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Institute for Computational and Experimental Research in Mathematics (ICERM)

It is practically rare that a natural phenomenon or engineering problem can be accurately described by a single law of physics. The striking diversity of rules of life forces scientists to continuously increase the complexity of models to address the ever-growing requirements for their prediction capabilities. It remains a formidable challenge to derive and analyze numerical methods which are universal enough to handle complex multiphysics problems with the same ease and efficiency as traditional methods do for textbook PDEs. The workshop will focus on recent trends in the field of numerical methods for multiphysics problems that include the development of monolithic approaches, structure preserving discretizations, geometrically unfitted methods, data-driven techniques, and modern algebraic methods for the resulting linear and nonlinear discrete systems. The topics of interest include models and discretizations for fluid - elastic structure interaction, non-Newtonian fluids, phase field models for fluid mixtures, bulk-surface coupled problems, and biological flows. The workshop will also address emerging topics in scientific computing such as randomized algorithms, tensor methods, and structured numerical linear algebra methods, with the goal to better understand advances they offer for multiphysics problems.

Email.: info@icerm.brown.edu

Physique mathématique,    Mathématiques générales et evénement multidisciplinaires

Institute for Computational and Experimental Research in Mathematics (ICERM)

The development and analysis of numerical methods for PDEs whose formulation or interpretation is derived from an underlying geometry is a persistent challenge in numerical analysis. Examples include PDEs posed on complicated manifolds or graphs, PDEs that describe interactions across complex interfaces, and equations derived from intrinsically geometric concepts such as curvature-driven flows or highly nonlinear Monge-Ampere equations arising in optimal transport. In recent years, these PDEs have gained significance in diverse areas such as machine learning, optical design problems, meteorology, medical imaging, and beyond. Hence, the development of numerical methods for this class of PDEs is poised to lead to breakthroughs for a wide range of timely problems. However, designing methods to accurately and efficiently solve these PDEs requires careful consideration of the interactions between discretization methods, the PDE operators, and the underlying geometric properties. This workshop aims to foster new interactions and collaborations between researchers in PDEs related to geometry. The expertise of the participants will span the analysis, computational implementation, and application of these problems. This collaborative effort will facilitate the identification of key problems in the field and the development of novel discretizations that respect both the underlying geometry of the problem and the needs of current applications.

Email.: info@icerm.brown.edu

Géométrie et topologie,    Mathématiques appliquées (en général)

Institute for Computational and Experimental Research in Mathematics (ICERM)

Systems of interacting particles or agents are studied across many scientific disciplines. They are used as effective models in a wide variety of sciences and applications, to represent the dynamics of particles in physics, cells in biology, people in urban mobility studies, but also, more abstractly in the context of mathematics, as sample particles in Monte Carlo simulations or parameters of neural networks in machine learning. This workshop aims at bringing together researchers in analysis, computation, inference, control and applications, to facilitate cross-fertilization and collaborations.

Email.: info@icerm.brown.edu

Simulation,    Mathématiques appliquées (en général)

Society for Industrial and Applied Mathematics (SIAM)

Mathématiques appliquées (en général),    Calcul infinitésimal, équations différentielles et intégrales