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We consider a compression method for boundary element matrices arising in thecontext of the computation of electrostatic fields. Green cross approximationcombines an analytic approximation of the kernel function based on Green'srepresentation formula and quadrature with an algebraic cross approximationscheme in order to obtain both the robustness of analytic methods and theefficiency of algebraic ones. One particularly attractive property of the newmethod is that it is well-suited for acceleration via general-purpose graphicsprocessors (GPUs).

GCA-$\mathcal{H}^2$ matrix compression for electrostatic simulations