  We present a real-space computational method called treecode-accelerated
Green Iteration (TAGI) for all-electron Kohn-Sham Density Functional Theory.
TAGI is based on a reformulation of the Kohn-Sham equations in which the
eigenvalue problem in differential form is converted into a fixed-point problem
in integral form by convolution with the modified Helmholtz Green's function.
In each self-consistent field (SCF) iteration, the fixed-points are computed by
Green Iteration, where the discrete convolution sums are efficiently evaluated
by a GPU-accelerated barycentric Lagrange treecode. Other techniques used in
TAGI include adaptive mesh refinement, Fej\'er quadrature, singularity
subtraction, gradient-free eigenvalue update, and Anderson mixing to accelerate
convergence of the SCF and Green Iterations. Ground state energy computations
of several atoms (Li, Be, O) and small molecules (H$_2$, CO, C$_6$H$_6$)
demonstrate TAGI's ability to efficiently achieve chemical accuracy.
