Chapter 3. Dynamical Quadrature Grids
Applications in Density Functional Calculations
Nathan Luehr, Ivan Ufimtsev and Todd Martinez
In this chapter we present a GPU accelerated quadrature grid scheme designed for situations where the grid points move in time. We discuss the relative merits of several schemes for parallelization, introduce mixed precision as a valuable optimization technique, and discuss problems arising from necessary branching within a warp.
Quadrature grids are often custom built to match the topography of a particular integrand. For example, additional points may be allotted near known discontinuities. A subtle complication arises when the integrand evolves in time. In such cases, the quadrature points dynamically ...