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Research Spending & Results

Award Detail

Awardee:MISSISSIPPI STATE UNIVERSITY
Doing Business As Name:Mississippi State University
PD/PI:
  • Amanda E Diegel
  • (662) 325-7153
  • adiegel@math.msstate.edu
Award Date:06/23/2021
Estimated Total Award Amount: $ 125,000
Funds Obligated to Date: $ 125,000
  • FY 2021=$125,000
Start Date:09/01/2021
End Date:08/31/2024
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Collaborative Research: Numerical Methods and Adaptive Algorithms for Sixth-Order Phase Field Models
Federal Award ID Number:2110768
DUNS ID:075461814
Parent DUNS ID:075461814
Program:COMPUTATIONAL MATHEMATICS
Program Officer:
  • Malgorzata Peszynska
  • (703) 292-2811
  • mpeszyns@nsf.gov

Awardee Location

Street:PO Box 6156
City:MISSISSIPPI STATE
State:MS
ZIP:39762-9662
County:Mississippi State
Country:US
Awardee Cong. District:03

Primary Place of Performance

Organization Name:Mississippi State University
Street:175 President Circle
City:Mississippi State
State:MS
ZIP:39762-9715
County:Mississippi State
Country:US
Cong. District:03

Abstract at Time of Award

This project will use computational mathematics models to further the understanding of two applications, microemulsions systems and crystal formation models. The first class of applications has relevance for oil-water-surfactant systems, which are important in oil recovery, development of environmentally friendly solvents, consumer and commercial cleaning product formulations, and drug delivery systems. The crystal models to be studied will be useful in detecting topological defects within crystalline materials, a task which is of great interest in the material science community. Specific examples include supercooled liquids, crack propagation in a ductile material, and applications relating to photonics and semiconductors, cell structure substrates and MRI contrast agents. A major challenge impeding their use by the general mathematical and scientific community has been a lack of understanding of these complex systems. This project will build efficient algorithms for simulation that will support the study of these processes and the design of advanced materials. The project will provide opportunities to undergraduate and graduate students and introduce them to the theory and implementation of state-of-the-art numerical methods. In this project the PIs will develop C0 interior penalty finite element methods for the two classes of applications and mathematical models. The C0 interior penalty finite element method was originally constructed to handle fourth-order elliptic problems arising in mechanics, but its adaptations have been applied to other fourth- and sixth-order partial differential equations. The focus of this project is on numerical methods for time-dependent sixth-order partial differential equations. The high derivative order in combination with a time-dependent component presents many challenges to the creation of stable, convergent, and efficient numerical methods approximating solutions to these models. The work to be accomplished includes the establishment of formal proofs for the unique solvability, stability, and convergence of the proposed numerical methods. The largest challenge will be to develop a framework which establishes optimal order error estimates. Finally, in order to improve upon the efficiency of the proposed numerical methods, the PIs plan to develop efficient solvers for space-time discretized systems using operator-splitting techniques and space-time adaptivity based on a posteriori error estimates obtained by the goal-oriented dual weighted approach. This project is jointly funded by Computational Mathematics program, and by the Established Program to Stimulate Competitive Research (EPSCoR). This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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