Melting reactive metals and alloys, such as titanium, poses a significant challenge due to the risk of crucible damage and contamination of the molten material. Full levitation melting presents a promising solution; however, its application has largely been limited to small laboratory samples. This paper introduces a methodology for modeling (in a 2D axisymmetric domain) and optimizing a new large-scale levitation melting system and demonstrates its application to pure titanium. The system features a torus-shaped load positioned within a gutter-shaped coil. Numerical experiments using this approach confirm the feasibility of stable levitation for a substantial mass (2.6 kg) within a newly designed electromagnetic levitation system.