Congratulations to the following 2023 SIAM prize recipients who will be recognized at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place August 20 – 25, 2023, in Tokyo, Japan. All SIAM prize recipients were recognized at the SIAM Reception for Prize Winners on Sunday, August 20.
Douglas N. Arnold
Douglas N. Arnold, University of Minnesota, is the recipient of the 2023 Peter Henrici Prize for fundamental contributions of extraordinary originality, depth, and impact to the finite element analysis of partial differential equations, ranking amongst the classics in numerical analysis literature. Dr. Arnold delivered a lecture on Monday, August 21, at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place August 20 – 25, 2023, in Tokyo, Japan.
The prize is awarded every four years at the International Congress on Industrial and Applied Mathematics (ICIAM) jointly by ETH Zurich and SIAM. It is awarded for original contributions to applied analysis and numerical analysis and/or for exposition appropriate for applied mathematics and scientific computing. The award is intended to recognize broad and extended contributions to these subjects more than for a single outstanding work.
Douglas Arnold is a McKnight Presidential Professor of mathematics at the University of Minnesota. He received his bachelor's degree in mathematics in 1975, followed by a Ph.D. at the University of Chicago in 1979. After graduating, Dr. Arnold took a faculty position at University of Maryland, where he remained for 10 years. In 1989, he moved to Penn State University where he was named Distinguished Professor in 1995. In 2001, he was recruited to the School of Mathematics at the University of Minnesota and served as Director of the Institute for Mathematics and its Applications until 2008. That same year, he was appointed McKnight Presidential Professor by University of Minnesota and was also awarded a Guggenheim Fellowship.
Dr. Arnold's research focuses on the design and analysis of accurate, robust, and efficient methods to solve the complex systems of differential equations that model important physical systems such as elasticity, fluid dynamics, general relativity, and quantum mechanics. Much of the work concerns finite element methods, where he works both on the design of numerical methods extending or improving our ability to accurately simulate complex physical systems, and, especially, in the theoretical understanding and rigorous validation of such methods. Many numerical methods he has introduced have been widely adopted for research or industrial computations, and some are now standard material in mathematical and engineering finite element texts. More recently, Arnold has been working together with a diverse international group of physicists and mathematicians on wave propagation in disordered media, especially phenomena related to localization of eigenfunctions.
Dr. Arnold is a past SIAM President (2009-2010) and Fellow (2009). He has delivered several distinguished plenary talks and has received many professional honors including fellow of American Mathematical Society (AMS) and the American Association for the Advancement of Science. He was elected a foreign member of the Norwegian Academy of Science and Letters (2009) and was awarded the SIAM Prize for Distinguished Service to the Profession (2013) and the J. Tinsley Oden Medal of the U.S. Association for Computational Mechanics (2015). Additionally, Dr. Arnold is the Editor-in-Chief of Acta Numerica (2021-present), having formerly served as founding co-Editor-in-Chief of SMAI Journal on Computational Mathematics. He currently serves on the editorial boards of Foundations of Computational Mathematics, Communications of the AMS, and Forum of Mathematics. Learn more about Dr. Arnold.
Q: Why are you excited to receive the award?
A: I am really delighted to receive the 2023 Peter Henrici Prize. The prize recognizes a body of work in the area of applied analysis and numerical analysis with no further restrictions to eligibility. Moreover, it has only been awarded six times since its inception 25 years ago. So, the pool of possible prize winners is vast, and I feel tremendously honored to have been selected by my peers to receive it, and to hear that they view some of my papers as "classics of the numerical analysis literature."
The award is also an occasion to remember Peter Henrici, whose work and exposition I greatly admire. Henrici's book on discrete variable methods for ODEs was actually the first numerical analysis book I ever read, and what I learned there about the interplay of consistency, stability, and convergence followed me throughout my career. It is indisputable that numerical analysis has a huge impact on our lives, and that is certainly one reason that I chose to dedicate my career to it. But of, perhaps, even greater importance to me, is the structure and elegance which numerical analysis, at its best, exhibits. Peter Henrici's writings are wonderful exemplars of this.
Q: Could you tell us about the research that won you the award?
A: The prize recognizes a body of work over an extended time, rather than one particular work, so I will only describe the general area in which I have worked, and not go into depth on any specific contribution. When I finished grad school in the seventies, the finite element method was still a very young technology, used only in a few specialized settings mostly by civil and aerospace engineers. Fortunately, thanks to the pioneering efforts of a number of intrepid mathematicians, there already existed a basic mathematical convergence theory for finite element methods, which was rigorous and even elegant.
This mathematical foundation turned out to be a key strength of the finite element approach used to assess the accuracy of finite element simulations to determine the limitations of their applicability, to discover shortcomings, and to point towards better algorithms. However, both the methods and the theory of finite elements had to overcome tremendous challenges in order to meet the ever-growing demands of industrial and scientific applications. The extension of finite element methodology to new domains of physics required both very novel finite element methods and new techniques for their analysis. Increasingly stringent demands for accuracy, efficiency, and reliability required more and more sophisticated numerical methods and computer implementations. The need for methods to robustly handle problems with more complex inputs, solutions, geometries, and so forth, added further complications. With the benefit of hindsight, we see that the efforts of many researchers to meet these requirements have been remarkably successful. Today, the finite element method is one of the most successful techniques for simulating and exploring the behavior of physical systems.
As the finite element method matured, so did my career as a computational mathematician, and I devoted much of my research efforts towards its advancement. My contributions – almost all made jointly with one or two collaborators – are primarily of two sorts.
The first sort are new algorithms to extend and improve finite element simulations. I will just give key words related to a few these: the "mini element" for incompressible flow; the Arnold-Falk plate elements; weak imposition of the symmetry of the elastic stress tensor and the PEERS element; the Arnold-Winther elements for elasticity; multigrid preconditioners for H(div) and H(curl); and the extension of the serendipity finite elements, first to three or more dimensions, and then to differential forms of positive order. The second sort of my contributions are advances to the theoretical analysis of finite element methods. These commenced with my thesis, which provided the first full analysis of discontinuous Galerkin methods for elliptic and parabolic problems. Some others are my resolution of the reduced integration paradox using mixed methods, the first convergence proof for boundary element collocation for integral equations of the first kind, the connection between mixed and nonconforming FEM using hybridization, and, especially, the finite element exterior calculus.
Q: What does your work mean to the public?
A: In the late 20th century there was a scientific revolution, as scientific computation advanced to become the third pillar of science alongside experiment and theory. Advances in computer simulation of physical reality were equally transformative in virtually all areas of engineering and technology. We now depend on finite element simulation to design, test, predict, and optimize natural and engineered systems of all sorts, ranging from mechanical to chemical to electronic with scales ranging from atomic to terrestrial to cosmological. As a consequence, one encounters applications of finite element methods in everyday life all the time. I can list a few of these applications which have incorporated computational methods coming from my research: automobile crash testing, aircraft design, remote sensing, groundwater flow, and weather and climate modeling.
Q: What does being a member of SIAM mean to you?
A: Fully told, that would be a long story, so here is a précis. I am a lifetime member of SIAM, both in the formal sense of my membership category and in the informal sense that SIAM has been important to me for all my adult life. At first, I mostly benefited from its excellent journals, both as reader and as author. I later came to realize what an important service the SIAM Journals furnish the applied and computational math community with, thanks to their well-deserved reputation for quality and professionalism delivered at a reasonable price.
During my early career, I attended SIAM meetings only occasionally, but in time, I came to feel more and more part of a SIAM community. During mid-career, it was time to start giving back, and I began to serve on SIAM Committees. After a decade or so, I was elected to the SIAM Council. There, I was struck by how well SIAM operated with a collaboration of members serving the society as volunteers, like I was, and its excellent, professional staff. Several years later, I was elected SIAM President from 2009 to 2010. Naturally, the presidency was a big responsibility, and had a great impact on me in many ways – and, I hope, I had some impact on SIAM. Now, almost 15 years post-presidency, my relationship with SIAM is somewhat less intense, but SIAM remains an important part of my professional life.
Annalisa Buffa
Annalisa Buffa, Ecole Polytechnique Fédérale de Lausanne (EPFL), will deliver the 2023 AWM-SIAM Sonia Kovalevsky Lecture. Dr. Buffa is among the most influential applied mathematicians of her generation; she has made pioneering contributions to modeling electromagnetism in non-smooth spaces, numerical methods in electromagnetics and beyond, as well optimizing the design-through analysis process. These results are of seminal importance as they impact engineering applications and industrial mathematics, as well as offer deep contributions to the development and analysis of numerical methods in their own right.
Dr. Buffa delivered the lecture on Wednesday, August 23, at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place August 20 – 25, 2023, in Tokyo, Japan.
The AWM-SIAM Sonia Kovalevsky Lecture is awarded annually by the Association for Women in Mathematics (AWM) and SIAM to highlight significant contributions of women to applied or computational mathematics. The lecture is normally given at the SIAM Annual Meeting unless it is an ICIAM year.
Annalisa Buffa has been a professor of mathematics at EPFL since 2016. Prior to this, she was the director and a research director of the Instituto di Matematica Applicata e Tecnologie informatiche of the Italian National Research Council. As a corresponding member of the Accademia dei Lincei, foreign member of the Académie des Sciences, and member of Academia Europaea, Dr. Buffa is a leading expert in the numerical analysis of partial differential equations. Her interests span from geometric design, computational mechanics, and computational electromagnetics to approximation theory and functional analysis for PDEs.
Dr. Buffa has been a plenary speaker at several venues, including the 2022 European Community on Computational Methods in Applied Sciences Conference, the 2018 American Institute of Mathematical Sciences Conference on Dynamical Systems, Differential Equations and Applications in 2018, and ICIAM 2015. She has also received a European Research Council Starting grant (2008) and Advanced grant (2016) and is a recipient of the ICIAM Collatz Prize (2015). Learn more about Dr. Buffa.
Q: Why are you excited to receive the award?
A: It's a great honor to deliver AWM-SIAM Sonia Kovalevsky Lecture!
Q: Could you tell us about the research that won you the award?
A: I have worked in the field of numerical approximation of partial differential equations for many years. Among my main contributions, I have given seminal contributions to electromagnetic scattering by defining suitable discretization techniques that are able to mimic the structure of magnetic fields. In the last ten years, I have also done research within the interplay between geometric design and numerical analysis. I contributed to the development of highly efficient numerical techniques for a number of problems from fluid to solid mechanics and electromagnetics.
Q: What does your work mean to the public?
A: I think the most important message that my work brings to the public is that mathematical reasoning is useful and a key ingredient in many technological solutions.
Q: What does being a member of SIAM mean to you?
A: SIAM is a vibrant community. Every good applied mathematician should be a member of SIAM!
Yingda Cheng
Yingda Cheng, Virginia Polytechnic Institute and State University and Michigan State University, is the 2023 recipient of the Germund Dahlquist Prize for her outstanding work on discontinuous Galerkin methods, including structure preservation and sparse grid methods for kinetic and transport equations. She was recognized at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place in Tokyo, Japan from August 20 – 25, 2023.
The Germund Dahlquist Prize is awarded every two years to one individual for original contributions to numerical solution of differential equations and numerical methods for scientific computing.
Yingda Cheng is currently professor of mathematics and an affiliate faculty with computational modeling & data analytics program at Virginia Polytechnic Institute and State University (Virginia Tech). She was born in Hefei, China in 1983 and received her B.S. degree from the University of Science and Technology of China in 2003. She graduated with a Ph.D. degree in applied mathematics from Brown University in 2007. After a postdoctoral position at the University of Texas at Austin, Dr. Cheng was a faculty member at Michigan State University before the recent move to Virginia Tech.
Dr. Cheng's area of research is in scientific computing, numerical analysis, applied mathematics and data-driven modeling and computation, with applications in plasma physics, semiconductor devices, fluid mechanics, etc. She is interested in developing numerical schemes for PDEs governing complex physical behaviors in science and engineering. She has worked extensively on the construction and analysis of discontinuous Galerkin schemes and structure-preserving numerical schemes that tackles the curse of dimensionality for kinetic transport equations. Learn more about Dr. Cheng.
Q: Why are you excited to receive the award?
A: The Germund Dahlquist Prize is a highly prestigious award in the areas of numerical solution of differential equations and numerical methods for scientific computing. I have been long inspired by the work of many pioneers in numerical analysis, including previous Germund Dahlquist prize winners. It is a great honor for me to receive this award and to learn that our work has been recognized by the community.
Q: Could you tell us about the research that won you the award?
A: One of the focus of my research is the design of discontinuous Galerkin (DG) schemes. DG methods are a class of finite element methods that have found great success in many applications in science and engineering. I have worked on the design and analysis of DG schemes with provable structure preserving properties for Hamilton-Jacobi equations, kinetic transport equations, and Maxwell's equations in nonlinear media.
The work mentioned in the award citation is the sparse grid DG method. We developed this method which builds upon the advantages of DG methods for transport equations and sparse grid techniques for high dimensional problems to offer an accurate and computationally tractable solver for high dimensional kinetic equations. I am very proud of this work, and I want to acknowledge my students, postdocs, and collaborators who have contributed significantly to many aspects of the project.
Q: What does your work mean to the public?
A: With the advances in computing hardware and software platforms, we are now more likely to have an accurate depiction of large-scale complex physical behaviors happening in nature. Advanced numerical solvers are crucial to take advantages of the modern-day computing resources and designing such novel numerical schemes is where my work lies. I hope that our schemes can assist the numerical simulations of challenging problems that cannot be handled by traditional numerical solvers, such as nuclear fusion, star formation, and many other complex physical processes.
Q: What does being a member of SIAM mean to you?
A: Being a member of SIAM makes me part of a large and vibrant community of researchers in applied mathematics. SIAM hosts many conferences which provide excellent opportunities for us to learn about the latest research and to network. I always enjoy reading and publishing in SIAM journals.
Hannah Fry
Hannah Fry, University College London, is the 2023 recipient of the George Pólya Prize for Mathematical Exposition for sustained excellence in conveying the power and appeal of mathematics to large audiences of colleagues, domain experts, students, and the public. Dr. Fry was recognized at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place August 20 – 25, 2023, in Tokyo, Japan.
SIAM awards the Pólya Prize for Mathematical Exposition every two years to an outstanding expositor of the mathematical sciences. The prize may be awarded for a specific work or for the cumulative impact of multiple expository works that communicate mathematics effectively. Following Pólya’s example, the nature of the work may range from popular accounts of mathematics and mathematical discovery to pedagogy to systematic organization of mathematical knowledge.
Hannah Fry is a professor in the Mathematics of Cities at the Centre for Advanced Spatial Analysis of the University College London, where she uses mathematical models to study patterns in human behavior. Dr. Fry is also a well-recognized presenter as the winner of the Zeeman Medal in recognition of her work in engaging the UK public with mathematics. Her expertise is regularly called upon to develop and host documentaries, present radio shows and podcasts, and give talks to a range of audiences. Learn more about Dr. Fry.
Q: Why are you excited to receive the award?
A: Winning this award is such an honor. I feel so passionate about what I do and having my work recognized in this way by SIAM is simultaneously affirming and humbling.
Q: Could you tell us about the research that won you the award?
A: My academic career has only solidified my belief that mathematics is the key to so many fascinating stories, and that through it, we can learn so much about ourselves and the world we live in. But so many people feel like it is something separate, scary, or inaccessible. I am driven to bridge that gap and through my writing and presenting, I have worked to demystify mathematics and data and guide the public to discover the joy, humor, and insights the subjects hold for themselves.
Q: What does your work mean to the public?
A: I hope that my work helps the public to understand the relevance of mathematics to their own lives and how exciting that can be. It can be too easy to be overwhelmed by data and statistics and forget about the humanity that it represents. I feel like mathematics gives me a window into the world that is like a juicy bit of gossip, and I can't help but want to break it down and share that feeling with as many people as I can.
Q: What does being a member of SIAM mean to you?
A: It means being a part of an exciting and supportive community.
Thomas Yizhao Hou
Thomas Y. Hou is the recipient of the 2023 Ralph E. Kleinman Prize for highly original and pioneering research contributions positioned at the meeting point between analytical and computational approaches to partial differential equations with multiscale or singular behavior. Dr. Hou was recognized at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place August 20 – 25, 2023, in Tokyo, Japan.
SIAM awards the prize every two years to one individual for outstanding research or other contributions that bridge the gap between mathematics and applications. Work that uses high-level mathematics and/or invents new mathematical tools to solve applied problems from engineering, science, and technology is particularly appropriate. The prize may be awarded for a single notable achievement or for a collection of such achievements.
Thomas Y. Hou is the Charles Lee Powell Professor of Applied and Computational Mathematics at the California Institute of Technology. His research interests include computational fluid dynamics, multiscale problems, and 3D Euler singularity. Dr. Hou received his Ph.D. from the University of California, Los Angeles, in 1987, before joining the Courant Institute as a postdoc. Two years later, he became a tenure track assistant professor and then a tenured associate professor in 1992 at Courant. He moved to the California Institute of Technology the following year and was named the Charles Lee Powell Professor in 2004.
Additionally, Dr. Hou has received numerous honors and awards, including USACM Computational and Applied Sciences Award from in 2005; Fellow of American Academy of Arts and Sciences (2011); a member of the inaugural class of SIAM Fellows (2009) and AMS Fellows (2012); the SIAM Outstanding Paper Prize (2018); and the SIAM Review SIGEST Award (2019). He was also the founding Editor-in-Chief of SIAM Journal on Multiscale Modeling and Simulation (2002-2007). Learn more about Dr. Hou.
Q: Why are you excited to receive the award?
A: SIAM is the most influential society for applied and industrial mathematics in the world. It is my great honor to receive the Ralph E. Kleinman Prize from SIAM. This is the best way to recognize my works in applied mathematics, especially in multiscale analysis and computation, and in the study of 3D Euler singularity. The previous recipients of this prestigious award are all outstanding research leaders in applied mathematics. I am very proud to be a member of this very distinguished group of applied mathematicians.
Q: Could you tell us about the research that won you the award?
A: One of my important contributions is to develop a very unique integrated numerics and analysis approach and apply it to solve some of the most challenging problems that were previously considered intractable. The best example to demonstrate the power of this approach is my recent major breakthrough on the 3D Euler singularity with smooth initial data, which is considered as one of the most challenging problems. By combining sharp functional inequalities, energy estimates, with space-time numerical solutions with rigorous error control, my former Ph.D. student, and Courant Institute professor, Jiajie Chen, and I proved the finite time blowup of 3D Euler with smooth initial data. This work was inspired by my joint work with my former postdoc Guo Luo, in which we discovered a new blowup scenario for the 3D axisymmetric Euler equations with boundary. In this paper published by SIAM Journal on Multiscale Modeling and Simulation in 2014, we obtained strong numerical evidence for finite time singularity by verifying various blowup criteria. This new blowup scenario is now called the Hou-Luo blowup scenario.
Very recently, Jiajie Chen and I provided the first rigorous justification of the Hou-Luo blowup scenario by developing a powerful constructive proof strategy that integrates numerics and analysis. We first constructed an approximate self-similar profile using the dynamic rescaling formulation, then established nonlinear stability of this approximate profile. This novel method of analysis has been used to prove finite time self-similar blowup of several important nonlinear partial differential equations.
The Ralph E. Kleinman Prize also recognized my pioneering contributors in multiscale analysis and computation. My works have bridged the gap between different disciplines and demonstrated the importance of multiscale methods in upscaling complex problems, developing efficient solvers, designing preconditioners, uncertainty quantification, and inverse problems. Partly due to my efforts in promoting multiscale computation through my research papers and as the founding Editor-in-Chief of SIAM Journal on Multiscale Modeling and Simulation, researchers have developed and applied many advanced multiscale computational techniques to solve challenging real-world problems.
The Multiscale Finite Element Method (MsFEM) developed by myself and my former postdoc Xiaohui Wu in 1997 was considered as a highly original and pioneering contribution to applied mathematics. It has generated considerable impact in both the applied math and the engineering communities. The main idea of the MsFEM is to capture the small-scale effect of the solution by constructing localized multiscale basis functions within each coarse grid element. The global coupling of small scales is naturally accounted for via the variational formulation. Though similar ideas were discussed earlier, my work was a first systematic attempt to solve challenging multiscale and high contrast problems. A novel over-sampling technique was introduced to alleviate the numerical boundary layer effect of multiscale basis functions. One important feature of the MsFEM is that it applies to general multiscale problems without scale separation. Another important property of the MsFEM is that the small-scale solution can be reconstructed locally by using the multiscale basis functions. Due to this important property, the MsFEM has found many applications within engineering. Some major oil companies (e.g., Chevron and Schlumberger) have adopted a variant of the MsFEM in their next generation flow simulators.
Q: What does your work mean to the public?
A: My works on the 3D Euler and Navier-Stokes singularities could have a broader impact for the mathematical and scientific community for national technology and society. The understanding of the mechanism leading to potential finite-time singularity in 3D Euler and Navier-Stokes equations could lead to important insights on the energy transfer from large to small scale in 3D turbulent flows. It may also lead to improved travel safety when we design airplanes and ships by taking into account potential singular behavior of the fluid flow under special circumstances. My works on multiscale analysis and computation have led to improved design in materials science, environmental science, control of underground water pollution transport, more efficient oil exploration, and improved energy production. The savings from the oil industry using their new generation of flow simulators based on multiscale methods is tremendous. The idea of representing a complex high dimensional solution through a sequence of locally constructed feature elements or multiscale elements can be considered an earlier version of the neural networks in which they learn important featured elements through data, multi-layer neural networks, and intensive training. The multiscale finite elements are based on analytic learning without using data. This multiscale and multi-level divide-and-conquer strategy has many implications to other important practical applications in our daily life.
Q: What does being a member of SIAM mean to you?
A: I have benefited a lot from being a member of SIAM through its publications, professional conferences, and activity groups. SIAM also represents the voice of the applied mathematics community and promotes the importance of applied and computational mathematics to the public and the industry. It also fosters a community of our own by supporting each other and providing new opportunities to students and junior researchers.
Fadil Santosa
Fadil Santosa, Johns Hopkins University, is the recipient of the 2023 SIAM Prize for Distinguished Service to the Profession in recognition of his extraordinary dedication to bridging the gap between industry and academia. Through his leadership of the Institute for Mathematics and its Applications, he played a central role in supporting young researchers; this valuable mentoring has continued through his work with the BIG Math Network. He has also advanced the field of applied mathematics through his editorial work, for instance on the Princeton Companion for Applied Mathematics. His tireless efforts will have a lasting impact on our profession.
Dr. Santosa was recognized at the 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023) taking place August 20 – 25, 2023, in Tokyo, Japan.
SIAM awards the prize every year to an applied mathematician who has made distinguished contributions to the furtherance of applied mathematics on the national or international level. The prize can be presented to any member of the scientific community who meets the general principal guideline of the prize description.
Fadil Santosa is a professor and the Yu Wu and Chaomei Chen Department Head of Applied Mathematics and Statistics. His research interests include inverse problems, wave phenomena in complex media and in photonic devices, and optimal design. He is currently focusing his efforts on optimal experiment design for inverse problems and modeling of direct air capture of CO2. He holds two patents: one for multifocal optical device design and another for symbol-based decoding of optical codes. Dr. Santosa earned his bachelor’s degree in mechanical engineering from the University of New Mexico in 1976. He received both his master’s and Ph.D. in theoretical and applied mechanics from the University of Illinois, Urbana in 1977 and 1980, respectively. Learn more about Dr. Santosa.
Q: Why are you excited to receive the award?
A: It is a total surprise for me. I am humbled by the appreciation of my efforts by my peers. I am grateful to them for supporting me.
Q: Could you tell us about the research that won you the award?
A: It is a service award. I strive to be a cheer leader for mathematics. I think it needs to be appreciated more as an enabler of solving the world's scientific, technological, and social problems. I also feel that mathematics is undervalued in industry, and I strive to raise awareness of its importance.
Q: What does your work mean to the public?
A: I hope I have made mathematics more valued in industry and in society. I hope that students I have mentored are making a difference. I hope I have provided opportunities for mathematicians.
Q: What does being a member of SIAM mean to you?
A: SIAM is my community.