Multigrid Methods Professors and Supervisors in Canada

Stephen A. VavasisView profile

Professor

University of WaterlooCanada

Stephen A. Vavasis is a Professor in the Department of Combinatorics and Optimization at the University of Waterloo, part of the Faculty of Mathematics. He holds a PhD in Computer Science from Stanford University (1989) and has held academic positions at Cornell University (1989–2006) before joining Waterloo. His research focuses on continuous optimization, data science, first-order methods, scientific computing, and computational mechanics. Current teaching includes courses on convex optimization and portfolio optimization methods. He has served as Associate Dean of Computing (2017–2020) and Interim Director of Data Science graduate programs. His work is supported by NSERC grants. Notable awards include the Hertz Fellowship, Churchill Scholarship, and Guggenheim Fellowship. Vavasis's research emphasizes applications of optimization to clustering, machine learning, and fracture mechanics. His publications span convex optimization frameworks, algorithmic analysis of gradient methods, and numerical methods in mechanics. Recent work explores unifying analyses of first-order optimization algorithms and robust optimization techniques for high-dimensional data problems.

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Justin WanView profile

Professor

University of WaterlooCanada

Justin Wan is a Professor in the Department of Computer Science at the University of Waterloo. His research focuses on scientific computing, medical image processing, computational finance, and machine learning. He holds a Ph.D. from UCLA (1998), an M.A. from UCLA (1995), and a B.Sc. from the Chinese University of Hong Kong (1992). Wan’s work bridges numerical methods, optimization, and deep learning, with applications in financial modeling, medical imaging, and fluid dynamics. His research interests include advanced techniques in scientific computing (e.g., multigrid methods), computer graphics simulation, and medical image enhancement (e.g., CT scan artifact reduction). He has pioneered applications of machine learning to computational finance, including option pricing and hedging using deep neural networks and GANs. His recent work explores denoising diffusion models and multi-agent systems for optimal execution in finance. Publications span topics like volatility surface computation, optimal mass transport for image registration, and parallel solvers for fluid dynamics. His methods address challenges in high-dimensional problems, robust numerical valuation, and scalable algorithms for large datasets. Wan collaborates across disciplines, integrating mathematical rigor with practical engineering solutions.

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Chen GreifView profile

Professor

University of British ColumbiaCanada

Chen Greif is a Professor in the Department of Computer Science at the University of British Columbia (UBC). His research focuses on numerical linear algebra, iterative solvers, preconditioning techniques, and scientific computing. He has held editorial roles in SIAM journals and book series, and served as Head of the Department of Computer Science from 2016 to 2020. Greif co-authored the SIAM bestselling textbook A First Course in Numerical Methods and has published extensively in top journals. Education: Ph.D., Mathematics, University of British Columbia, 1998 M.Sc., Mathematics, Tel Aviv University, 1994 B.Sc., Mathematics, Tel Aviv University, 1991 Research Interests: Scientific computing, numerical linear algebra, iterative methods for sparse linear systems, saddle-point systems, and elliptic PDEs. His work emphasizes preconditioning techniques and numerical stability. Publications Trends: Recent work includes multigrid methods for complex systems, preconditioners for saddle-point matrices, and eigenvalue bounds analysis. His contributions bridge theory and applications in computational science and engineering. Awards: SIAM Fellow (2022) CAIMS Research Prize (2023) Multiple teaching awards (2025, 2024, 2017, 2006, 2004) Advising & Grants: Greif has advised numerous students and contributed to grants in numerical methods and computational science. He has led major conferences (e.g., International Conference on Preconditioning Techniques, 2017) and served on SIAM committees. Labs/Teams: Engaged in interdisciplinary research groups at UBC, focusing on numerical algorithms and their applications in fluid dynamics, image processing, and computational geometry.

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Scott MacLachlanView profile

Professor

Memorial University of NewfoundlandCanada

Scott MacLachlan is a Professor of Mathematics at Memorial University of Newfoundland. He holds a B.Sc. (Hon.) from the University of British Columbia and a Ph.D. in Applied Mathematics from the University of Colorado at Boulder. Previously, he served as Associate Professor at Tufts University. His research focuses on computational applied mathematics and scientific computation, particularly multigrid methods, finite-element discretizations, and numerical linear algebra. He is an associate editor for the SIAM Journal on Scientific Computing and SIAM Journal on Matrix Analysis and Applications, and co-chairs the program committee for the Copper Mountain Conference on Multigrid Methods. Education: B.Sc. (Hon.) in Mathematics and Computer Science (UBC, 2000), Ph.D. in Applied Mathematics (CU Boulder, 2004). Postdoctoral work at University of Colorado, University of Minnesota, and Delft University of Technology. Research interests include multiscale numerical analysis, PDE-based models in fluid/solid mechanics, and algorithm development for scientific computing. His work integrates functional analysis, numerical linear algebra, and physical modeling. He develops open-source software such as XBraid for parallel time integration and adaptive AMG codes. Publications span multigrid methods, domain decomposition, and liquid crystal simulations. He collaborates on projects involving thermal slip, magnetohydrodynamics, and geophysical electromagnetics. Teaching includes courses on numerical methods for PDEs at both Memorial University and Tufts. Professional activities include editorial roles, conference organization, and contributions to international workshops on multiscale modeling. His software tools and algorithmic innovations address challenges in parallel computing and large-scale simulations.

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Paul CarterView profile

Teaching Professor

University of British ColumbiaCanada

Paul Carter is a Teaching Professor in the Computer Science department at the University of British Columbia (UBC), Faculty of Science. He has been a faculty member at UBC since 2001, previously teaching at Capilano University. His academic background includes a PhD and MSc from UBC (1993 and 1988) and a BSc in Applied Mathematics from Sheffield University (1985). Research & Teaching: Dr. Carter focuses on innovative pedagogy including flipped classrooms and active learning. He developed multimedia pre-instruction tools and Docker-based grading systems for CS courses. His earlier research involved multigrid methods in computer vision. Awards: Multiple teaching awards including the prestigious Killam Teaching Prize and repeated recognition from UBC's CS Department. Courses Taught: Extensive teaching in CPSC 210 (Software Construction) and CPSC 110/APSC 160 (Introduction to Computation) across multiple terms since 2001. Courses emphasize practical coding skills and computational literacy. Professional Engagement: Collaborated on auto-grading systems with Reid Holmes and Andrew Stec. Maintains a lab focused on educational technology and computational methods.

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Conor McCoidView profile

Research Fellow

McMaster UniversityCanada

Conor McCoid is a Research Fellow in Mathematics at McMaster University, specializing in numerical analysis, scientific computing, and computational geometry. His research focuses on domain decomposition methods, spectral collocation techniques, and algorithm development for computational problems such as phase field models and geometric intersections. He holds a PhD from the University of Geneva, where he worked on domain decomposition under Martin Gander, and a Master's from Simon Fraser University in spectral collocation methods with Manfred Trummer. His postdoctoral work at McMaster involves accelerating phase field models for fractures and optimizing Schwarz methods. McCoid's research interests include developing robust algorithms for geometric intersections (e.g., triangles and tetrahedra), improving spectral collocation methods for boundary value problems, and prototyping machine learning algorithms for music analysis (e.g., Mozart classification). His GitHub repository includes code for tetrahedral intersections, adaptive Schwarz methods, and music data processing using tools like music21 and scikit-learn. His publications explore numerical methods for multigrid cycles, nonlinear solvers, and geometric algorithms, often emphasizing robustness and efficiency in computational contexts. Collaborations include work with Blaise Bourdin (McMaster), Felix Kwok (Université Laval), and Martin Gander (Geneva).

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John C. BowmanView profile

Professor

University of AlbertaCanada

John C. Bowman is a Professor in the Department of Mathematical and Statistical Sciences at the University of Alberta. He has maintained an active teaching career with courses spanning undergraduate to graduate levels, including Honours Calculus (Math 117/118), Real Variables (Math 417), Coding Theory (Math 422), Linear Algebra II (Math 225), and Statistical Theories of Turbulence (Math 655). His office is located in CAB 521, and he has consistently provided regular office hours for student consultation across multiple courses. Dr. Bowman earned his BS in Engineering from the University of Alberta, followed by an MA and PhD from Princeton University. His educational background has informed his diverse research trajectory spanning mathematical physics, computational mathematics, and scientific visualization. His teaching philosophy emphasizes deep conceptual understanding, as evidenced by his development of comprehensive hyperlinked 3D lecture notes for Honours Calculus. His primary research focuses on statistical theories of turbulence, particularly his development of Spectral Reduction as a reduced statistical description of turbulence. His work shows remarkable agreement with full numerical simulations, even in flows containing long-lived coherent structures. Additional research interests include 3D vector graphics (notably the Asymptote language he developed), implicit dealiasing of convolutions, exponential integrators, and exactly conservative integrators for numerical simulations. He has been involved with the University of Alberta's Geophysical Fluid Dynamics Research Group, where his work bridges theoretical mathematics with practical computational applications. Dr. Bowman's publication record demonstrates consistent contributions to computational mathematics and fluid dynamics over several decades. His recent work (2015-2024) shows continued innovation in computational methods for turbulence simulation, with particular attention to dealiasing techniques, efficient convolution algorithms, and novel approaches to spectral methods. His research has practical applications in assessing dissipation mechanisms in large-eddy simulations and modeling high-Reynolds number turbulence. As an educator, Dr. Bowman has developed comprehensive teaching materials and maintains an active engagement with students through office hours and detailed course websites. His commitment to mathematical education extends to high school outreach through contributions to the "Pi in the Sky" mathematics magazine. His work on the Asymptote vector graphics language has created a valuable tool for mathematical visualization and scientific publishing that integrates seamlessly with TeX.

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Christopher BattyView profile

Associate Professor

University of WaterlooCanada

Christopher Batty is an Associate Professor and Director of Infrastructure at the University of Waterloo's Department of Computer Science. His research focuses on computer graphics and scientific computing, with an emphasis on physics-based numerical simulation of fluids and solids for applications in animation, visual effects, and interactive environments. He holds a Ph.D. from the University of British Columbia (2010) and a B.C.Sc. from the University of Manitoba (2004). His work spans fluid dynamics, solid mechanics, and geometry processing, addressing challenges like surface reconstruction, multi-scale simulations, and efficient solvers for complex fluid-solid interactions. Recent contributions include novel methods for divergence-free fluid editing, discrete elastic rod optimization, and Monte Carlo-based approaches for PDEs on surfaces. Batty’s research integrates computational geometry, numerical analysis, and optimization to create scalable and accurate tools for procedural fluid and solid simulation. His articles emphasize robustness in handling thin obstacles, narrow gaps, and intricate boundary conditions, often leveraging advanced techniques like closest point methods and monolithic solvers. No scientific awards are listed, though his extensive publication record reflects significant contributions to the field. He leads projects on adaptive liquid simulations, surface-only deformable models, and high-resolution embedded fluid surfaces.

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Justin W.L. WanView profile

Professor

University of WaterlooCanada

Justin W.L. Wan is a Professor at the David R. Cheriton School of Computer Science, University of Waterloo. He holds a Canada Research Chair in Scientific Computing and is currently Co-Director for the Computing and Financial Management Program. He earned his BSc from Hong Kong (1992), MA (1995) and PhD (1998) from UCLA's Applied Math Program. Research interests include: Scientific computing Medical image processing (CT scans, cell segmentation, image registration) Computational finance (option pricing, regime switching, hedging parameters) Computer graphics simulation of natural phenomena Development of robust multigrid methods for PDEs Recent publications span: 2021: Multigrid methods for mean-field games and optimal mass transport 2020: Deep learning approaches for high-dimensional finance and CT artifact reduction 2019: Multigrid for Monge-Ampere equations and multi-asset options 2018: Cellular image segmentation algorithms Research team includes: PhD students: Hossein Aboutalebi, Andrew Na, Connor Tannahill, Chris West Master's students: Ying Kit (Marco) Hui, Shujie Liu, Lufan Wang Administrative roles held: Director, Centre of Computational Mathematics for Industry and Commerce (2010-2015) Associate Director, Cheriton School of Computer Science (2015-2018) Director of Graduate Studies (2019-2021) Professional service: Secretary, Canadian Applied and Industrial Mathematics Society (2015-2020) Organizer, CAIMS Annual Meeting (2021) Journal editor and program committee member

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