Qiang Du - US grants

There has been an increasing trend to conduct scientific research using numerical simulations on modern high performance computers in recent years. Considerable progress has been made in the area of computational material sciences. Computational tools have been used in the design of new materials as well as in the study of their properties. The central objectives of this project are: 1) to develop or refine certain mesoscale and macroscale models, so to enlarge the range of physical problems for which such models are valid; 2) to analyze these models in order to gain further understanding of their properties and solutions; 3) to develop, analyze, and implement algorithms, in particular, parallel and adaptive algorithms, for the numerical simulation of these models; and 4) to use our algorithms and codes to study some interesting phenomena in material sciences.

In the proposed work, the principal investigator will study models and develop numerical algorithms for some interesting material sciences problems that involve multiscale (mesoscale and macroscale) and stochastic effects, such as problems related to vortices and other defects in superconductivity and magnetism. A major part of the project is aimed at increasing the range of applications for the mesoscale codes and allow more comparative studies between the mesoscale and macroscopic models through the use of domain and scale decomposition/integration and adaptive computation techniques. The codes for mesoscale models can be of use in gaining information and insight about the physical behavior and interaction of the fine structures (such as vortices) with, for example, boundaries, interfaces, impurities, currents, and thermal fluctuations. They can be of indirect use to device designers, in particular, when connections with macroscopic properties can be identified. Models based on the stochastic partial differential equations and their numerical simulations will also be given emphasis, so as to gain insight to the macroscopic effect of thermal fluctuations and impurities in the materials like superconductors and liquid crystals. The work will be aimed at making the computational codes robust, efficient, flexible, accurate, scalable and user-friendly. It is hoped that these codes can be used by physicists, material scientists, and engineers in laboratories, universities, and industrial organizations as a tool for studying some specific material properties and also a tool in designing devices.

This award is made under the Information Technology Research initiative and is funded jointly by the Division of Materials Research and the Advanced Computational Infrastructure Research Division.

This collaborative research project involves two materials scientists, a computer
scientist, a mathematician, and two physicists from academia, industry and a national laboratory. The project is a synergistic effort that leverages the overlapping and complimentary expertise of the researchers in the areas of scalable parallel scientific computing, first-principles and atomistic calculations, computational thermodynamics, mesoscale microstructure evolution, and macroscopic mechanical property modeling. The main objective of the proposal is to develop a set of integrated computational tools to predict the relationships among the chemical, microstructural, and mechanical properties of multicomponent materials using technologically important aluminum-based alloys as model materials. A prototype GRID-enabled software will be developed for multicomponent materials design with efficient information exchange between design stages. Each design stage will incorporate effective algorithms and parallel computing schemes. Four computational components will be integrated, these are: (1) first-principles calculations to determine thermodynamic properties, lattice parameters, and kinetic data of unary, binary and ternary compounds; (2) CALPHAD data optimization computation to extract thermodynamic properties, lattice parameters, and kinetic data of multicomponent systems combining results from first-principles calculations and experimental data; (3) multicomponent phase-field modeling to produce microstructure; and (4) finite element analysis to obtain the mechanical response from the simulated microstructure. The research involves a parallel effort in information technology with two main components: (1) advanced discretization and parallel algorithms, and (2) a software architecture for distributed computing system. The first component includes: (a) a coupling of spectral and finite element approximations, (b) local adaptivity and multi-scale resolution, (c) high order stable semi-implicit in time schemes, (d) parallelization through domain decomposition, and (e) scalable sparse system solvers. The second component involves computational GRID-enabled software for the overall design process; this software architecture enables the use of geographically distributed high performance parallel computing resources to reduce application turnaround time while providing a flexible client-server interface that allows multiple design cycles to proceed.

The research project will be integrated with education and training of graduate students in the broad area of computational science and engineering through the participation of students and the PIs in the "High Performance Computing Graduate Minor" offered through the Institute of High Performance Computing at The Pennsylvania State University. Existing programs at Penn State will be used to integrate undergraduates into the project.
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This award is made under the Information Technology Research initiative and is funded jointly by the Division of Materials Research and the Advanced Computational Infrastructure Research Division.

This collaborative research project involves two materials scientists, a computer
scientist, a mathematician, and two physicists from academia, industry and a national laboratory. The project is a synergistic effort that leverages the overlapping and complimentary expertise of the researchers in the areas of scalable parallel scientific computing, first-principles and atomistic calculations, computational thermodynamics, mesoscale microstructure evolution, and macroscopic mechanical property modeling. The main objective of the proposal is to develop a set of integrated computational tools to predict the relationships among the chemical, microstructural and mechanical properties of multicomponent materials using technologically important aluminum-based alloys as model materials. Prototype GRID-enabled software will be developed for multicomponent materials design. Effective algorithms and parallel computing schemes will be incorporated into the design. The GRID-enabled software allows geographically distributed high performance parallel computing resources to be harnessed bringing greater computational power to bear on a given problem and enabling practical application of these computational tools. The prototype software, with improved predictive power in multicomponent materials design, may enable scientists to develop new materials with unique properties and to tailor existing materials for better performance.

The research project will be integrated with education and training of graduate students in the broad area of computational science and engineering through the participation of students and the PIs in the "High Performance Computing Graduate Minor" offered through the Institute of High Performance Computing at The Pennsylvania State University. Existing programs at Penn State will be used to integrate undergraduates into the project.
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Abstract

Molecular Dynamics simulations are powerful
tools to study problems of materials science,
nanoscience, and biology. It naturally provides
ample opportunities for interdisciplinary research
that requires knowledge in mathematics, statistics,
computer science, physics, materials and biology.
The focus of this project is on developing learning-based
computational and statistical methods for potential
energy landscape modeling to accelerate ab-initio
molecular dynamics simulations. The set of tools
developed will substantially expand the limits of time
and system size without compromising the precision and
quality of the ab-initio simulation results.

Hongyuan Zha, Qiang Du, Runze Li and Jorge Sofo will
investigate learning and
computational methods 1) to characterize both the local and global
structures of the low-dimensional manifold in which the simulation
really occurs through manifold learning from the trajectories of the
ab-initio simulation; 2) to identify and extract suitable clusters in
the reduced dimension spaces corresponding to regions in the
configuration space that naturally emerge from the ab-initio
simulation and are visited frequently by the particles throughout the
simulation; 3) to conduct efficient energy and force interpolation
using Gaussian Kriging models with penalized likelihood. In this
learning and computational
framework, the interpolated potential energy surface will be
evaluated and it will replace the costly ab-initio evaluation when its
precision is good enough. As the simulation evolves, the interpolated
potential energy surface will be retested to detect the
eventual need of a retraining in case the simulation is exploring
new regions of the configuration space.

This project is concerned with the study of interfaces and defects which are ubiquitous in physical and biological systems and are essential to the materials properties and biological functions. Building on the previous research work, the PI will develop and apply analytical and numerical simulation tools to study both deterministic and stochastic effects associated with various material interfaces and defects with particular emphasis on defects in superconductors and Bose-Einstein condensates as characterized by quantized vortices, and soft interfaces as characterized by model biomimetic cell membranes. The investigation will be largely following the general Ginzburg-Landau (diffuse interface, phase field) formalism with connections to other multiscale and stochastic modeling approaches. Systematic model derivations, analysis and simplifications will be conducted. Adaptive algorithms and statistics retrieval algorithms will be designed and analyzed. These research activities will enhance the simulation capability of complex systems and the predictive power of large scale numerical computation. While focusing on specific applications, the central algorithmic development work in this project will be in tune with the modern theme of integrated, adaptive and intelligent scientific computation.

This project lies at the interface of computational mathematics, physics, materials and biological sciences. The physical and biological objects to be studied through mathematical analysis and numerical simulations include quantized vortices which are well-known signatures of superfluidity, and biological membranes which are soft interfaces designed by nature as the fundamental building blocks of life. The PI will develop new analytical theory on the complex nonlinear models and new tools for extracting useful statistics and exploring hidden structures from massive simulations. The research activities will bring new advances to mathematics and provide better understanding of various basic physical and biological processes. They in turn may aid the efforts in discovering new technology based on the superconductivity and superfluidity, and new design of drug and drug delivery vehicles based on biomimetic membranes, both are of significant economic value and national priority. In addition, this project will provide valuable training environment and interdisciplinary research experience to the future generation of workforce and young researchers that showcases the TEAMS (Training in Experiments, Analysis, Modeling and Simulations) spirit.

Center for Computational Materials Design (CCMD)

IIP-1034965 Pennsylvania State University (PSU)
IIP-1034968 Georgia Tech (GT)

This is a proposal to renew the Center for Computational Materials Design (CCMD), an I/UCRC center that was created in 2005. The lead institution is Pennsylvania State University, and the research partner is Georgia Tech. The main research mission of the CCMD is to develop simulation tools and methods to support materials design decisions and novel methods for collaborative, decision-based systems robust design of materials.

The intellectual merit of CCMD is based on the integration of multiscale, interdisciplinary computational expertise at PSU and GT. CCMD provides leadership in articulating the importance of integrated design of materials and products to industry and the broad profession of materials engineering; and is developing new methods and algorithms for concurrent design of components and materials.

CCMD has operated successfully in Phase I, and has helped develop a partnership amongst academe, industry and national laboratories. Based on feedback received from the various members, CCMD has outlined in the renewal proposal research thrusts and initiatives for Phase II; and has also identified gaps that will be addressed as research opportunities in Phase II.

CCMD will have a large impact on how industry addresses material selection and development. The expanded university/industry interaction of this multi-university center offers all participants a broader view of material design activities in all sectors. CCMD contributes to US competitiveness in computational materials design by educating new generations of students who have valuable perspectives on fundamental modeling and simulation methods, as well as industry-relevant design integration and materials development. CCMD participates in programs at PSU and GT that support K-12 STEM issues, women and underrepresented groups, undergraduate students, and high school teachers. CCMD plans to disseminate research results via papers, conferences and the CCMD website.

The project is concerned with mathematical and computational issues related to the simulation and analysis of equilibria, metastable and transition states and minimum energy paths for complex energy landscapes of practical interests, and associated stochastic dynamics. The research to be carried out is closely motivated by applications in a number of areas of federal strategic interests: the development of effective algorithms and codes is a crucial part of high-performance computing, and numerical methods and software tools to be developed may be potentially useful for effective computational materials and drug design.

The principal investigator will carry out interdisciplinary research that encompassing subjects like computational mathematics, physics, information, materials and biological sciences. He will focus on new algorithmic development and analysis which have the potential to significantly improve the usual practice on the modeling and simulation of rare events. He will consider some specific and important applications, including systems of interacting particles and interfaces in geometrically confined and frustrated configurations or deformable geometry which arise in many areas of physics, chemistry and biology (such as formation of nano-clusters, bimolecular conformation, vesicle mediated interactions, and critical nucleation in solid state transformations). He will attempt to draw strong connections with some of the algorithms developed by practitioners implemented in existing software codes such as those for first principle calculation and computational chemistry. Most of the problems involved in the research project are associated with either infinite dimensional spaces such as deterministic or stochastic partial differential equations or finite dimensional spaces with high dimensions (discretization of differential equations or particle systems involving a large number of particles), which lead to many computational challenges. Various mathematical and numerical issues will be studied, ranging from efficient local saddle point search and its robust numerical implementation to rigorous analysis and effective multiscale simulations of relevant dynamics and rare events. It is expected that the progress made during the project will have a broad impact on the community interested in the study of rare events. The project will also contribute to education and training as it will provide students valuable training ground and research experience in an interdisciplinary environment. Much effort will be devoted to promoting active engagement of student participation at all levels and integrating research findings into teaching and training.

Computational fluid dynamics is an important research field that plays a crucial role in the understanding of fluid flows appearing in many mechanical, hydrodynamic and biophysical processes. It occupies a central place in the development of computational science. The proposed research intends to help designing effective numerical algorithms, particularly those related to the so-called smoothed particle hydrodynamics (SPH), for modeling complex fluids and interfacial phenomena. The overall research objective is consistent with the long term vision of predictive and reliable computational science, and in the near term, it serves to complement ongoing research on SPH related methods and their applications currently being carried out by various academic institutions and national laboratories. The PI will not only work to facilitate the research effort but also to strengthen the training and education of young students and junior researchers. He will team up with collaborators to ensure the timely translation and integration of new theoretical findings into enhanced simulation capability for a variety of applications such as those involving heterogeneous transport in underground, atmospheric and biophysical systems, energy and high-strength materials, which are highly relevant to important national and societal interests.

Particle based computational methods such as the Smoothed Particle Hydrodynamics (SPH) and related methods offer great flexibility in numerical simulations and are becoming widely used in various scientific and engineering applications. As these techniques get populated into major simulation codes to be used by a large computational science and engineering community, it is imperative to carry out a more quantitative assessment and mathematical analysis as part of the rigorous validation and verification process. Assessing SPH based simulations is challenging since these methods have been historically applied to solve complex problems where either traditional methods do not work well or the formal accuracy is of secondary concern. Studies based on conventional numerical analysis techniques may not always produce mathematical findings that are strongly relevant in practice. Our proposed research is to improve the theoretical understanding of SPH and related methods. A novelty of our approach draws on the recently developed nonlocal models and their numerical approximations by the PI's group. It leads to new avenues to analyze SPH type methods by both distinguishing and relating the different roles of integral kernel representations/approximations of the locally defined spatial derivatives and numerical discretization of the resulting nonlocal operators. Indeed, inappropriate nonlocal relaxations of differential operators on the continuum level may be the root cause of some problematic issues inherent to particle based simulations. Incompatible discretization can also contribute to the loss of fidelity and stability. By taking nonlocal integral operators and nonlocal continuum formulations as bridges connecting continuum PDE models and particle like discrete approximations, our approach represents a significant departure from conventional numerical analysis that compares the discrete schemes with the underlying continuum PDEs directly. The focus on algorithm robustness is particularly relevant to SPH like methods given their intended application to complex systems involving multiple scales and extreme operating conditions. Specific objectives for the next few years include: developing continuum reformulations of SPH like methods with nonlocal/integral operators; and studying SPH type methods using discretization of nonlocal models as a bridge. In carrying out the proposed work, we use an integrated analytical and computational approach to provide both mathematical infrastructure needed for theoretical analyses and practical insight for code development. We pay close attention to techniques that work for solutions lacking regularity or exhibiting strong variations and for particle distributions and boundary conditions that are frequently encountered in practical implementations.

The study of nonlocal models has attracted much attention in many science and engineering disciplines such as materials science, mechanics, biology, and social science, and they are therefore of interest to applied and computational mathematics. Nonlocal models differ from the more common local models because they account for the factors active on a range rather than only at a point at which they are considered. The project is aimed at advancing the mathematical and numerical analysis of robust and effective numerical methods for those nonlocal models with a finite range of interactions. The research will complement the ongoing development of effective simulation platforms for nonlocal modeling in various application domains. It will also contribute to the integrated interdisciplinary education and research training of students.

An important class of robust numerical schemes for nonlocal models is provided by asymptotically compatible (AC) discretization schemes. The latter are designed to assure the convergence of approximate solutions, as numerical resolution gets refined, to correct physical solutions for problems with changing or even diminishing ranges of nonlocal interactions. The project will include a comprehensive study of AC schemes for nonlocal problems with heterogeneously distributed ranges of nonlocal interactions and/or having boundary/interfaces. Further investigations of AC schemes will be carried out for problems involving coupled local/nonlocal models and nonlinear problems motivated by important applications. The focus on robust discretization methods like the AC schemes is particularly relevant to reliable and efficient simulations of nonlocal models with application to complex physical systems involving multiscale, singular, and anomalous behaviors. An integrated analytical and computational approach will be used to develop both fundamental ideas and practical insight so that the research findings will not only enrich the mathematical theory of AC schemes but also offer guidance to their practical applications.

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.