This $399,998 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences, under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program, aims to develop new nonlinear solution methods for solving systems of partial differential equations (PDEs). The proposed research seeks to create "lifted Newton nonlinear preconditioning" techniques that can improve the convergence of iterative solvers for severely nonlinear PDE problems, which...
This $172,450 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences will support the development of novel time integration methods for stiff and highly oscillatory systems. The award will enable researchers at Texas Tech University to derive and implement mixed exponential integrators, preconditioned rational exponential integrators, stiffly-accurate embedded multirate exponential methods, and stiffly-accurate exponential Nyström methods. These...
This National Science Foundation project grant of $361,251 will support research at Louisiana State University from July 1, 2022 to June 30, 2025 under the Mathematical and Physical Sciences program (CFDA 47.049). The university will investigate novel numerical schemes for least squares problems involving elliptic partial differential equations that model steady state problems in science and engineering. This includes developing finite element methods for least squares problems in data fitting...
This $138,732 National Science Foundation Division of Mathematical Sciences Project Grant supports research into instability, chaos, and mixing in stochastic fluid mechanics and related models at Tulane University from August 1, 2022 to July 31, 2025. The research aims to develop mathematical tools to rigorously prove exponential sensitivity to initial conditions for various fluid mechanics models in the presence of small noise, gaining new insights into the unstable nature of fluid motion and...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
This National Science Foundation (NSF) Project Grant award, under the Mathematical and Physical Sciences (CFDA 47.049) program, will support research on stochastic methods and isoperimetric inequalities at Texas A&M University. The $238,406 award, active from July 2024 to June 2027, will develop techniques to bridge fundamental conjectures in Brunn-Minkowski theory and dual Brunn-Minkowski theory, with a focus on intersection bodies and higher-dimensional generalizations. The research aims...
This $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
This three-year National Science Foundation Project Grant of $197,999 supports research and education activities at Worcester Polytechnic Institute under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund the development of novel mathematical methods to analyze partial differential equations describing singularities in continuum mechanics and materials science systems. The principal investigator will extend differential inclusion theory on rigidity and flexibility,...
This $219,782 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences aims to develop innovative and robust numerical methods for simulating high-frequency electric charge transport phenomena. The research program under this 3-year award from September 2024 to August 2027 will advance space and time discretization techniques for hydrodynamic models of electric charge transport, such as the Euler-Maxwell and Euler-Poisson systems. The resulting numerical...
This $397,375 Project Grant award from the National Science Foundation's Engineering program (CFDA 47.041) supports the development of new computational methods and algorithms to enable the analysis and control of nonlinear partial differential equations (PDEs). The project, a collaborative effort between U.S. and U.K. researchers, aims to construct a parameterization of polynomials on distributed Hilbert spaces to reformulate nonlinear PDEs in a way that allows for efficient computational...