| NSF Org: |
CCF Division of Computing and Communication Foundations |
| Recipient: |
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| Initial Amendment Date: | August 1, 2017 |
| Latest Amendment Date: | August 1, 2017 |
| Award Number: | 1714844 |
| Award Instrument: | Standard Grant |
| Program Manager: |
A. Funda Ergun
CCF Division of Computing and Communication Foundations CSE Directorate for Computer and Information Science and Engineering |
| Start Date: | August 1, 2017 |
| End Date: | June 30, 2022 (Estimated) |
| Total Intended Award Amount: | $88,619.00 |
| Total Awarded Amount to Date: | $88,619.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
201 PRESIDENTS CIR SALT LAKE CITY UT US 84112-9049 (801)581-6903 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Salt Lake City UT US 84112-0090 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | Algorithmic Foundations |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.070 |
ABSTRACT
Modeling material processes, like interaction of a drug molecule docking with a receptor site, must capture interactions, often by systems of partial differential equations (PDEs), both in the bulk and on the surface. These PDEs must be calculated numerically, since they often have non-linear couplings between bulk and surface whose geometries often evolve in time. This project develops and implements scalable, high-order, meshfree algorithms -- based on radial basis functions (RBFs) -- for complex multi-scale bulk-surface biomechanical modeling in three-dimensional evolving geometries. The algorithms and software developed under this grant will directly enable researchers to explore scientific questions in lipid membrane morphology and physiology of platelets in the clotting process. The algorithms will have broad applicability to other coupled bulk-surface processes -- in biology, material science, and many industrial problems. The grant will help bolster the research portfolio of the new Computational Science and Engineering (CSE) PhD program at Boise State University, and will support one of the first graduate students in this program. The PIs will continue to build upon their successful track record of recruiting graduate students in computational mathematics from underrepresented groups as part of this project by working with the LSAMP program at Boise State University.
A specific focus of this proposal is on developing RBF algorithms for two biomechanical and physiological problems that are at the forefront of what current numerical techniques can handle and that have features common to general bulk-surface problems: morphology of the lipid bilayer and platelet aggregation and coagulation. These problems will drive the development of the following advances in numerical discretizations and algorithms for RBFs: 1) Scale-free kernels for high-order solutions of surface PDEs; 2) Stable, scalable meshfree schemes for advection in geometrically complex domains without any tuning parameters; 3) High-order meshfree geometric modeling techniques with optimal computational complexity; 4) SIMD-friendly algorithms for automatic scattered node generation with variable spatial; 5) Algorithms for low-cost automatic stencil selection for upwinding and adaptive node refinement; 6) Preconditioning strategies for implicit discretizations of bulk-surface; 7) Consistent, accuracy preserving meshfree techniques for visualizing solutions from RBF-based high-order methods. The developments will be made publicly available through an open-source software package.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Bulk-surface processes arise in many areas of the physical and engineering sciences. Perhaps the most prevalent area is biology and medicine, where these processes are fundamental in biomechanical and physiological systems from the molecular to the macroscopic scale; for example, in drug molecule docking, cell polarization, cell-motility, tumor growth, wound healing, and organ development. Realistic mathematical models of bulk-surface biomechanical and physiological problems give rise to systems of partial differential equations (PDEs) posed both in the bulk and on the surface, with possible non-linear couplings between the two. Solving these complex models using pen-and-paper methods is not an option, so one must use approximation (or simulation) techniques based on numerical methods. However, there are several features in these models that pose significant challenges to existing numerical methods, including geometrically complicated shapes that evolve in time and processes which evolve over curved surfaces.
To address these shortcomings, a collaborative, interdisciplinary effort was undertaken consisting of an applied mathematician, a computer scientist, and graduate students to develop and implement new numerical algorithms for bulk-surface PDE models. These algorithms are based on localized meshfree radial basis function (RBF) methods, which provide several benefits, such as scalability to many-core computer systems, fast adaptability to evolving geometries, and highly accurate approximations. The PIs and students made several advances with these methods that culminated in 10 journal publications, 2 PhD theses, and 1 MS thesis. Additionally, four open-source software packages were released with implementations of the algorithms developed:
KernelPack: General (parallelized) library for approximating PDE models over complex geometries with meshfree RBF methods
KernelNode: Package for discretizing complex geometries with point clouds
MGM: Algorithm for solving large linear systems associated with meshfree approximations of elliptic PDE models posed on curved surfaces
CFPU: Package for surface reconstruction from organized point clouds
These algorithms have broad applicability to coupled bulk-surface processes in biology, material science, and many industrial problems and provide researchers working in these fields with new tools for simulating mathematical models for these processes.
Over the course of the project, one MS and two PhD students were mentored and provided training in computational mathematics, scientific computing, and software development. All three students participated in conferences & workshops and gave oral & poster presentations on their work. The two PhD students are from underrepresented groups in STEM and received further mentoring through the Broader Engagement Initiative of the Sustainable Horizons Institute (SHI). In addition to the publications and mentoring activities, the PIs broadly disseminated the findings from the grant, giving 12 invited talks, four posters at conferences/workshops/seminars, and five minisymposia co-organized at international conferences.
This collaborative project between applied mathematics and computer science was influential in strengtheing the newly created (Fall 2016) interdisciplinary PhD program in Computing at Boise State University. The first and third students to graduate (2020 & 2022, respectively) from the Computational Mathematics, Science, and Engineering (CMSE) emphasis of the computing PhD program were supported under this grant. Furthermore, these students are from underrepresented groups. Both students are pursuing careers in STEM fields - one is working as a senior scientist in the tech industry while the other is working at a national lab.
Last Modified: 12/06/2022
Modified by: Grady B Wright
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