Structural, electronic properties and Fermi surface of the new non-centrosymmetric superconductors: $3.6$ K CaIrSi$_3$ and $2.3$ K CaPtSi$_3$

First-principles FLAPW-GGA calculations were performed to investigate structural properties, electronic band structure, and Fermi surface topology of the newly discovered non-centrosymmetric superconductors: $3.6$ K CaIrSi3 and $2.3$ K CaPtSi$_3$. As a result, the peculiarities of the crystal structure, electronic bands, total and site-projected $l$-decomposed DOSs, and the shape of the Fermi surface for CaIrSi$_3$ and CaPtSi$_3$ were obtained and analyzed.