We present GPU implementations of two fast force calculation methods,based on series expansions of the Poisson equation.One is the Self-Consistent Field(SCF)method,which is a Fourier-like expansion of the density field in some basis set; the other is the Multipole Expansion(MEX)method,which is a Taylor-like expansion of the Greens function.MEX,which has been advocated in the past,has not gained as much popularity as SCF.Both are particle-field method and optimized for collisionless galactic dynamics,but while SCF is a “pure” expansion,MEX is an expansion in just the angular part; it is thus capable of capturing radial structure easily,where SCF needs a large number of radial terms.We show that despite the expansion bias,these methods are more accurate than direct techniques for the same number of particles.The performance of our GPU code,which we call ETICS,is profiled and compared to a CPU implementation.On the tested GPU hardware,a full force calculation for one million particles took~0.1 seconds(depending on expansion cutoff),making simulations with as many as 108 particles fast on a comparatively small number of nodes.