We deliver here the discoveries of the ERC project 321 funded by the European Research Council and of the Program FARE, CELER funded by the Italian Ministry of University and Research.
The library Open321 provides efficient tools to stabilize and manipulate discrete electromagnetic integral equations. These stabilizations include low and very low frequency regularization techniques which rely on the use of the quasi-Helmholtz projectors, implemented to be compatible with fast iterative and fast direct methods. In particular, it makes use of an algebraic multigrid implementation provided by AMGCL in order to compute fast matrix-vector products with the quasi-Helmholtz projectors, which is required to efficiently solve the system with iterative solvers. Moreover, it is fully compatible with standard acceleration strategies such as hierarchical matrices and fast multipole method with possibilities to provide classes implementing fast matrix-vector products instead of the full matrices of the discretized integral operators. An example of the stabilization of the electric field integral equation (EFIE) together with the solving via the library Eigen is given as an example. The implementation of other integral equations directly follows.
The library has to be used within an existing integral equation solver that computes separately the integral operator matrix-vector products.
Open321 allows to fasten the electromagnetic simulations for a wide frequency range. We present bellow a non-exhaustive list of applications already presented in numerous publications carried out in the context of ERC321.
Fast and efficient solvers for the simulation of volume integral equations, with biomedical applications.
Inverse source formulations are key elements of antenna design procedures.
Challenging simulation scenarios such as complex geometries in extreme frequency regime are now possible in a lower amount of time.
Industrial applications often consist in structures that are complex because of the presence of holes and metallic junctions.