Computational Electromagnetics (CEM) is the scientific field at the origin of all new modeling and simulation tools required by the constantly arising design challenges of emerging and future technologies in applied electromagnetics. CEM is at the interface between electrical engineering, advanced computing, and applied mathematics and it focuses on developing fast and efficient solvers to characterize the electromagnetic interactions, radiation, and scattering of large, multiscale, and complex objects. As in many other technological fields, however, the trend in all emerging technologies in electromagnetic engineering is going towards miniaturized, higher density and multi-scale scenarios. Computationally speaking this translates into a steep increase of the number of degrees of freedom. Given that the design cost (the cost of a multi-right-hand side problem dominated by matrix inversion) can scale as badly as cubically with these degrees of freedom, this can sensibly compromise the practical impact of CEM on future and emerging technologies. The Grand Challenge of 321 is to tackle this Holy Grail in Computational Electromagnetics by investigating a dynamic Fast Direct Solver for Maxwell Problems that would run in a linear-instead-of-cubic complexity for an arbitrary number and configuration of degrees of freedom. To attain this, the project’s objectives include the investigation of new modelling and solution strategies for a large plethora of scenarios and frequencies, new fast solution strategies, and impacting applications in dosimetry, bioelectromagnetism, and neuroimaging. The action has achieved all foreseen objectives resulting in several impactful results, including new mathematical and computational tools, fast solvers, and their applications to important real case scenarios. The new paradigm in fast solution strategies and a new plethora of technologies to achieve them that the project has obtained will have a substantial impact on the discipline within and well beyond the scope of this action.
