Award Abstract # 2110773
Collaborative Research: Multiscale Simulations and Imaging of Viscoelastic Media in Reduced Order Model Framework

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: WORCESTER POLYTECHNIC INSTITUTE
Initial Amendment Date: August 10, 2021
Latest Amendment Date: August 10, 2021
Award Number: 2110773
Award Instrument: Standard Grant
Program Manager: Yuliya Gorb
ygorb@nsf.gov
 (703)292-2113
DMS
 Division Of Mathematical Sciences
MPS
 Direct For Mathematical & Physical Scien
Start Date: August 15, 2021
End Date: July 31, 2024 (Estimated)
Total Intended Award Amount: $159,552.00
Total Awarded Amount to Date: $159,552.00
Funds Obligated to Date: FY 2021 = $159,552.00
History of Investigator:
  • Vladimir Druskin (Principal Investigator)
    vdruskin@wpi.edu
Recipient Sponsored Research Office: Worcester Polytechnic Institute
100 INSTITUTE RD
WORCESTER
MA  US  01609-2247
(508)831-5000
Sponsor Congressional District: 02
Primary Place of Performance: Worcester Polytechnic Institute
100 Institute Rd
Worcester
MA  US  01609-2380
Primary Place of Performance
Congressional District:
02
Unique Entity Identifier (UEI): HJNQME41NBU4
Parent UEI:
NSF Program(s): COMPUTATIONAL MATHEMATICS
Primary Program Source: 01002122DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 9263
Program Element Code(s): 1271
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

Imaging and noninvasive evaluation of viscoelastic material properties have paramount importance in medical diagnostics, geophysical exploration, and engineering applications. Viscoelastic properties of materials are a result of dissipative processes that could stem from nonlinear wave energy dissipation in atomic lattices, from grain boundaries dislocations in thin films and polycrystalline materials, or from damage, fracturing, and repairing at the microscale in polymers and biological materials. In biomedical applications, changes in viscoelasticity of soft tissues often serve as an important biomarker associated with specific malignancies and have a diagnostic value for the detection, characterization, and monitoring of arteriosclerosis, osteoporosis, and various cancers. Recent advances in reduced order modeling of large scale systems have enabled us to approach many practical problems viewed as unsolvable ten years ago. However, viscoelastic modeling and imaging are still challenging problems. Wave propagation in viscoelastic media is characterized by attenuation and dispersion effects, which are absent in the case of elastic materials. This project will develop an efficient computational method for imaging of viscoelastic media and simulation of attenuating waves propagating in dissipative materials.

The project develops an extension of the Stieltjes-Krein continuous fraction reduced order modeling method to dissipative viscoelastic systems. This very efficient method is based on the Stieltjes network realizations of nondissipative problems and currently cannot be applied to problems with dissipation and dispersion. The project will eliminate this limitation and extend the method to dissipative viscoelastic systems. Three main components of the approach are the following: (1) Efficient dissipative sparse network realizations of ROMs for viscoelastic problems by generalizing the matrix continued-fraction approach beyond Stieltjes-Krein theory; (2) Multiscale simulation framework based on dissipative sparse network approximations of Neumann-to-Dirichlet maps; (3) Extension of the network embedding approach to dissipative problems and direct nonlinear imaging algorithms for viscoelastic media. The method will lead to an orders-of-magnitude reduction in the computational cost of large-scale wave propagation simulations as well as novel direct imaging algorithms for scattering problems based on network embedding.

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.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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Druskin, V and Moskow, S and Zaslavsky, M "On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays" Inverse Problems , v.38 , 2022 https://doi.org/10.1088/1361-6420/ac7a59 Citation Details
Druskin, Zaslavsky "Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems" 2022 Spring Central Sectional Meeting , 2022 https://doi.org/10.1088/1361-6420/abfca4 Citation Details
Vladimir Druskin "Finite-difference quadrature and inverse scattering" Numerical Methods for large scale problems , 2022 Citation Details
Druskin, Vladimir and Güttel, Stefan and Knizhnerman, Leonid "Model order reduction of layered waveguides via rational Krylov fitting" BIT Numerical Mathematics , 2022 https://doi.org/10.1007/s10543-022-00922-2 Citation Details
Druskin, Guddati "Embedding properties of network realizations of dissipative reduced order models" HOUSEHOLDER SYMPOSIUM XXI , 2022 Citation Details

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