Traditional FMM based approaches for evaluating potentials due to continuous source distributions use large number of source points, require smoothing functions, and need frequent remeshing for time varying distributions. We instead use piecewise polynomials and adaptive octree to represent source distribution and output potential. Our method uses kernel independent FMM, enabling use of wide range of kernels (Laplace, Stokes, Helmholtz etc.). The implementation scales to the largest supercomputers available and demonstrates excellent per core performance.