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Project Information

STRUCTURE-PRESERVING NUMERICAL METHODS FOR STRONGLY NONLINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS

Agency:
NSF

National Science Foundation

Project Number:
1818861
Contact PI / Project Leader:
ZHANG, WUJUN
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
The goal of this research project is to develop accurate and efficient numerical methods to solve strongly nonlinear elliptic partial differential equations (PDEs). Nonlinear problems are ubiquitous in science and engineering and arise naturally from materials science, nonlinear elasticity, fluid dynamics and image processing. This proposal studies the analysis and design of efficient numerical algorithms which preserve essential properties of nonlinear PDEs. The project will provide efficient numerical algorithms for researchers in liquid crystal materials and shape design. In addition to the design of efficient algorithms, the project will also analyze the stability and rates of convergence of the methods. Compared with the vast literature on linear problems, the work on numerical analysis for strongly nonlinear elliptic problems are relatively few. The success of the project will provide insight in future development of numerical methods in studying nonlinear phenomena. The project splits into three different parts, namely, numerical approximation of the Landau-De Gennes model of nematic liquid crystals, numerical approximation of the Monge Ampere PDEs, numerical optimal transportation problem. The specific goal of the project includes (i) construction of novel numerical methods based on piecewise linear or nodewise functions to preserve discrete maximum principle, an essential property of these problems, (ii) combination of robust lower order method with accurate higher order methods and development of a posteriori error estimation and adaptivity to improve the accuracy and efficiency of the methods, (iii) analysis of these methods based on discrete version of nonlinear PDE tools, such as Gamma convergence and discrete Alexandroff maximum principle, (iv) applying these methods in simulating liquid crystal materials and antenna design.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.
Project Terms:
Algorithms; Award; base; design; Development; Differential Equation; Elasticity; Engineering; Evaluation; Foundations; Future; Goals; image processing; improved; insight; liquid crystal; Liquid substance; Literature; materials science; method development; Methods; Mission; Modeling; Names; novel; Property; Research Personnel; Research Project Grants; Science; Shapes; success; tool; Transportation; Work

Details

Contact PI / Project Leader Information:
Name:  ZHANG, WUJUN
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  PISCATAWAY    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2018
Award Notice Date: 26-Jul-2018
DUNS Number: 001912864
Project Start Date: 01-Aug-2018
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-Jul-2021
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2018:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2018 NSF

National Science Foundation

$55,947

Results

i

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