An Improved GPU-Optimized Fictitious Surface Charge Method for Transcranial Magnetic Stimulation

The fictitious surface charge method (FSCM) is used for the calculation of the induced electrical field in magnetic stimulation. The method was embedded and optimized in Python. It was designed to allow for the computation of large problems. An element-wise Jacobi method was combined with vectorized matrix operations to increase the parallelization capabilities and enable GPU computing. The induced fields are compared against an analytical solution for a homogeneous sphere and an FEM solution on a realistic head model. The results for both cases show that the normalized root mean square error (NRMSE) of less than
${0.5}{\%}$
can be achieved with the integral-free FSCM even on low-performance computer hardware.