The field of numerical methods for wave propagation and scattering is experiencing significant developments, driven by the need for efficient and accurate solutions to complex problems. Recent research has focused on improving the robustness and scalability of domain decomposition methods, particularly in the context of heterogeneous media and high-frequency regimes. Innovations in quasi-Trefftz methods, spectral coarse spaces, and fast multipole methods have shown promise in achieving better performance and accuracy. Additionally, advances in integral equation methods, complex scaling, and least-squares isogeometric analysis have expanded the range of applicable problems and improved the overall efficiency of numerical simulations. Notable papers include:

• A quasi-Trefftz space for a second order time-harmonic Maxwell's equation, which introduces a new discrete space for electro-magnetic wave propagation in inhomogeneous media.
• Fast Evaluation of Derivatives of Green's Functions Using Recurrences, which provides a hybrid symbolic-numerical procedure for efficient computation of high-order derivatives of Green's functions.
• Fast Multipole Method with Complex Coordinates, which develops a variant of the fast multipole method for efficiently evaluating standard layer potentials on geometries with complex coordinates.