Investigation and implementation of fast direct solvers for general case scenarios including homogeneous, inhomogeneous, anisotropic, and chiral dielectric and magnetic materials
Homogeneous penetrable and chiral electromagnetic problems:
The solution of this task has lead to a very powerful formulation which is the first full wave stabilized formulation capable of modelling the Eddy Current regime without low frequency approximations. This has attracted substantial interest especially from the industrial sector and will impact several fields in circuit design and electromagnetic compatibility. In fact, the state of the art in Eddy Current solvers has a breakdown for high frequencies/high clock circuits. The modelling of the frequency transition region was an open problem of the domain that the technique we have obtained has successfully addressed for the first time.
Inhomogeneous and anisotropic problems:
The main formulation obtained solving this task have already found impacting applications in neuroimaging. Under the work for this task we have also investigated an inhomogeneous stabilized framework. This new framework has already received recognition from the community receiving an honorable mention award at the flagship conference of our discipline.
Parallelization on High-Performance-Computing platforms:
The formulations have been accelerated on HPC platforms. Accelerations have been based on Multilevel Adaptive Cross Approximation Algorithms and on the Multilevel Fast Multipole Method.
