Discovery of New Materials: why we care and how we are doing it*

Discovery of new materials---from plastics, electronics, synthetic fabrics, and metal alloys---has  a tremendous impact on our quality of life.  The number of possible new materials to explore is immense, numbering in the trillions at least. Materials scientists explore these possibilities experimentally and computationally, but both approaches would require billions of years to try all possibilities. Our goal is to speed up such simulations. One of the key challenges is to accelerate the numerical integral for computing the band energy. Knowing band energy is essential to compute the stability of a candidate material.  The numerical integral for band energy converges slowly (high accuracies require a dense integration mesh). In order to speed up the convergence, we integrate the bands analytically using  a high-order polynomial interpolation method.  We will discuss results for a 2D toy problem that illustrates our approach.