The simulation of electromagnetic (EM) wave problems plays a key role in many fields, ranging from object characterization and inspection to radar stealth. A common approach consists in transforming the initial 3D volumetric problem into a 3D surface integral equation defined at material interfaces and discretizing it using a Boundary Element Method (BEM). High-order (HO) discretization schemes accelerate approximation convergence and thus provide a significant gain in accuracy for a given number of mesh elements, but complicates the assembly of the linear system. In particular, the calculation of singular and quasi-singular integrals becomes challenging, while the integration of HO methods into fast compression algorithms based on the hierarchical matrix formalism (HMAT) raises questions about the overall efficiency of the BEM. This postdoctoral position aims to address these in order to obtain a solution that is both efficient and robust for the targeted EM applications.