Superconducting quantum devices are corner stones in modern quantum technology, where they are used both as fundamental building blocks in larger quantum devices and circuits, but also as sensors in quantum metrology. These superconducting devices are often realized on a mesoscopic scale, bridging the microscopic and macroscopic regimes. However, our fundamental understanding of how superconductivity behaves on the mesoscopic scale is far from complete, partly owing to the technical challenges with simulating such systems with full microscopic theory. Recent investigations of mesoscopic superconductivity have unveiled surprising results that challenge our basic assumptions of superconductivity, where the mesoscopic degrees of freedom for example trigger spontaneous symmetry breaking, pattern formation and lead to competing orders. To study these phenomena, we are investigating a novel finite-element method (FEM) to model mesoscopic superconductivity which is developed by one of us (Phys. Rev. B 106, 144511 (2022); https://link.aps.org/doi/10.1103/PhysRevB.106.144511). The code runs efficiently on CPU with MPI using an open-source FEM library. These simulations are compared with our open source code SuperConga (Applied Physics Reviews 10, 011317 (2023); https://doi.org/10.1063/5.0100324), which run instead on GPU (Berzelius-2023-343). By combining these methods, we will unravel novel phenomena in mesoscopic unconventional superconductors, and investigate competing orders. In addition, we will be investigating proximitized superconductivity in hybrid structures and heterostructures using fully atomistic approaches based on Bogoliubov-de Gennes theory. This approach is based on eigenvalue solution using standard libraries such as LAPACK and BLAS.