Treecode-Accelerated Green's Iteration for Kohn-Sham DFT

We present a real-space method for Kohn-Sham Density Functional Theory based on an integral equation formulation of the Kohn-Sham equations, called Treecode-Accelerated Green's Iteration (TAGI). In this approach, the eigenvalue problem for the Kohn-Sham differential operator is converted to a fixed point problem for an integral operator by convolution with a Green's function, then the fixed points are computed using Green's iteration. Essential to this method is the accurate and efficient evaluation of the convolution integrals arising in the iteration. TAGI achieves accuracy and efficiency through the use of adaptive mesh refinement to represent the fields, singularity subtraction schemes to reduce the quadrature error due to the singular Green's functions, and a GPU-accelerated treecode to reduce the computational complexity of the convolution integrals. We have performed all-electron calculations on non-periodic systems and demonstrated systematic convergence to chemical accuracy with respect to tightly converged reference values.