A year of calculations in a second: electromagnetic modeling in real time

Title of the research project

321 - from Cubic3 To2 Linear1 complexity in computational electromagnetics

Scientific area (up to three scientific fields)

Computational Electromagnetics, Numerical Analysis, Mathematical Modelling

Project coordinator

Francesco Paolo Andriulli


The project targets the transformation of the computational complexity of mathematical models in Computational Electromagnetics by drastically reducing the computational cost of numerical simulations. This will pave the way to new applications in brain activity assessments, in mind-machine interactions, in cancer imaging, and in electromagnetic dosimetry.

Description of the research project 

Computational Electromagnetics is the scientific discipline focusing, through modelling and simulation, on complex electromagnetic scenarios emerging in advanced engineering and applied sciences. There is a push in cutting-edge electromagnetic technologies towards miniaturization and higher densities. This leads to mathematical models with even higher numbers of physical degrees of freedom which are increasingly expensive and difficult to handle due to their ever-growing computational cost. The ERC project “321” targets the transformation of this computational cost from cubic to linear (which explains the acronym 3 to 1). In other words, while with standard techniques when the complexity of the model doubles the computational cost increases cubically (it is multiplied by a factor 8), with the outcomes of the project the computational cost will increase only linearly (it will be multiplied only by a factor 2). This complexity reduction translates in a drastic drop of simulation time. In real case scenarios, characterized by a very high number of physical degrees of freedom, years of calculations of a standard algorithm will be computed only in a few seconds. This will enable applications and technologies that are completely out of reach today.

All research activities required in “321” are extremely multidisciplinary in nature and will call for collaborations between engineers, mathematicians, neuro and computer scientists. The project is also an interesting example of how theoretical studies can lead to concurrent advancements to both abstract and applied fields.

Impact on society 

The new computational technology which “321” will deliver will enable substantial improvements in brain imaging and modeling for epilepsy diagnostics, it will contribute to early cancer detection, but it will also impact the development of new mind-machine interfaces (allowing, for example, the control of a wheel-chair or of a computer with your mind) or new technologies for advanced neurocognitive techniques. The project outcomes will also enable new technologies and practices in electromagnetic dosimetry, since more precise and wideband assessments of electromagnetic radiation will be possible. This is a key step of any industrial process of devices involving radiating elements including mobile phones and connected objects.

Short CV of project coordinator

Francesco Paolo Andriulli is full professor at the Politecnico di Torino, where he obtained his degree in Electronic Engineering in 2004. He pursued his studies in United States at the University of Illinois at Chicago for the Master of Science and at the University of Michigan at Ann Arbor for his Ph.D. (2008).

His career continued in France at the École Nationale Supérieure Mines-Télécom Atlantique (IMT-Atlantique) where he has been full professor and where he chairs the Computational Electromagnetics Research Laboratory (CERL). He is a member of many scientific societies such as the Institute of Electrical and Electronics Engineers (IEEE) and the Society for Industrial and Applied Mathematics (SIAM). He authored more than 40 articles published on ISI journals and more than 80 conference proceedings.

       321 project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme  grant agreement No 724846

  • Start date: 1/09/2017
  • End date: 31/08/2022