CUDA-Based Library for the Integration of the Newtonian Potential and Its Gradient over Triangular Cells

We present an open-source CUDA-based library for integrating the fundamental solution to Laplace’s equation and its gradient in the three-dimensional case. This problem arises during the discretization of boundary integral equations (BIE). We use analytic formulae for integration over triangular cells and rely upon numerical integration in Galerkin-type schemes for iterated integrals. In the event of unbounded integrands, the computations are carried out semi-analytically with explicit additive separation of singularities. Also, we implement an automatic recurrent refinement procedure for numerical integration that ensures the required tolerance according to Runge’s rule. Moreover, we provide test results and the corresponding code, including some involving tens of thousands of cells.