This $399,583 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research to develop numerical algorithms that can estimate solutions to partial differential equations (PDEs) without full boundary condition information. The research aims to enable improved modeling and forecasting capabilities across various applications, including meteorology, biology, and engineering design. The primary awardee, Texas...
This Project Grant award, valued at $270,195, was provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049). The award supports collaborative research to develop highly efficient, positivity-preserving, and entropy-stable numerical schemes for variable-temperature phase field equations with singular energy potentials. The goal is to enhance the understanding of two-phase flows and phase separation in...
This $250,518 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports the development of physics-preserving adaptive finite element methods for thermo-poroelasticity modeling at the University of Texas at El Paso from July 2022 through June 2025. The award aims to gain a fundamental understanding of key mechanisms controlling dynamics in enhanced geothermal systems, such as solid displacement, fluid flow and heat transfer, through...
This $420,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports the development of new numerical algorithms for simulating complex multiscale, multiphysics systems. The primary awardee, Virginia Polytechnic Institute & State University (Virginia Tech), will construct a novel hybrid time integration framework to enable accurate and efficient co-simulation of systems governed by time-dependent partial differential...
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 Project Grant award for $249,454, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports research conducted by the University of Alabama in two areas within mathematical analysis: harmonic analysis and partial differential equations. The key objectives are to expand knowledge in harmonic analysis and its applications to the study of partial differential equations, as well as to provide education and mentoring...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) in the amount of $209,999 supports research on the theoretical understanding of partial differential equations arising from physics and how kinetic models can elaborate on the shortcomings of original scientific theories. The research project, conducted by Louisiana State University, consists of four main components: 1) establishing the well-posedness and conditional...
This $224,608 Project Grant award, made by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports collaborative research on stochastic functional systems. The research aims to (i) explore long-term properties of stochastic functional differential equations, (ii) formulate new approaches to study fundamental properties of McKean-Vlasov stochastic functional differential equations, and (iii) propose a framework for functional stochastic...
This Project Grant award, funded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports the development of efficient and scalable computational methods for solving complex kinetic equations. The key products and services to be delivered include: Developing learning-enhanced, structure-preserving particle methods for nonlinear partial differential equations, with a focus on plasma models. These methods are intended to complement...
The National Science Foundation (NSF) awarded a $299,998 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to Georgia Tech Research Corporation to conduct fundamental research on the dynamics of nonlinear partial differential equation (PDE) systems that model fluid flow and nonlinear waves. The research will focus on analyzing the local dynamics near steady states in incompressible fluid PDEs with free surfaces, as well as a class of nonlinear...