Our ERC Project 321

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 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. Computational Electromagnetics is the underpinning of a plethora of electrical, electronic, optical, wireless, geophysical sensing, and biomedical applications. Because electromagnetic theory has strong predictive power, EM simulators play a dominant role in the advancement of today's physics and engineering science.

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 in the 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.

For this reason, the CEM scientific community has been looking for years for a FFT-like paradigm shift: a dynamic fast direct solver providing a design cost that would scale only linearly with the degrees of freedom. Such a fast solver is considered today a Holy Grail of the discipline.

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 impact of the FFT's quadratic-to-linear paradigm shift shows how computational complexity reductions can be groundbreaking on applications. The cubic-to-linear paradigm shift, which the 321 project will aim for, will have such a rupturing impact on electromagnetic science and technology.

The research activities required in ''321'' span a broad range of disciplines. Here are the main topics on which the scientists of the group will focus:

Publications from the project

    Journal papers

  1. M. Monin, L. Rahmouni, A. Merlini, and F. P. Andriulli A Hybrid Volume-Surface-Wire Integral Equation for the Anisotropic Forward Problem in Electroencephalography IEEE Journal of Electromagnetics, RF and Microwaves in Medicine and Biology Early Access, 2020


  2. A. Dély, F. P. Andriulli, and K. Cools Large Time Step and DC Stable TD-EFIE Discretized With Implicit Runge–Kutta Methods IEEE Transactions on Antennas and Propagation Vol. 68, 2020, n.2, pp. 976-985


  3. L. Rahmouni, A. Merlini, A. Pillain, and F. P. Andriulli On the modeling of brain fibers in the EEG forward problem via a new family of wire integral equations. Journal of Computational Physics: X Vol. 5, 2020, 100048


  4. A. Merlini, Y. Beghein, K. Cools, E. Michielssen, and F. P. Andriulli Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors IEEE Transactions on Antennas and Propagation. 2020, 1558-2221


  5. S. B. Adrian, F. P. Andriulli, and T. F. Eibert On a refinement-free Calderon multiplicative preconditioner for the electric field integral equation Journal of Computational Physics Vol. 376, 2019, pp. 1232-1252.


  6. A. Pillain, L. Rahmouni, and F. P. Andriulli Handling anisotropic conductivities in the EEG forward problem with a symmetric formulation Physics in medicine and biology Vol. 64, 2019, 035022.


  7. J. E. Ortiz Guzman, A. Pillain, L. Rahmouni, and F. P. Andriulli A Calderon regularized symmetric formulation for the electroencephalography forward problem Journal of Computational Physics Vol. 375, 2018, pp. 291-306.


  8. L. Rahmouni, S. B. Adrian, K. Cools, and F. P. Andriulli Conforming discretizations of boundary element solutions to the electroencephalography forward problem Comptes Rendus Physique Vol. 16, n.1-2, 2018, pp. 7-25.


  9. Conference papers

  10. M. Y. Monin, L. Rahmouni, and F. P. Andriulli Diffusion MRI Consistent Wire Models for Efficient Solutions of the Anisotropic Forward Problem in Electroencephalography . Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019.


  11. T. L. Chhim, J.E. Ortiz, L. Rahmouni, A. Merlini, and F. P. Andriulli A Quasi-Helmholtz Projector Stabilized Full Wave Solver Encompassing the Eddy Current Regime . Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019.


  12. L. Rahmouni, and F. P. Andriulli A New Preconditioner for the EFIE Based on Primal and Dual Graph Laplacian Spectral Filters . Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019.


  13. A. Dély, A. Merlini, S.B. Adrian, and F. P. Andriulli On Preconditioning Electromagnetic Integral Equations in the High Frequency Regime via Helmholtz Operators and quasi-Helmholtz Projectors . Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA), 2019.


  14. T. L. Chhim, Simon B. Adrian, and F. P. Andriulli On the Spectral Behavior and Normalization of a Resonance-Free and High-Frequency Stable Integral Equation . Proceedings of the IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, 2018.


  15. M. Y. Monin, L. Rahmouni, and F. P. Andriulli A Hybrid Integral Equation Approach to Solve the Anisotropic Forward Problem in Electroencephalography . Proceedings of the IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, 2018.