Development of real-space ab-initio calculation based on finite-element method aiming for nano-interface structural optimization.

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For the development of a fast ab initio calculation software, the finite-element techniques, especially shape functions and meshing methods, in real-space ab initio calculation have been investigated. Through the investigation, we revealed the following issues : (1) Curving-mesh method maintains the convergence property of the finite-element method even in the 3-dimensional case and proves useful to reduce the number of grid points. (2) Higher-order shape function generated by spectral element method yields sufficiently accurate results with fewer number of grid points compared to lower-order shape function. (3) Quartic serendipity finite-element with curving grid can significantly improve the computational efficiency compared to the quadratic serendipity element with regular grid.