretized into a set of tetrahedral elements and linear shape functions are used to interpolate the field variables. Then the smoothing domains (SDs) are constructed based on the edges, nodes, and faces of the background mesh. The smoothed gradient of electric potential and smoothed magnetic flux density over each SD are obtained by using the gradient smoothing technique (GST). The generalized smoothed Galerkin weakform is utilized to derive the discretized system equations. Numerical examples, including both spherical and realistic shaped heads, illustrate that the SFEM has the following important characteristics: (1) easier pre-processing; (2) better accuracy; (3) faster convergence; (4) higher computational efficiency.