Title: Recent advances in computational electromagnetics for high resolution neuroimaging

Abstract: Electroencephalography (EEG) is one of the most used non-invasive acquisition methods to reconstruct the brain electrical activity from scalp potential recordings. As a clinical diagnostic tool, EEG source imaging plays a crucial role in epilepsy evaluation. This particularly applies to patients suffering from focal epilepsy, when source characterization and localization are two decisive stages of a pre-surgical epilepsy evaluation which prepares for the ablation of the patient’s brain area where the seizure originates. Moreover, EEG source imaging also extends to the development of Mind-Machine Interfaces (MMIs or BCIs): non-muscular communication channels leveraging brain signals for the control of external devices.

Modern high-resolution EEGs are computationally intensive devices where a large part of the imaging process is underpinned by advanced tools in the physical modeling of brain electric propagation. For this reason, several cross-disciplinary research efforts are focused on developing advanced tools for brain-related computational electromagnetics. Unfortunately, however, these tools often turn out to be computationally intensive, limiting the resolution of the physical model that can be achieved.

This talk will focus on recent advances in electromagnetic modeling and computational strategies for high resolution EEGs. Theoretical, algorithmic, and experimental advances will be presented together with their promising applications in next-generation high-resolution electroencephalographies, epilepsy diagnostics, computationally enhanced brain-computer interfaces, and real-time neurofeedback. In addition to the theoretical frameworks, this talk will present recent discoveries and achievements together with open Grand Challenges, including current research efforts about diagnostic, BCIs and immersive neurofeedback in the framework of the projects ERC “321” and EIC pathfinder “CEREBRO”, both at the theoretical and experimental level.

Bio: 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 (2010-2014) and then Full Professor with the 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 with focus on 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 with a special focus on Brain Imaging.

Prof. Andriulli received several best paper awards at conferences and symposia (URSI NA 2007, IEEE AP-S 2008, ICEAA IEEE-APWC 2015) also in co-authorship with his students and collaborators (ICEAA IEEE-APWC 2021, EMTS 2016, URSI-DE Meeting 2014, ICEAA 2009) with whom received also a second prize conference paper (URSI GASS 2014), a third prize conference paper (IEEE–APS 2018), seven honorable mention conference papers (ICEAA 2011, URSI/IEEE–APS 2013, 4 in URSI/IEEE–APS 2022, URSI/IEEE–APS 2023) and other three finalist conference papers (URSI/IEEE-APS 2012, URSI/IEEE-APS 2007, URSI/IEEE-APS 2006, URSI/IEEE–APS 2022)). Moreover, he received the 2014 IEEE AP-S Donald G. Dudley Jr. Undergraduate Teaching Award, the triennium 2014-2016 URSI Issac Koga Gold Medal, and the 2015 L. B. Felsen Award for Excellence in Electrodynamics. He is a Fellow of the IEEE.

Prof. Andriulli is a member of Eta Kappa Nu, Tau Beta Pi, Phi Kappa Phi, and of the International Union of Radio Science (URSI). He is the Editor-in-Chief of the IEEE Antennas and Propagation Magazine, he serves as a Track Editor for the IEEE Transactions on Antennas and Propagation, and as an Associate Editor of URSI Radio Science Letters. He served as an Associate Editor for the IEEE Antennas and Wireless Propagation Letters, IEEE Access, and IET-MAP. He is the PI of the ERC Consolidator Grant: 321 – From Cubic3 To2 Linear1 Complexity in Computational Electromagnetics.

Title: How dark is the unilluminable room?

Abstract: The 1958 Christmas issue of The New Scientist contained two pages with puzzles posed by Sir Roger Penrose (and his father S. L. Penrose). One of these puzzles asks the reader to design a smooth closed reflecting surface (a mirror) which contains two regions and has the property that a source of light placed in one region cannot be seen from the other region. This "room" has become known as the unilluminable room and there are now numerous fascinating solutions to the problem.

The original puzzle assumes that the light is described by rays (a so-called billiards problem) so that the light cannot “bend around corners”. Here we model light by solving the Helmholtz equation with a point source in one of the regions of the room and study (among other things) how dark the other region of the room actually is as we change the frequency of the light-source.

To model the unilluminable room we introduce and discuss the WaveHoltz iteration for solving the Helmholtz equation. This method makes use of time domain methods for wave equations to design frequency domain Helmholtz solvers. We show that the WaveHoltz iteration results in a positive definite linear system whose solution gives the solution to the (indefinite) Helmholtz equation.

Bio: Daniel Appelö holds a Ph.D. degree in Numerical Analysis from the Royal Institute of Technology in Sweden and will join the Department of Mathematics at Virginia Tech as a Professor in Fall 2023. Prior to joining VT he was on the faculty of Michigan State University, University of Colorado Boulder and the University of New Mexico and held postdoctoral positions at California Institute of Technology and Lawrence Livermore National Laboratory.

Title: Conditional moment closure methods for turbulent combustion modelling

Abstract: Combustion processes have been around for a long time; however, turbulent combustion simulations remain challenging with many unresolved issues that need to be carefully examined. With increasing demands for sustainable energy, additional problems are encountered related to new fuel blends and their impact on flame stability, ignition/extinction and atmospheric emissions. In this presentation, the physical/numerical closure problem resulting from the interactions of turbulence and chemistry will be explained. Several turbulent combustion models exist with pros and cons for each. Methods relying on conditional moment closure will be reviewed. These models include at least one additional variable space to better capture the level of turbulent fluctuations in the determination of the mean chemical source term in the species transport equations. This conditioning approach may be implemented differently leading to different numerical treatments. Within this framework, numerical techniques will be reviewed in the context of applications in Computational Fluid Dynamics (CFD). This will be followed by some recent developments and illustrations from our research group.

Bio: Dr. Cecile Devaud is a Professor in the Department of Mechanical and Mechatronics Engineering at the University of Waterloo. She studied mechanical engineering in France (INSA Rouen), obtained her Master’s degree from the University of Cranfield (UK) and received her PhD from the University of Cambridge (UK). After graduation, she worked for 1.5 years at British Gas and a total of 3 years at the University of Cranfield and Sydney (Australia) as a post-doctoral research fellow, before moving to Canada. She has extensive expertise in the development of turbulent combustion models using conditional averages and numerical simulations of complex engineering flows in industry relevant conditions. Part of her research is also focused on fire modelling in various scenarios. She has been an active member of the combustion research community. Currently, she is the Chair of the Canadian Section of the Combustion Institute and has been collaborating with many numerical and experimental groups for best research.

Title: Optimization in the presence of chaos

Abstract: Many important engineered artifacts and processes can be accurately modelled as chaotic dynamical systems --- fusion reactors, wind turbines, and aircraft, to name a few. Furthermore, improving the performance of these engineered systems could play a critical role in addressing some of humanity's present and future challenges. Despite the strong impetus to improve engineered systems that are governed by chaotic dynamics, we lack the algorithmic tools to efficiently optimize these systems, especially when there are many (> 10) design parameters.

The goal of this presentation is to convey why chaotic systems are difficult to optimize, and to review the techniques that have been proposed to overcome this difficulty. I will first explain why conventional sensitivity-analysis and optimization algorithms, which work well for steady and periodic systems, fail when applied to chaotic problems. I will then describe the various techniques that have been proposed over the past twenty years to optimize time averages from chaotic systems. These techniques can be categorized as either sensitivity-analysis methods or regularization methods; the former aim to produce useful derivatives that approximate the trend/slope of time-averaged outputs, while the latter "smooth" out, or regularize, the optimization problem by eliminating problematic oscillations in the time-averaged output. The presentation will conclude with my lab's recent work developing a regularization-type method related to unstable periodic orbits.

Bio: Dr. Jason Hicken is an associate professor in the Mechanical, Aerospace, and Nuclear Engineering Department at Rensselaer Polytechnic Institute (RPI) in Troy, NY. Dr. Hicken received his doctoral degree in aerospace engineering from the University of Toronto Institute for Aerospace Studies in 2009. Before joining RPI in 2012, he held a Natural Sciences and Engineering Research Council of Canada Postdoctoral Fellowship at Stanford. He was awarded an AFOSR Young Investigator Award in 2015 and an NSF CAREER Award in 2016. His primary research interests are computational fluid dynamics and numerical design optimization.

Title: Numerical modelling of dispersed flow

Abstract: Emulsion-based products are widely encountered in our daily lives and industrial processes: food emulsions, pharmaceutical emulsions for drug delivery, emulsions in agriculture, and petroleum extraction. Emulsions are systems where one liquid is dispersed in the form of drops into another immiscible liquid and stabilized with surfactants. An emulsion-based product design involves three major aspects: product formulation (ingredients), process conditions during manufacturing, and properties of the final product, such as flavour, texture, and stability. The critical features of the final product are determined by the drop size distribution (DSD) of the emulsion, which, in turn, depends on emulsion composition and the manufacturing process. Therefore, prediction and control of the DSD are crucial factors for successful emulsion-based product design and production.

In my research group, we create numerical techniques to study the behaviour of liquid and gas dispersions in different flow conditions. Such in silico experiments aim to minimize trial-and-error and costly laboratory experiments and, therefore, to develop sustainable and environmentally benign process design, scale-up and optimization of emulsion-based products. In my talk, I will explain the lattice Boltzmann methods for dispersed flows, show their capabilities to perform direct numerical simulations (DNS) of immiscible flows and explain how the results of such methods lead to a better understanding and prediction of the DSD. In addition, our most recent extension of the diffuse interface free energy and conservative phase field methods to include soluble surfactants will be demonstrated.

Bio: Dr. Komrakova is an Associate Professor at the Department of Mechanical Engineering at the University of Alberta. She obtained her BSc and MSc equivalent degrees in Mechanical Engineering at the Bauman Moscow State Technical University, Moscow, Russia. She holds a Ph.D. degree in Chemical Engineering from the University of Alberta. Upon graduation, Dr. Komrakova worked as a postdoctoral fellow at the Chemical and Materials Engineering Department at the University of Alberta, where she was involved in developing a mechanistic model for a complex precipitation process. Dr. Alexandra Komrakova’s research area of interest is the development of numerical models and their application to study multiphase flows. The main focus of her current research work is the coupling of direct numerical simulations, population balance equation models, and machine learning techniques to get a better fundamental understanding of dispersed flows. The gained insights of numerical studies then get translated into simple models and guidelines to assist industry in making informed decisions on safe and sustainable design, production and operation of systems with bubbles and drops. Along with the research work, Dr. Komrakova is actively engaged in teaching. She also holds the position of Associate Dean Graduate Students for Mechanical Engineering.

Title: Moment limiter framework for solution stabilization with the discontinuous Galerkin method

Abstract: Solutions of hyperbolic conservation laws develop discontinuities in final time even with smooth initial data. High-order numerical methods have difficulty approximating such solutions because they develop oscillations near discontinuities of exact solutions, making computations impossible. To control oscillations and to guarantee convergence of a numerical scheme, we apply limiters. The main challenge in designing limiters is to preserve high-order accuracy while stabilizing numerical solutions.

We present a framework for constructing limiters on arbitrary grids, i.e. on triangular, quadrilateral, tetrahedral, as well as for nonconforming meshes arising with adaptive mesh refinement. The limiter reduces (limits) solution coefficients (moments) by reconstructing the slopes along a set of directions in which the moments decouple. We perform the reconstruction of the slopes on a compact stencil consisting of only a small number of elements, regardless of a mesh configuration. Our algorithm is implemented entirely on the graphics processing unit (GPU) and avoids race conditions. For second order approximations, we prove that the limited solutions satisfy a local maximum principal (LMP). For higher order approximations, we provide numerical experiments to validate the robustness of the limiter in the presence of discontinuities and high-order accuracy on smooth solutions.

Bio: Lilia Krivodonova is a professor of Applied Mathematics at the University of Waterloo. Before coming to Waterloo, she obtained a PhD in mathematics from Rensselaer Polytechnic Institute and was a postdoc at the Courant Institute for Mathematical Sciences at New York University. She works on analysis of numerical methods for solution of hyperbolic problems, with an emphasis on stability properties.

Title: hp-adaptive high order methods for high accuracy resolution of partial differential equations

Abstract: High order spectral element methods are now routinely used for high resolution studies of complex engineering and geoscience phenomena. However, they remain expensive and are hampered by structured grid topologies. Massively parallel implementations and the increasing power of high performance computing platforms have steadily increased their efficiency, so that they have become competitive with more traditional numerical methods, especially when high accuracy is needed: for example, in the calculation of transition to turbulence in complex flows. Adaptive mesh refinement promises to add significant savings of computational resources and ease the task of finding suitable grids. While high order computations and the discontinuous Galerkin approach are ideal for parallel computing, on both CPUs and GPUs, the dynamic nature of the adaptive gridding poses significant challenges.

We present parallel adaptive continuous and discontinuous Galerkin spectral element methods, where both h-refinement (splitting of elements) and p-refinement (elemental polynomial order increase) are used, guided by a posteriori error estimators that depend only on the quality of the resolution of any variable. To address load imbalance and interprocessor communication, we use a Hilbert (space filling) curve ordering of elements to maintain locality in connectivity information as the grid adapts. Parallel adaptive algorithms are implemented and tested on both CPU and GPU platforms.

Examples ranging from simple wave propagation to Direct Numerical Simulation (DNS) of flows transitioning to turbulence on a high-lift wing and iced airfoils are presented.

Bio: Catherine Mavriplis is Full Professor of Mechanical Engineering at University of Ottawa where she works on advanced numerical methods for aerodynamics and other simulations. She earned her Bachelor of Mechanical Engineering (Honours) from McGill, and her Master’s and PhD from MIT in Aeronautics. She was a postdoctoral scientist in the Program in Applied and Computational Mathematics at Princeton. She earned her tenure in Mechanical and Aerospace Engineering at George Washington University in Washington, where she also worked as Program Manager in Applied and Computational Mathematics at the US National Science Foundation.

In Canada, Dr. Mavriplis held the NSERC Chair for Women in Science and Engineering for Ontario from 2011 to 2021, leading a program to recruit, retain and advance women to leadership. She has been awarded the 2019 Partners-In-Research Technology & Engineering Ambassador Award, has been the President of the Computational Fluid Dynamics Society of Canada and sat on the Council of the Canadian Aeronautics and Space Institute. She is a Fellow of Engineers Canada and the Canadian Academy of Engineering.

Title: Numerical solution of entropy-inspired moment-based models

Abstract: Many physically interesting situations are made up of a large number of particles, each of which follows simple evolution laws. However, the sheer number of particles often precludes a direct, particle-based treatment. Moment models offer a method of generating PDEs that govern the evolution of high-order statistics of the particles. This talk demonstrates how an entorpy-maximization principle can be used as a guide to generate models for the evolution of such many-particle systems that take the form of first-order hyperbolic balance laws with local relaxation. This talk demonstrates the development of such moment models for non-equilibrium gas flows, plasma flows, and multiphase flows. A discontinuous-Galerkin-Hancock method that was specifically designed for the efficient solution of the resulting models is shown. This technique achieves third-order accuracy in both space an time, while only using first-order basis functions. An implementation that has been shown to scale with near-100% efficiency past 250,000 cores is demonstrated. Numerical solution to illustrative problems are shown.

Bio: James McDonald works in the fields of moment methods for kinetic equations and high-order numerical methods for PDEs. He has proposed novel moment-based models for rarefied gases, non-equilibrium plasmas, multiphase flows, and radiation transport. He is the main developer of an efficient implementation of a high-order accurate discontinuous-Galerkin-Hancock solver for hyperbolic PDEs with stiff local relaxation source terms. James graduated from UTIAS in 2011. He was then a post-doctoral researcher at the Rheinisch-Westfälische Technische Hochschule (RWTH) University in Aachen Germany. He is currently an Associate professor in the department of Mechanical Engineering at the University of Ottawa.

Title: Nonlinear stability of numerical methods for conservation laws: then, now and the future

Abstract: The celebrated Lax–Richtmyer theorem or more popularly knows as the Lax Equivalence Theorem unfortunately does not hold for nonlinear partial differential equations (PDE). The prevailing idea that to guarantee convergence, some form of stability is sufficient is inadequate. For nonlinear equations an L2 bound on the solution is typically insufficient to ensure convergence for the nonlinear fluxes; which leads to numerical schemes that are perfectly stable but fails to converge to a solution. The early work of Harten and Tadmor raised the need for conservation laws such as the Euler equations to satisfy an additional condition namely, the second law of thermodynamics to ensure that the correct weak solution is realized. Over the past decade, this has led to a small but growing community of entropy-conservative and-stable schemes.

The research group of Nadarajah has been extending the high-order flux reconstruction approach to discontinuous Galerkin methods over the past decade. The flux reconstruction method allows for larger time-steps than DG while ensuring linear stability on linear elements. Over the past two years we have developed a new Nonlinearly Stable Flux Reconstruction (NSFR) approach based on modal uncollocated schemes in split forms that ensure energy and entropy stability. In this presentation, we will begin with an historical overview, provide a comprehensive review of the current state of the field and end with concluding remarks on the future of the approach.

Bio: Siva Nadarajah leads the Computational Aerodynamics Group at McGill University, where they are developing the next-generation of algorithms to analyze and design complex aerodynamic surfaces through a conjunction of the engineering, applied mathematics and computer science disciplines. He graduated at Stanford University under the supervision of Antony Jameson in 2003 and has been a Professor at McGill University since. He has collaborated with many Aerospace companies and algorithms developed within his research group over the years form the backbone of numerical methods at Bombardier Aerospace providing them the ability to simulate complex flows and redesign aircraft wings. He is an Associate Fellow of the American Institute of Aeronautics and Astronautics, co-founded its Aerodynamic Design Optimization Working Group and Workshop. He is currently serving as the Director of the McGill University Institute for Aerospace Engineering as well as an associate editor of the Springer Journal of Optimization Theory and Applications and recently a guest editor of the Elsevier Computers and Fluids Journal.

Title: High-fidelity CFD and FSI of blood flow dynamics in the brain

Abstract: About a decade ago our group demonstrated that the assumption of laminar flow in blood vessels of the brain served to spin a vicious cycle, producing predictions of laminar flow owing to the convenient use of stabilization schemes to accelerate the CFD. Since then, high-fidelity CFD has shown that cerebrovascular blood flow dynamics may exhibit high-frequency vortex-shedding, transitional or possibly turbulent flow, with attendant flow-induced vibrations. In this presentation, I will show how high-fidelity CFD and fluid-structure-interaction (FSI) modelling has allowed us to gain insights into cerebrovascular disorders like brain aneurysms and pulsatile tinnitus, and into the poorly-understand mechanisms of intracranial sound production. I will also show how this work has inspired novel strategies for visualizing and sonifying complex fluid dynamics data.

Bio: David A. Steinman, PhD, is a professor of mechanical and biomedical engineering at the University of Toronto. He is recognized as a pioneer in the integration of medical imaging and computational modelling and their use in the study of cardiovascular disease development, diagnosis, and treatment planning. Professor Steinman is a Fellow of the American Society of Mechanical Engineers, and is currently an Associate Editor of the Journal of Biomechanics and the Journal of Neurointerventional Surgery.