<p>A longstanding challenge in materials science has been the computational modeling of interfaces between materials with different lattice parameters. Traditional approaches using plane-wave basis sets require either introducing artificial strain through unified lattice parameters or constructing prohibitively large supercells to accommodate the mismatch. These limitations have often deterred researchers from investigating large, mismatched interfaces, creating a gap in the understanding of these important systems. This work introduces an innovative algorithm that adaptively tunes the plane-wave basis sets to match the periodic structure of each material across the interface. By eliminating the need for extensive supercells or compromised lattice parameters, this new method reduces computational costs while retaining reliable results. The ability to efficiently calculate the eigen-energies of such mismatched systems, a crucial step for full density functional theory (DFT) calculations, is demonstrated with two dimensional versions of InAs/Si and SiC/Si interface potentials.</p>