Collaborative Research: Multiscale Simulations and Imaging of Viscoelastic Media in Reduced Order Model Framework

协作研究：降阶模型框架中粘弹性介质的多尺度模拟和成像

基本信息

批准号：
2110773
负责人：
Vladimir Druskin
金额：
$ 15.96万
依托单位：
Worcester Polytechnic Institute
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-08-15 至 2024-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2110773&HistoricalAwards=false
关键词：
Collaborative Research Multiscale Simulations Imaging

项目摘要

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.

粘弹性材料特性的成像和非侵入性评估在医学诊断，地球物理探索和工程应用中至关重要。材料的粘弹性性能是耗散过程的结果，这些过程可能源于原子晶格中的非线性波能量耗散，薄膜和多晶材料中的晶界位错，或损坏，破坏和在聚合物和生物材料中的微观材料上修复。在生物医学应用中，软组织的粘弹性变化通常是与特定恶性肿瘤相关的重要生物标志物，并且具有对动脉粥样硬化，骨质疏松症和各种癌症的检测，表征和监测的诊断价值。大规模系统降低的订单建模的最新进展使我们能够解决十年前认为无法解决的许多实际问题。但是，粘弹性建模和成像仍然是具有挑战性的问题。粘弹性培养基中的波传播的特征是衰减和分散效应，在弹性材料的情况下不存在。该项目将开发一种有效的计算方法，用于成像粘弹性介质，并模拟耗散材料中传播的波浪的衰减波。该项目开发了stieltjes-krein连续分数的延伸，将订购式建模方法降低到耗散粘弹性系统。这种非常有效的方法基于非解剖问题的Stieltjes网络实现，目前不能应用于耗散和分散问题。该项目将消除此限制，并将方法扩展到耗散粘弹性系统。该方法的三个主要组成部分是：（1）通过概括矩阵持续分数方法，超越了stieltjes-krein理论，对粘弹性问题的有效耗散稀疏网络实现；（2）基于Neumann到Dirichlet地图的耗散稀疏网络近似值的多尺度仿真框架；（3）扩展网络嵌入方法以耗散性问题和粘弹性介质的直接非线性成像算法。该方法将导致大规模波传播模拟的计算成本以及基于网络嵌入的散射问题的新型直接成像算法的计算成本降低。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识级别的功能和广泛影响来评估的支持，并被认为是值得通过评估的支持。