IEEE IMAS 2026 Computational Electromagnetics Workshop

Francesco P. Andriulli received the Laurea in electrical engineering from the Politecnico di Torino, Italy, in 2004, the MSc in electrical engineering and computer science from the University of Illinois at Chicago in 2004, and the PhD in electrical engineering from the University of Michigan at Ann Arbor in 2008.

From 2008 to 2010 he was a Research Associate with the Politecnico di Torino. From 2010 to 2017 he was an Associate Professor and then Full Professor with École Nationale Supérieure Mines-Télécom Atlantique (IMT Atlantique), Brest, France. Since 2017 he has been a Full Professor with the Politecnico di Torino, Turin, Italy.

His research interests are in computational electromagnetics, including frequency- and time-domain integral equation solvers, well-conditioned formulations, fast solvers, low-frequency electromagnetic analyses, and modeling techniques for antennas, wireless components, microwave circuits, and biomedical applications.

Prof. Andriulli received several best paper awards at conferences and symposia and numerous other awards and recognitions for his research contributions.

He received the 2014 IEEE AP-S Donald G. Dudley Jr. Undergraduate Teaching Award, the 2014-2016 URSI Isaac Koga Gold Medal, and the 2015 L. B. Felsen Award for Excellence in Electrodynamics.

Prof. Andriulli is a Fellow of the IEEE and of the International Union of Radio Science (URSI). He serves as the 2026 President-Elect of the IEEE Antennas and Propagation Society.

Computational Electromagnetics (CEM) is a scientific discipline positioned at the intersection of electrical engineering, high-performance computing, and applied mathematics. It is primarily concerned with the modeling and simulation of complex electromagnetic phenomena.

Historically, CEM has provided the predictive framework underlying applications in electrical and electronic engineering, optics, wireless communications, geophysical exploration, and biomedical systems.

In recent years, the scope of CEM has broadened significantly, engaging with interdisciplinary fields including information retrieval, computational neuroscience, machine learning, and brain-computer interfaces.

A pervasive trend across these domains is the substantial growth in the dimensionality and scale of the problems being addressed. This evolution has led to increasing computational complexity and cost associated with electromagnetic modeling, design, and simulation.

This talk will provide an overview of the major challenges, both longstanding and emerging, facing the field of CEM, with examples spanning from canonical problems to those of “Holy Grail”-like complexity.

Emphasis will be placed on recent research efforts aimed at achieving paradigm shifts in simulation methodologies, with the objective of overcoming computational bottlenecks inherent in conventional approaches.

Applications discussed will include brain imaging and modeling, electromagnetic dosimetry, epilepsy diagnosis, and brain-computer interfaces.

Simon B. Adrian received the B.Sc. degree in Electrical Engineering and Information Technology from the Technische Universität München (TUM), Munich, Germany, in 2009.

He received the M.S. degree in Electrical and Computer Engineering from the Georgia Institute of Technology, Atlanta, GA, USA, in 2010, the Dipl.-Ing. degree in Electrical Engineering and Information Technology from TUM in 2012, and the Dr.-Ing. degree from TUM and IMT Atlantique, Brest, France, in 2018.

From 2012 to 2019, he was a Research Assistant at TUM. He was a Visiting Professor with the Politecnico di Torino in 2018. From 2019 to 2020, he was a Senior Engineer with Infineon AG, Neubiberg, Germany.

From 2020 to 2024, he was an Assistant Professor with the Universität Rostock, where he has been a Professor since 2024.

His research interests include computational electromagnetics, integral equation solvers, preconditioning techniques, low-frequency stable formulations, and fast solvers, with applications in antenna modeling and bio-electromagnetic problems.

A variety of fast methods has been developed to accelerate the solution of surface integral equations discretized using the boundary element method.

For electrically small problems, algebraic low-rank factorization methods, such as adaptive cross approximation (ACA) and nested cross approximation (NCA), can be utilized.

These methods exploit the fact that blocks of the system matrix associated with well-separated parts of the geometry are approximately low rank.

As the frequency increases and the problem becomes electrically large, the rank of these blocks can grow, rendering these techniques less attractive.

Directional compression techniques, such as directional H²-matrices, have therefore been introduced to exploit directional low-rank structures of high-frequency interactions.

The construction of H²-matrices begins with hierarchical partitioning of the underlying geometry, followed by a block decomposition of the system matrix.

The computation of the nested low-rank factorization of compressible blocks is typically performed using ACA.

To overcome limitations of standard ACA, the incomplete adaptive cross approximation (IACA) reduces the unused portion of the factorization and improves overall performance.

In this contribution, we present recent progress on IACA for standard and directional H²-matrices applied to the electric field integral equation (EFIE).

Funded by the Bundesministerium für Forschung, Technologie und Raumfahrt (BMFTR) – Project 05H24HRA

[1] Bebendorf, M., C. Kuske, and R. Venn. “Wideband nested cross approximation for Helmholtz problems.” Numerische Mathematik 130, no. 1 (2015): 1–34.

[2] Börm, Steffen. “Directional H²-Matrix compression for high-frequency problems.” Numerical Linear Algebra with Applications 24, no. 6 (2017): e2112.

[3] Tetzner, Joshua M., and Simon B. Adrian. “The Incomplete Adaptive Cross Approximation for the Fast Construction of H²-Matrices and Its Application to the Electric Field Integral Equation for Electrically Small Problems.” Preprint, 2025.

A variety of fast methods has been developed to accelerate the solution of surface integral equations discretized using the boundary element method.

For electrically small problems, algebraic low-rank factorization methods such as ACA and NCA can be utilized.

These methods exploit the fact that blocks of the system matrix associated with well-separated parts of the geometry are approximately low rank.

As the frequency increases and the problem becomes electrically large, the rank of these blocks can grow as the mesh is simultaneously refined.

Directional compression techniques, such as directional H²-matrices, have been introduced to exploit directional low-rank structures of high-frequency interactions.

Directional H²-matrices allow a compressed representation of the system matrix to be constructed using low-rank approximation techniques with log-linear complexity.

The construction of H²-matrices begins with hierarchical partitioning of the underlying geometry, followed by a block decomposition of the system matrix.

For directional H²-matrices, an additional directional hierarchy is introduced into the geometrical partitioning.

The computation of the nested low-rank factorization of compressible blocks is typically performed using ACA.

The incomplete adaptive cross approximation (IACA) reduces the unused portion of the factorization and thereby improves overall performance.

Recent progress on IACA for standard and directional H²-matrices applied to the electric field integral equation demonstrates the benefits of incomplete ACA algorithms.