Obtaining the theoretical and algorithmic framework for a dynamic fast direct solver for well-conditioned HPD problems equipped with a fast forward algorithm. The metallic case.
The Dynamic Fast Direct Solver:
One important objective was to obtain inversion strategies for the dynamic operators. As foreseen under this task we have completed the analysis allowing for a uniform regularization of both the low and the high frequency regime, this has been achieved thanks to an ad-hoc investigation of Laplacian based modified projectors. The strategy has been studied on canonical geometries for which we have used a spherical harmonics analysis and it has also been extended to vector operators both with an approach based on explicit Helmholtz decompositions and with projector based implicit decomposition approaches.
Fast matrix vector products for T and K - right hand side and radiator calculators and a first dynamic fast direct solver for metallic problems:
We have developed a new theory and associated technology leveraging on a new concept, the quasi-Helmholtz spectral projector filter, which allowed us to overcome the challenge posed by this task. The new tools developed are extremely powerful and will impact future discoveries even beyond this project. Our new approach has already been recognized by the scientific community with a Best Paper Award.
