Research Groups
Applied Mathematics and Computational Science (AMCS)
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The Advanced Algorithms and Numerical Simulations Lab (AANSLab) focuses on developing stable and efficient high-order numerical methods for solving hyperbolic and mixed hyperbolic-parabolic PDEs, addressing multi-scale industrial flow problems, and leveraging advanced computing architectures to handle complex simulations.
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The Applied Partial Differential Equations Group focuses on mathematical modeling, analysis and the development of numerical methods for evolutionary partial differential equations in fluid and solid mechanics.
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The TREES research group, led by Prof. Mikhail Moshkov, focuses on extensions of dynamic programming, machine learning and data mining, discrete optimization, and applied healthcare analytics.
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Led by Prof. Miguel Urbano, the FBIP research group specializes in free boundary problems, focusing on applications like ocean-atmosphere interactions, porous media flows, fire propagation, and financial option pricing. The group studies weak solutions and the regularity and geometry of associated interfaces.
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Led by Prof. David Keyes, HiCMA at KAUST focuses on optimal-complexity algorithms for high-intensity computations. Their software toolkit supports optimization applications like matrix-free methods and is integrated into major vendor libraries.
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The MMDE group focuses on the modeling and analysis of PDEs that describe phenomena in biological growth, mechanical engineering, and fluid dynamics. Key areas of research include well-posedness, existence and nonexistence of solutions, and qualitative properties. The group employs methods from PDE theory, calculus of variations, operator semigroup theory, and geometric measure theory.
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Professor Gomes's Mean-field Games and Nonlinear PDE Research Group focuses on partial differential equations, including viscosity solutions and mean-field models, with applications in population modeling, price formation, and computer vision.
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Led by Prof. David I. Ketcheson, the Numerical Mathematics research group focuses on designing, analyzing, and implementing numerical methods for ordinary and partial differential equations, with applications in nonlinear wave propagation.
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Led by Prof. Daniele Boffi, the Numerical Methods for PDEs research group focuses on numerical approaches grounded in rigorous mathematical analysis of approximation schemes, including well-posedness, stability, and convergence, alongside numerical validation of theoretical results.
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Led by Omar Knio, the O-Knio research group develops advanced methods and algorithms for simulating complex multiscale systems, focusing on applications such as renewable energy systems, uncertainty quantification, Bayesian inference, computational fluid mechanics, turbulent flows, and optimization under uncertainty. The group's work spans diverse areas, including combustion, oceanic and atmospheric dynamics, microfluidic devices, and data-enabled predictive science.
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Led by Prof. Peter Markowich, the P-Markowich research group focuses on the mathematical and numerical analysis of partial differential equations (PDEs) and their applications in physics, biology, and engineering.
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Professor Krause's research group focuses on numerical simulation, machine learning, and optimization, designing efficient algorithms for large-scale problems on supercomputers like KAUST’s Shaheen III, with applications in medicine and geology.
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Professor Jinchao Xu's research group focuses on developing and analyzing fast methods for finite element discretization, large-scale equation solutions, and deep learning, with applications in scientific computing and big data.
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Led by Prof. Raul F. Tempone, the Stochastic Numerics (Stochnum) research group focuses on developing efficient and robust numerical methods for solving problems involving stochastic models and differential equations in engineering and the sciences through numerical analysis.
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Led by Prof. Ying Wu, the Waves in Complex Media (WCM) research group focuses on multidisciplinary areas related to waves, spanning mathematics, material sciences, theory, simulation, modeling, and algorithms.