This $299,992 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) is funding research conducted by Louisiana State University (LSU) to develop novel computational techniques for controlling geometric shapes and motion. The research objectives include: Advancing the theoretical development of unfitted finite element methods to create robust numerical techniques for optimizing shape and time-dependent geometric motion. Developing new tools to optimize the swimming motions, or gaits, of microorganisms, which can help explain their behavior and inform the design of underwater robotic systems. Extending optimal control techniques to the self-assembly dynamics of geometric structures, with a focus on liquid crystals. The research aims to unite contrasting approaches to shape optimization, yield new types of level set methods for simulating changing geometry, and extend unfitted finite element methods to address time-dependent, tensor-valued partial differential equations. The grant also supports the development of open-source software packages to enable broader use of the computational methods developed under this award. No subawards are planned as part of this 3-year project, which commenced on July 1, 2025.
Mod # | Description | Reason For Modification | Federal Obligation (Click to sort descending) | Date (Click to sort ascending) |
|---|---|---|---|---|
| Not listed | $300.0k | 6/30/25 |