The method of fundamental solutions for pointwise source reconstruction

This work deals with the reconstruction of point sources in the modified Helmholtz equation in two and three dimensions. This problem has critical applications in engineering and medicine, such as the identification of dipoles and monopoles in electroencephalography and magnetoencephalography and locating sources of environmental pollution. From the numerical point of view, we apply the method of fundamental solutions to solve the direct problems arising from the sensitivity analysis. In addition to the recognized advantages of this meshless spectral method over the traditional mesh-based numerical methods, this approach represents the pointwise sources adequately. Our numerical examples show that the algorithm is capable of accurate reconstruction even when noisy data are inverted.