Simple Numerical Quadrature Rules for Gaussian ChainPolymer Density

We present new quadrature rules (stencil operators) for the eecient integration of Gaus-sian chain polymer density functionals on a uniform 3D grid for diierent ratios between the Gaussian bond strength parameter and the mesh width. The algorithm is in essence oo-lattice. The quadrature rules are such that the isotropy on the grid is maximal. Also the long length scaling of the numerical functionals is guaranteed to be identical to analytical results. Furthermore, we achieve a good accuracy in the entire frequency domain. A comparison with existing lattice models is included. It is shown that the traditional cubic lattice chain model may lead to unphysical singularities in copolymer melt inverse structure factors. Finally, we brieey discuss the implementation of stencil operations on parallel platforms.