Calculating Surface Laplacians as a Boundary Element Method Postprocess

Postprocessing boundary element method solutions to Laplace's equation in arbitrarily shaped domains is routinely used to find surface fluxes (first-order partial derivatives) in normal and tangential directions. This paper describes a method to calculate second-order partial derivatives by postprocessing the same solutions. These derivatives allow the calculation of the surface Laplacian at the centre nodes of each element on the surface of the volume conductor. In the examples considered, the relative error between analytically determined surface Laplacians and those calculated via the methods presented is 1.0% or less, with correlation coefficients very close to 10.