# Plenary Speakers

## Susanne C. Brenner, Louisiana State University

TITLE: DD-LOD

ABSTRACT: DD-LOD is a multiscale finite element method for problems with rough coefficients that is based on a domain decomposition approach to the localized orthogonal decomposition methodology. I will present the construction and analysis of DD-LOD for elliptic boundary value problems with rough coefficients that only require basic knowledge of finite element methods, domain decomposition methods and numerical linear algebra. An application to elliptic optimal control problems will also be discussed.

Dr. Brenner earned a Ph.D. in mathematics from the University of Michigan, 1988. She is a Louisiana State University System Boyd Professor. She holds a joint appointment with the Department of Mathematics and Center for Computation and Technology (CCT). At CCT she serves as the Associate Director for Academic Affairs.

During 2021-2022 she served as President of the Society for Industrial and Applied Mathematics (SIAM). Currently she is serving a one year term as Past President. In 2005 she was awarded a Humboldt-Forschungspreis (Humboldt Research Award) from the German Alexander von Humboldt Foundation. In 2011 she was awarded the AWM-SIAM Sonia Kovalevsky Lecture Prize. She is a SIAM Fellow (Class of 2010), AMS Fellow (Inaugural Class 2013), AAAS Fellow (2012), and AWM Fellow (2020).

Currently she serves as Managing Editor of Mathematics of Computation. She also serves on the editorial boards of the SIAM Journal on Numerical Analysis, Numerische Mathematik, Numerical Algorithms, Electronic Transactions on Numerical Analysis, the Journal of Numerical Mathematics, and Computational Methods in Applied Mathematics. Dr. Brenner is also the Editor-in-Chief of the SIAM Classics in Applied Mathematics book series, all while serving on the the SIAM and AMS Councils.

Research interests include: numerical analysis, scientific computing, finite element methods, multigrid and domain decomposition methods, computational mechanics, computational electromagnetics, variational inequalities, and PDE constrained optimization.

## Marta D'Elia, Pasteur Labs

TITLE: Scientific Machine Learning in industrial pipelines: methods and examples.

ABSTRACT: Scientific machine learning (SciML) has shown great promise in the context of accelerating classical physics solvers and discovering new governing laws for complex physical systems. However, while the SciML activity in foundational research is growing exponentially, it lags in real-world utility, including the reliable and scalable integration into industrial pipelines. SciML algorithms need to advance in maturity and validation, which in the context of traditional and advanced industrial settings, requires operating in cyber-physical environments marked by large-scale, three-dimensional, streaming data that is confounded with noise, sparsity, irregularities and other complexities that are common with machines and sensors interacting with the real, physical world. In this talk, I will highlight some of the current challenges in applying SciML in industrial contexts. By using a practical example, the heat exchanger simulation and design, I will discuss why these are necessary bottlenecks to break through and describe possible strategies. Special attention will be on the generation of fast and flexible surrogates for flow and heat exchange problems with emphasis on graph-based Neural Operators and Gaussian processes.

Dr. Marta D'Elia earned a Ph.D. in applied mathematics at Emory University, 2011. She is a Principal Scientist at Pasteur Labs and an Adjunct Professor at Stanford ICME.Previously, she was a Research Scientist at Meta and a Principal Member of the Technical Staff at Sandia National Laboratories, California.

Dr. D'Elia's work deals with Scientific Machine Learning, Optimization and Optimal Design, and Nonlocal and Fractional Problems.

## Robert Kirby, Baylor University

TITLE: High-level software for numerical PDE

ABSTRACT: FORTRAN was originally a radical and subversive proposal. Writing raw binary code was the “only way” to achieve good performance on early computers. A computer program that would translate formulas into binary met widespread opposition of the form 1) it can’t be done 2) If it can be done it will waste computer resources and 3) even if it works, “real” programmers won’t use it. This refrain was repeated at the introduction of MATLAB, the adoption of Python and other scripting languages, and the development of domain-specific languages and libraries for highly specialized fields such as partial differential equations. Despite the headwinds, the last few decades have seen the development of high-level, robust, and efficient software tools for numerical PDE These tools, such as Deal.II, FEniCS, and Firedrake, expedite the implementation of finite element methods, allowing users to deploy complex, accurate simulations in relatively compact, high-level code code. In this talk, I hope to discuss three major themes: i) Survey the historical development and challenges these projects have faced ii) Explore how different design decisions taken affect the user and developer experiences, especially contrasting a “bottom-up” approach via library development (e.g. Deal.II) with a “top-down” approach of domain-specific languages (e.g. FEniCS/Firedrake) and iii) how there is great value-added for composing such tools with “outer loop” simulation.

Dr Kirby earned a Ph.D. from the University of Texas at Austin, 2000 and is Professor of Mathematics at Baylor University.

Dr. Kirby's work focuses on finite elements for partial differential equations, preconditioners for multiphysics problems, mathematical software, multicore computing.

## Maxim A. Olshanskii, University of Houston

TITLE: Unfitted Finite Element Methods for PDEs Posed on Surfaces

ABSTRACT: Partial differential equations posed on surfaces arise in mathematical models for many natural phenomena, such as diffusion along grain boundaries, lipid interactions in biomembranes, pattern formation, and the transport of surfactants on fluidic interfaces, to name a few. Numerical methods for solving PDEs posed on manifolds have recently received considerable attention. In this presentation, we will discuss finite element methods for solving PDEs on both stationary surfaces and surfaces with prescribed evolution. The focus of this discussion is on geometrically unfitted methods—methods that circumvent the need for surface parametrization and triangulation in a conventional sense. We will elucidate how these unfitted discretizations facilitate the development of a fully Eulerian numerical framework and enable easy handling of time-dependent surfaces, including scenarios involving topological transitions.

Dr. Olshanskii received his Ph.D. degree from Moscow State University in 1996 and a second doctorate (Habilitation) in Mathematics from the Institute of Numerical Mathematics, Russian Academy of Science in 2006. He is currently a professor of Mathematics at the University of Houston. He also holds an adjunct professorship at Emory University. Until 2012, he was a professor at the Department of Mathematics and Mechanics at Moscow State University.

His research interests lie in numerical analysis and scientific computing, with a focus on applications to fluid problems, interface and free boundary problems, geometric PDEs, reduced order modeling, and cardiovascular models. He has been recognized with research awards from multiple agencies in the USA, Russia, and the European Union.

Dr. Olshanskii serves as the Editor in Chief of the Journal of Numerical Mathematics and is a member of the editorial boards of the journals Computational Methods in Applied Mathematics and European Journal of Mathematics.

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