Real-time time-dependent density functional theory using higher-order finite-element methods

We present a computationally efficient approach to solve the time-dependent Kohn-Sham (TDKS) equations in real-time using higher-order finite-element spatial discretization, applicable to both pseudopotential and all-electron calculations. To this end, we develop an a priori mesh adaption technique, based on semi-discrete error estimate on the time-dependent density, to construct a close to optimal finite-element discretization. We employ spectral finite-elements along with Gauss-Legendre-Lobatto quadrature to render the overlap matrix diagonal, thereby simplifying the inversion of the overlap matrix that features in the evaluation of the discrete propagator. We demonstrate a staggering reduction in the computational time afforded by higher-order finite-elements over linear finite-elements. We also perform a comparative study of the computational efficiency of the proposed method against finite difference (FD) based method and Gaussian basis for pseudopotential and all-electron calculations, respectively. Lastly, we demonstrate the capability and scalability of the proposed method on various large-scale systems.