Recent technological advancements in material science and manufacturing offer new possibilities in the design of innovative products requiring, at the same time, numerical simulations in the design process to fully exploit such potentials. In this context, advanced simulations provide a solid framework for studying complex, possibly coupled, phenomena. However, tailored numerical techniques are needed to limit the computational effort. The purpose of this mini-symposium is to gather experts in advanced numerical methods (e.g., Isogeometric Analysis [1], immersed methods, the p-version of the Finite Element Method [2]) working on different applications to share knowledge. [1] T. Hughes, J. Cottrell, and Y. Bazilevs, “Isogeometric analysis: Cad, finite elements, nurbs, exact geometry and mesh refinement,” Computer Methods in Applied Mechanics and Engineering, vol. 194, no. 39, pp. 4135–4195, 2005. [2] A. D¨uster, E. Rank, and B. Szab´o, “The p-version of the finite element and finite cell methods”, Encyclopedia of computational mechanics, vol. 3, no. Part 1, pp. 137–171, 2017