Eric Darve
Director, Institute for Computational and Mathematical Engineering (ICME) and Professor of Mechanical Engineering
Web page: https://me.stanford.edu/people/eric-darve
Bio
The research interests of Professor Darve span across several domains, including machine learning for science and engineering, large-language models, transformer models, surrogate and reduced order modeling, stochastic inversing, anomaly detection, numerical linear algebra, high-performance, parallel, and GPU computing.
Professor Darve received his Ph.D. in Applied Mathematics at the Jacques-Louis Lions Laboratory in the Pierre et Marie Curie University, Paris, France. His advisor was Prof. Olivier Pironneau, and his Ph.D. thesis was entitled "Fast Multipole Methods for Integral Equations in Acoustics and Electromagnetics." He was previously a student at the Ecole Normale Supérieure, rue d'Ulm, Paris, in Mathematics and Computer Science.
Prof. Darve became a postdoctoral scholar with Profs. Moin and Pohorille at Stanford and NASA Ames in 1999 and joined the faculty at Stanford University in 2001. He is a member of the Institute for Computational and Mathematical Engineering.
Prof. Darve has received many awards, including the H. Julian Allen Award, NASA (2010), the Habilitation à Diriger des Recherches, France (2007), the Leslie Fox Prize in Numerical Analysis, IMA (2001), and the James H. Clark Faculty Scholar, Stanford University (2001).
Administrative Appointments
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Director, Institute for Computational and Mathematical Engineering (ICME) (2024 - 2029)
Honors & Awards
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Kenneth and Barbara Oshman Faculty Scholar Award, Stanford University (2011)
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H. Julian Allen Award, NASA (2010)
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Habilitation à Diriger des Recherches, France (2007)
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Leslie Fox Prize in Numerical Analysis, IMA (2001)
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James H. Clark Faculty Scholar, Stanford University (2001)
Boards, Advisory Committees, Professional Organizations
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Associate Editor, SIAM Journal on Scientific Computing (SISC) (2014 - Present)
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Associate Editor, Journal of Computational Physics (JCOMP) (2013 - 2024)
Professional Education
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PhD, Paris VI University, Paris, Applied Mathematics (1999)
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MS, Paris IX University, Paris, Applied Mathematics (1994)
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BS, Paris VI University, Paris, Mathematics and Physics (1993)
Patents
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Daniel Ratner, Eric Felix Darve, Ryan Humble. "United States Patent US20230409422A1 Systems and Methods for Anomaly Detection in Multi-Modal Data Streams", Leland Stanford Junior University, Jun 20, 2023
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Ziyi Yang, Eric Felix Darve, Iman Soltani Bozchalooi. "United States Patent US20200410285A1 Anomaly Augmented Generative Adversarial Network", Ford Global Technologies LLC Leland Stanford Junior University, Jun 25, 2020
Current Research and Scholarly Interests
Professor Darve's research work emphasizes the development of numerical methods for machine learning in science and engineering applications, large-language models, anomaly detection, numerical linear algebra, fast algorithms, high-performance scientific computing, and parallel computing. In various engineering scenarios, the computational cost of simulating intricate and large systems is considerable and frequently exceeds the present computer capabilities. Therefore, the Darve research group is working on innovative numerical strategies to lower this computational cost and facilitate the simulation of complex systems over realistic timescales.
Keywords: large-language models, transformer models, numerical linear algebra (fast linear solvers, fast QR factorization, eigenvalue solvers, applications in geoscience and electric power grid), physics-informed machine learning (inverse modeling using PhysML, auto-encoders, GAN for uncertainty in predictive and inverse modeling, Kriging and statistical inversing, applications in geoscience, fluid mechanics and computational mechanics), anomaly detection (GAN-based algorithms, self-supervised machine learning, applications with the SLAC National Accelerator Laboratory), reinforcement learning for engineering applications.
2024-25 Courses
- First Year Seminar Series
CME 300 (Aut) - Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr) - Numerical Linear Algebra
CME 302 (Aut) -
Independent Studies (15)
- Curricular Practical Training
CME 390 (Aut, Win, Spr, Sum) - Engineering Problems
ME 391 (Aut, Win, Spr, Sum) - Engineering Problems and Experimental Investigation
ME 191 (Aut, Win, Spr, Sum) - Experimental Investigation of Engineering Problems
ME 392 (Aut, Win, Spr, Sum) - Honors Research
ME 191H (Aut, Win, Spr, Sum) - Master's Directed Research
ME 393 (Aut, Win, Spr, Sum) - Master's Directed Research: Writing the Report
ME 393W (Aut, Win, Spr, Sum) - Master's Research
CME 291 (Aut, Win, Spr, Sum) - Ph.D. Research
CME 400 (Aut, Win, Spr, Sum) - Ph.D. Research Rotation
CME 391 (Aut, Win, Spr, Sum) - Ph.D. Research Rotation
ME 398 (Aut, Win, Spr, Sum) - Ph.D. Teaching Experience
ME 491 (Aut, Win, Spr) - Practical Training
ME 199A (Win, Spr) - Practical Training
ME 299A (Aut, Win, Spr, Sum) - Practical Training
ME 299B (Aut, Win, Spr, Sum)
- Curricular Practical Training
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Prior Year Courses
2023-24 Courses
- Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr) - Numerical Linear Algebra
CME 302 (Aut) - Ordinary Differential Equations for Engineers
CME 102, ENGR 155A (Win)
2022-23 Courses
- Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr) - Machine Learning for Computational Engineering.
CME 216, ME 343 (Win) - Numerical Linear Algebra
CME 302 (Aut)
2021-22 Courses
- Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr) - Numerical Linear Algebra
CME 302 (Aut)
- Introduction to parallel computing using MPI, openMP, and CUDA
Stanford Advisees
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Doctoral Dissertation Reader (AC)
Mark Benjamin, Cedric Fraces Gasmi -
Doctoral Dissertation Advisor (AC)
Tiffany Fan, Jason Liang -
Master's Program Advisor
Baxter Bartlett, Baptiste Brugerolle, Luis Flores, Julian Zhiyuan Li, Ashish Mittal, Shishir Pandit-Rao, Sukeerth Ramkumar, Vishal Singh, Sidharth Tadeparti, Chenhao Zhu -
Doctoral Dissertation Co-Advisor (AC)
Luc Houriez, Natalia Rubio, Apoorv Srivastava -
Doctoral (Program)
Shai Bernard, Larry Marshall, Natalia Rubio
All Publications
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Hybrid physics-based and data-driven modeling of vascular bifurcation pressure differences.
Computers in biology and medicine
2024; 184: 109420
Abstract
Reduced-order models allow for the simulation of blood flow in patient-specific vasculatures. They offer a significant reduction in computational cost and wait time compared to traditional computational fluid dynamics models. Unfortunately, due to the simplifications made in their formulations, reduced-order models can suffer from significantly reduced accuracy. One common simplifying assumption is that of continuity of static or total pressure over vascular bifurcations. In many cases, this assumption has been shown to introduce significant errors in pressure predictions. We propose a model to account for this pressure difference, with the ultimate goal of increasing the accuracy of cardiovascular reduced-order models. Our model successfully uses a structure common in existing reduced-order models in conjunction with machine-learning techniques to predict the pressure difference over a vascular bifurcation. We analyze the performance of our model on steady and transient flows, testing it on three bifurcation cohorts representing three different bifurcation geometric types. We find that our model makes significantly more accurate predictions than other models for approximating bifurcation pressure losses commonly used in the reduced-order cardiovascular modeling community. We also compare the efficacy of different machine-learning techniques and observe that a neural network performs most robustly. Additionally, we consider two different model modalities: one in which the model is fit using both steady and transient flows, and one in which it is optimized for performance in transient flows. We discuss the trade-off between the physical interpretability associated with the first option and the improved accuracy in transient flows associated with the latter option. We also demonstrate the model's ability to generalize by testing it on a combined dataset containing two different bifurcation types. This work marks a step towards improving the accuracy of cardiovascular reduced-order models, thereby increasing their utility for cardiovascular flow modeling.
View details for DOI 10.1016/j.compbiomed.2024.109420
View details for PubMedID 39608038
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Coincident learning for unsupervised anomaly detection of scientific instruments
MACHINE LEARNING-SCIENCE AND TECHNOLOGY
2024; 5 (3)
View details for DOI 10.1088/2632-2153/ad64a6
View details for Web of Science ID 001283699200001
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A NUMERICALLY STABLE COMMUNICATION-AVOIDING s- STEP GMRES ALGORITHM
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
2024; 45 (4): 2039-2074
View details for DOI 10.1137/23M1577109
View details for Web of Science ID 001343416000013
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Resilient VAE: Unsupervised Anomaly Detection at the SLAC Linac Coherent Light Source
E D P SCIENCES. 2024
View details for DOI 10.1051/epjconf/202429509033
View details for Web of Science ID 001244151902084
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Learning reduced-order models for cardiovascular simulations with graph neural networks.
Computers in biology and medicine
2023; 168: 107676
Abstract
Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.
View details for DOI 10.1016/j.compbiomed.2023.107676
View details for PubMedID 38039892
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Temperature field optimization for laser powder bed fusion as a traveling salesperson problem with history
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2023
View details for DOI 10.1002/nme.7360
View details for Web of Science ID 001084235100001
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Probabilistic partition of unity networks for high-dimensional regression problems
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2023
View details for DOI 10.1002/nme.7207
View details for Web of Science ID 000940516600001
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Beam-based rf station fault identification at the SLAC Linac Coherent Light Source
PHYSICAL REVIEW ACCELERATORS AND BEAMS
2022; 25 (12)
View details for DOI 10.1103/PhysRevAccelBeams.25.122804
View details for Web of Science ID 000901771100001
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Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry
ADVANCES IN WATER RESOURCES
2022; 170
View details for DOI 10.1016/j.advwatres.2022.104323
View details for Web of Science ID 000883792800002
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HyKKT: a hybrid direct-iterative method for solving KKT linear systems
OPTIMIZATION METHODS & SOFTWARE
2022
View details for DOI 10.1080/10556788.2022.2124990
View details for Web of Science ID 000860640100001
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Second-order accurate hierarchical approximate factorizations for solving sparse linear systems
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2022
View details for DOI 10.1002/nme.7076
View details for Web of Science ID 000839974000001
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Linear solvers for power grid optimization problems: A review of GPU-accelerated linear solvers
PARALLEL COMPUTING
2022; 111
View details for DOI 10.1016/j.parco.2021.102870
View details for Web of Science ID 000800000400004
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Learning generative neural networks with physics knowledge
RESEARCH IN THE MATHEMATICAL SCIENCES
2022; 9 (2)
View details for DOI 10.1007/s40687-022-00329-z
View details for Web of Science ID 000796986600001
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Hierarchical Orthogonal Factorization: Sparse Least Squares Problems
JOURNAL OF SCIENTIFIC COMPUTING
2022; 91 (2)
View details for DOI 10.1007/s10915-022-01824-9
View details for Web of Science ID 000777186700002
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Physics constrained learning for data-driven inverse modeling from sparse observations
JOURNAL OF COMPUTATIONAL PHYSICS
2022; 453
View details for DOI 10.1016/j.jcp.2021.110938
View details for Web of Science ID 000762371600002
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On the fractional Laplacian of variable order
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
2022; 25 (1): 15-28
View details for DOI 10.1007/s13540-021-00003-1
View details for Web of Science ID 000810139800002
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Integrating deep neural networks with full-waveform inversion: Reparameterization, regularization, and uncertainty quantification
GEOPHYSICS
2022; 87 (1): R93-R109
View details for DOI 10.1190/GEO2020-0933.1
View details for Web of Science ID 000744653000004
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Soft Masking for Cost-Constrained Channel Pruning
SPRINGER INTERNATIONAL PUBLISHING AG. 2022: 641-657
View details for DOI 10.1007/978-3-031-20083-0_38
View details for Web of Science ID 000897106000038
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HIERARCHICAL ORTHOGONAL FACTORIZATION: SPARSE SQUARE MATRICES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
2022; 43 (1): 94-123
View details for DOI 10.1137/20M1373475
View details for Web of Science ID 000759673100004
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Memory-Augmented Generative Adversarial Networks for Anomaly Detection
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
2021
Abstract
We propose a memory-augmented deep learning model for semisupervised anomaly detection (AD). While many traditional AD methods focus on modeling the distribution of normal data, additional constraints in the modeling process are needed to distinguish between normal and abnormal data. The proposed model, named memory augmented generative adversarial networks (MEMGAN), is coupled with external memory units through attentional operations. One property of MEMGAN in the latent space is such that encoded normal data are expected to reside in the convex hull of the memory units, while the abnormal ones are separated outside. This property makes the AD process of MEMGAN more robust and reliable. Experiments on AD datasets adapted from MVTec, MNIST, CIFAR10, and Arrhythmia demonstrate that MEMGAN notably improves over previous AD models. We also find that the decoded memory units in MEMGAN are more diverse and interpretable than those in previous memory-augmented models.
View details for DOI 10.1109/TNNLS.2021.3132928
View details for Web of Science ID 000740066200001
View details for PubMedID 34962884
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Learning viscoelasticity models from indirect data using deep neural networks
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
2021; 387
View details for DOI 10.1016/j.cma.2021.114124
View details for Web of Science ID 000702650900001
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Solving inverse problems in stochastic models using deep neural networks and adversarial training
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
2021; 384
View details for DOI 10.1016/j.cma.2021.113976
View details for Web of Science ID 000681089400005
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PBBFMM3D: A parallel black-box algorithm for kernel matrix-vector multiplication
JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING
2021; 154: 64-73
View details for DOI 10.1016/j.jpdc.2021.04.005
View details for Web of Science ID 000657606800006
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A general approach to seismic inversion with automatic differentiation
COMPUTERS & GEOSCIENCES
2021; 151
View details for DOI 10.1016/j.cageo.2021.104751
View details for Web of Science ID 000641463400002
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Learning constitutive relations using symmetric positive definite neural networks
JOURNAL OF COMPUTATIONAL PHYSICS
2021; 428
View details for DOI 10.1016/j.jcp.2020.110072
View details for Web of Science ID 000612234200001
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Application of deep learning to large scale riverine flow velocity estimation
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
2021
View details for DOI 10.1007/s00477-021-01988-0
View details for Web of Science ID 000620880500002
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Deep learning technique for fast inference of large-scale riverine bathymetry
ADVANCES IN WATER RESOURCES
2021; 147
View details for DOI 10.1016/j.advwatres.2020.103715
View details for Web of Science ID 000606420300005
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Universal Sentence Representation Learning with Conditional Masked Language Model
ASSOC COMPUTATIONAL LINGUISTICS-ACL. 2021: 6216-6228
View details for Web of Science ID 000860727000017
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A Task-Based Distributed Parallel Sparsified Nested Dissection Algorithm
ASSOC COMPUTING MACHINERY. 2021
View details for DOI 10.1145/3468267.3470619
View details for Web of Science ID 000769991000015
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A Simple and Effective Method To Eliminate the Self Language Bias in Multilingual Representations
ASSOC COMPUTATIONAL LINGUISTICS-ACL. 2021: 5825-5832
View details for Web of Science ID 000855966305074
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Recent developments in fast and scalable inverse modeling and data assimilation methods in hydrology
JOURNAL OF HYDROLOGY
2020; 591
View details for DOI 10.1016/j.jhydrol.2020.125266
View details for Web of Science ID 000599757800006
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Learning constitutive relations from indirect observations using deep neural networks
JOURNAL OF COMPUTATIONAL PHYSICS
2020; 416
View details for DOI 10.1016/j.jcp.2020.109491
View details for Web of Science ID 000539999800003
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Coupled Time-Lapse Full-Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation
WATER RESOURCES RESEARCH
2020; 56 (8)
View details for DOI 10.1029/2019WR027032
View details for Web of Science ID 000582701700031
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Isogeometric collocation method for the fractional Laplacian in the 2D bounded domain
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
2020; 364
View details for DOI 10.1016/j.cma.2020.112936
View details for Web of Science ID 000527574600027
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Parallelization of the inverse fast multipole method with an application to boundary element method
COMPUTER PHYSICS COMMUNICATIONS
2020; 247
View details for DOI 10.1016/j.cpc.2019.106975
View details for Web of Science ID 000503093400011
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AN ALGEBRAIC SPARSIFIED NESTED DISSECTION ALGORITHM USING LOW-RANK APPROXIMATIONS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
2020; 41 (2): 715–46
View details for DOI 10.1137/19M123806X
View details for Web of Science ID 000546981500015
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Regularized Cycle Consistent Generative Adversarial Network for Anomaly Detection
IOS PRESS. 2020: 1618-1625
View details for DOI 10.3233/FAIA200272
View details for Web of Science ID 000650971301110
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TaskTorrent: a Lightweight Distributed Task-Based Runtime System in C plus
IEEE COMPUTER SOC. 2020: 16-26
View details for DOI 10.1109/PAWATM51920.2020.00007
View details for Web of Science ID 000674937700002
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SPARSE HIERARCHICAL PRECONDITIONERS USING PIECEWISE SMOOTH APPROXIMATIONS OF EIGENVECTORS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2020; 42 (6): A3907–A3931
View details for DOI 10.1137/20M1315683
View details for Web of Science ID 000600650400022
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A robust hierarchical solver for ill-conditioned systems with applications to ice sheet modeling
JOURNAL OF COMPUTATIONAL PHYSICS
2019; 396: 819–36
View details for DOI 10.1016/j.jcp.2019.07.024
View details for Web of Science ID 000481732600041
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Sparse hierarchical solvers with guaranteed convergence
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2019
View details for DOI 10.1002/nme.6166
View details for Web of Science ID 000479563600001
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Erratum: "Investigating the role of non-covalent interactions in conformation and assembly of triazine-based sequence-defined polymers" [J. Chem. Phys. 149, 072330 (2018)].
The Journal of chemical physics
2019; 150 (17): 179901
View details for PubMedID 31067890
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Investigating the role of non-covalent interactions in conformation and assembly of triazine-based sequence-defined polymers (vol 149, 072330, 2018)
JOURNAL OF CHEMICAL PHYSICS
2019; 150 (17)
View details for DOI 10.1063/1.5099377
View details for Web of Science ID 000467255500054
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The multi-dimensional generalized Langevin equation for conformational motion of proteins
JOURNAL OF CHEMICAL PHYSICS
2019; 150 (17)
View details for DOI 10.1063/1.5055573
View details for Web of Science ID 000467255500013
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Novel Data Assimilation Algorithm for Nearshore Bathymetry
JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY
2019; 36 (4): 699–715
View details for DOI 10.1175/JTECH-D-18-0067.1
View details for Web of Science ID 000465145300002
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The multi-dimensional generalized Langevin equation for conformational motion of proteins.
The Journal of chemical physics
2019; 150 (17): 174113
Abstract
Using the generalized Langevin equation (GLE) is a promising approach to build coarse-grained (CG) models of molecular systems since the GLE model often leads to more accurate thermodynamic and kinetic predictions than Brownian dynamics or Langevin models by including a more sophisticated friction with memory. The GLE approach has been used for CG coordinates such as the center of mass of a group of atoms with pairwise decomposition and for a single CG coordinate. We present a GLE approach when CG coordinates are multiple generalized coordinates, defined, in general, as nonlinear functions of microscopic atomic coordinates. The CG model for multiple generalized coordinates is described by the multidimensional GLE from the Mori-Zwanzig formalism, which includes an exact memory matrix. We first present a method to compute the memory matrix in a multidimensional GLE using trajectories of a full system. Then, in order to reduce the computational cost of computing the multidimensional friction with memory, we introduce a method that maps the GLE to an extended Markovian system. In addition, we study the effect of using a nonconstant mass matrix in the CG model. In particular, we include mass-dependent terms in the mean force. We used the proposed CG model to describe the conformational motion of a solvated alanine dipeptide system, with two dihedral angles as the CG coordinates. We showed that the CG model can accurately reproduce two important kinetic quantities: the velocity autocorrelation function and the distribution of first passage times.
View details for PubMedID 31067888
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Embedding Imputation with Grounded Language Information
ASSOC COMPUTATIONAL LINGUISTICS-ACL. 2019: 3356–61
View details for Web of Science ID 000493046105039
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BLOCK BASIS FACTORIZATION FOR SCALABLE KERNEL EVALUATION
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
2019; 40 (4): 1497–1526
View details for DOI 10.1137/18M1212586
View details for Web of Science ID 000546977600012
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FAST LOW-RANK KERNEL MATRIX FACTORIZATION USING SKELETONIZED INTERPOLATION
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2019; 41 (3): A1652–A1680
View details for DOI 10.1137/17M1133749
View details for Web of Science ID 000473033300012
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Investigating the role of non-covalent interactions in conformation and assembly of triazine-based sequence-defined polymers.
The Journal of chemical physics
2018; 149 (7): 072330
Abstract
Grate and co-workers at Pacific Northwest National Laboratory recently developed high information content triazine-based sequence-defined polymers that are robust by not having hydrolyzable bonds and can encode structure and functionality by having various side chains. Through molecular dynamics (MD) simulations, the triazine polymers have been shown to form particular sequential stacks, have stable backbone-backbone interactions through hydrogen bonding and pi-pi interactions, and conserve their cis/trans conformations throughout the simulation. However, we do not know the effects of having different side chains and backbone structures on the entire conformation and whether the cis or trans conformation is more stable for the triazine polymers. For this reason, we investigate the role of non-covalent interactions for different side chains and backbone structures on the conformation and assembly of triazine polymers in MD simulations. Since there is a high energy barrier associated with the cis-trans isomerization, we use replica exchange molecular dynamics (REMD) to sample various conformations of triazine hexamers. To obtain rates and intermediate conformations, we use the recently developed concurrent adaptive sampling (CAS) algorithm for dimers of triazine trimers. We found that the hydrogen bonding ability of the backbone structure is critical for the triazine polymers to self-assemble into nanorod-like structures, rather than that of the side chains, which can help researchers design more robust materials.
View details for PubMedID 30134719
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Sparse supernodal solver using block low-rank compression: Design, performance and analysis
JOURNAL OF COMPUTATIONAL SCIENCE
2018; 27: 255–70
View details for DOI 10.1016/j.jocs.2018.06.007
View details for Web of Science ID 000443665800022
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A distributed-memory hierarchical solver for general sparse linear systems
ELSEVIER SCIENCE BV. 2018: 49–64
View details for DOI 10.1016/j.parco.2017.12.004
View details for Web of Science ID 000428486900005
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Riverine Bathymetry Imaging With Indirect Observations
WATER RESOURCES RESEARCH
2018; 54 (5): 3704–27
View details for DOI 10.1029/2017WR021649
View details for Web of Science ID 000442351300025
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An efficient preconditioner for the fast simulation of a 2D stokes flow in porous media
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2018; 113 (4): 561–80
View details for DOI 10.1002/nme.5626
View details for Web of Science ID 000419121800001
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ON THE NUMERICAL RANK OF RADIAL BASIS FUNCTION KERNELS IN HIGH DIMENSIONS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
2018; 39 (4): 1810–35
View details for DOI 10.1137/17M1135803
View details for Web of Science ID 000453731100012
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LOW-RANK FACTORIZATIONS IN DATA SPARSE HIERARCHICAL ALGORITHMS FOR PRECONDITIONING SYMMETRIC POSITIVE DEFINITE MATRICES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
2018; 39 (4): 1701–25
View details for DOI 10.1137/17M1151158
View details for Web of Science ID 000453731100008
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Optimal estimation and scheduling in aquifer management using the rapid feedback control method
ADVANCES IN WATER RESOURCES
2017; 110: 310–18
View details for DOI 10.1016/j.advwatres.2017.10.011
View details for Web of Science ID 000418262400024
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Efficiently sampling conformations and pathways using the concurrent adaptive sampling (CAS) algorithm.
The Journal of chemical physics
2017; 147 (7): 074115
Abstract
Molecular dynamics simulations are useful in obtaining thermodynamic and kinetic properties of bio-molecules, but they are limited by the time scale barrier. That is, we may not obtain properties' efficiently because we need to run microseconds or longer simulations using femtosecond time steps. To overcome this time scale barrier, we can use the weighted ensemble (WE) method, a powerful enhanced sampling method that efficiently samples thermodynamic and kinetic properties. However, the WE method requires an appropriate partitioning of phase space into discrete macrostates, which can be problematic when we have a high-dimensional collective space or when little is known a priori about the molecular system. Hence, we developed a new WE-based method, called the "Concurrent Adaptive Sampling (CAS) algorithm," to tackle these issues. The CAS algorithm is not constrained to use only one or two collective variables, unlike most reaction coordinate-dependent methods. Instead, it can use a large number of collective variables and adaptive macrostates to enhance the sampling in the high-dimensional space. This is especially useful for systems in which we do not know what the right reaction coordinates are, in which case we can use many collective variables to sample conformations and pathways. In addition, a clustering technique based on the committor function is used to accelerate sampling the slowest process in the molecular system. In this paper, we introduce the new method and show results from two-dimensional models and bio-molecules, specifically penta-alanine and a triazine trimer.
View details for DOI 10.1063/1.4999097
View details for PubMedID 28830168
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Smoothing-based compressed state Kalman filter for joint state-parameter estimation: Applications in reservoir characterization and CO2 storage monitoring
WATER RESOURCES RESEARCH
2017; 53 (8): 7190–7207
View details for DOI 10.1002/2016WR020168
View details for Web of Science ID 000411202000044
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A numerical study of super-resolution through fast 3D wideband algorithm for scattering in highly-heterogeneous media
WAVE MOTION
2017; 70: 113-134
View details for DOI 10.1016/j.wavemoti.2016.08.012
View details for Web of Science ID 000397375900009
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Computing the non-Markovian coarse-grained interactions derived from the Mori-Zwanzig formalism in molecular systems: Application to polymer melts
JOURNAL OF CHEMICAL PHYSICS
2017; 146 (1)
Abstract
Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a single coarse particle, while DPD considers the dynamics of many interacting CG particles, with both CG systems governed by non-Markovian interactions. We compare two different methods for the practical implementation of the non-Markovian interactions in GLE and DPD systems. More specifically, a direct evaluation of the non-Markovian (NM) terms is performed in LE-NM and DPD-NM models, which requires the storage of historical information that significantly increases computational complexity. Alternatively, we use a few auxiliary variables in LE-AUX and DPD-AUX models to replace the non-Markovian dynamics with a Markovian dynamics in a higher dimensional space, leading to a much reduced memory footprint and computational cost. In our numerical benchmarks, the GLE and non-Markovian DPD models are constructed from molecular dynamics (MD) simulations of star-polymer melts. Results show that a Markovian dynamics with auxiliary variables successfully generates equivalent non-Markovian dynamics consistent with the reference MD system, while maintaining a tractable computational cost. Also, transient subdiffusion of the star-polymers observed in the MD system can be reproduced by the coarse-grained models. The non-interacting particle models, LE-NM/AUX, are computationally much cheaper than the interacting particle models, DPD-NM/AUX. However, the pairwise models with momentum conservation are more appropriate for correctly reproducing the long-time hydrodynamics characterised by an algebraic decay in the velocity autocorrelation function.
View details for DOI 10.1063/1.4973347
View details for Web of Science ID 000393431000007
View details for PubMedID 28063444
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Sparse Supernodal Solver Using Block Low-Rank Compression
IEEE. 2017: 1138–47
View details for DOI 10.1109/IPDPSW.2017.86
View details for Web of Science ID 000417418900123
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Efficient mesh deformation based on radial basis function interpolation by means of the inverse fast multipole method
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
2016; 308: 286-309
View details for DOI 10.1016/j.cma.2016.05.029
View details for Web of Science ID 000380512800013
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A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite-element matrices
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2016; 107 (6): 520-540
View details for DOI 10.1002/nme.5196
View details for Web of Science ID 000380035600004
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Task-based FMM for heterogeneous architectures
CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE
2016; 28 (9): 2608-2629
View details for DOI 10.1002/cpe.3723
View details for Web of Science ID 000378743500003
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A fast block low-rank dense solver with applications to finite-element matrices
JOURNAL OF COMPUTATIONAL PHYSICS
2016; 304: 170-188
View details for DOI 10.1016/j.jcp.2015.10.012
View details for Web of Science ID 000365041900008
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Real-time data assimilation for large-scale systems: The spectral Kalman filter
ADVANCES IN WATER RESOURCES
2015; 86: 260-272
View details for DOI 10.1016/j.advwatres.2015.07.017
View details for Web of Science ID 000365623500002
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The compressed state Kalman filter for nonlinear state estimation: Application to large-scale reservoir monitoring
WATER RESOURCES RESEARCH
2015; 51 (12): 9942-9963
View details for DOI 10.1002/2015WR017203
View details for Web of Science ID 000368421500031
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A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2015; 102 (12): 1784-1814
View details for DOI 10.1002/nme.4865
View details for Web of Science ID 000354625300002
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A comparison of weighted ensemble and Markov state model methodologies
JOURNAL OF CHEMICAL PHYSICS
2015; 142 (21)
Abstract
Computation of reaction rates and elucidation of reaction mechanisms are two of the main goals of molecular dynamics (MD) and related simulation methods. Since it is time consuming to study reaction mechanisms over long time scales using brute force MD simulations, two ensemble methods, Markov State Models (MSMs) and Weighted Ensemble (WE), have been proposed to accelerate the procedure. Both approaches require clustering of microscopic configurations into networks of "macro-states" for different purposes. MSMs model a discretization of the original dynamics on the macro-states. Accuracy of the model significantly relies on the boundaries of macro-states. On the other hand, WE uses macro-states to formulate a resampling procedure that kills and splits MD simulations for achieving better efficiency of sampling. Comparing to MSMs, accuracy of WE rate predictions is less sensitive to the definition of macro-states. Rigorous numerical experiments using alanine dipeptide and penta-alanine support our analyses. It is shown that MSMs introduce significant biases in the computation of reaction rates, which depend on the boundaries of macro-states, and Accelerated Weighted Ensemble (AWE), a formulation of weighted ensemble that uses the notion of colors to compute fluxes, has reliable flux estimation on varying definitions of macro-states. Our results suggest that whereas MSMs provide a good idea of the metastable sets and visualization of overall dynamics, AWE provides reliable rate estimations requiring less efforts on defining macro-states on the high dimensional conformational space.
View details for DOI 10.1063/1.4921890
View details for Web of Science ID 000355931800069
View details for PubMedID 26049485
View details for PubMedCentralID PMC4457661
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OPTIMIZING THE ADAPTIVE FAST MULTIPOLE METHOD FOR FRACTAL SETS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2015; 37 (2): A1040-A1066
View details for DOI 10.1137/140962681
View details for Web of Science ID 000353838400020
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AWE-WQ: Fast-Forwarding Molecular Dynamics Using the Accelerated Weighted Ensemble
JOURNAL OF CHEMICAL INFORMATION AND MODELING
2014; 54 (10): 3033-3043
Abstract
A limitation of traditional molecular dynamics (MD) is that reaction rates are difficult to compute. This is due to the rarity of observing transitions between metastable states since high energy barriers trap the system in these states. Recently the weighted ensemble (WE) family of methods have emerged which can flexibly and efficiently sample conformational space without being trapped and allow calculation of unbiased rates. However, while WE can sample correctly and efficiently, a scalable implementation applicable to interesting biomolecular systems is not available. We provide here a GPLv2 implementation called AWE-WQ of a WE algorithm using the master/worker distributed computing WorkQueue (WQ) framework. AWE-WQ is scalable to thousands of nodes and supports dynamic allocation of computer resources, heterogeneous resource usage (such as central processing units (CPU) and graphical processing units (GPUs) concurrently), seamless heterogeneous cluster usage (i.e., campus grids and cloud providers), and support for arbitrary MD codes such as GROMACS, while ensuring that all statistics are unbiased. We applied AWE-WQ to a 34 residue protein which simulated 1.5 ms over 8 months with peak aggregate performance of 1000 ns/h. Comparison was done with a 200 μs simulation collected on a GPU over a similar timespan. The folding and unfolded rates were of comparable accuracy.
View details for DOI 10.1021/ci500321g
View details for Web of Science ID 000343849600036
View details for PubMedID 25207854
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A Kalman filter powered by H-2-matrices for quasi-continuous data assimilation problems
WATER RESOURCES RESEARCH
2014; 50 (5): 3734-3749
View details for DOI 10.1002/2013WR014607
View details for Web of Science ID 000337672900008
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Method and advantages of genetic algorithms in parameterization of interatomic potentials: Metal oxides
COMPUTATIONAL MATERIALS SCIENCE
2014; 81: 453-465
View details for DOI 10.1016/j.commatsci.2013.08.054
View details for Web of Science ID 000326940300064
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CAUCHY FAST MULTIPOLE METHOD FOR GENERAL ANALYTIC KERNELS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (2): A396-A426
View details for DOI 10.1137/120891617
View details for Web of Science ID 000335817600005
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TASK-BASED FMM FOR MULTICORE ARCHITECTURES
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (1): C66-C93
View details for DOI 10.1137/130915662
View details for Web of Science ID 000333415500024
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An Fast Direct Solver for Partial Hierarchically Semi-Separable Matrices
JOURNAL OF SCIENTIFIC COMPUTING
2013; 57 (3): 477-501
View details for DOI 10.1007/s10915-013-9714-z
View details for Web of Science ID 000326401200003
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Large-scale stochastic linear inversion using hierarchical matrices
COMPUTATIONAL GEOSCIENCES
2013; 17 (6): 913-927
View details for DOI 10.1007/s10596-013-9364-0
View details for Web of Science ID 000328319900004
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ANALYSIS OF THE ACCELERATED WEIGHTED ENSEMBLE METHODOLOGY
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
2013: 171-181
View details for Web of Science ID 000328571500019
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The accuracy of the CHARMM22/CMAP and AMBER ff99SB force fields for modelling the antimicrobial peptide cecropin P1
MOLECULAR SIMULATION
2013; 39 (11): 922-936
View details for DOI 10.1080/08927022.2013.781599
View details for Web of Science ID 000323634200009
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A fast algorithm for sparse matrix computations related to inversion
JOURNAL OF COMPUTATIONAL PHYSICS
2013; 242: 915-945
View details for DOI 10.1016/j.jcp.2013.01.036
View details for Web of Science ID 000319049800046
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FOURIER-BASED FAST MULTIPOLE METHOD FOR THE HELMHOLTZ EQUATION
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2013; 35 (1): A79-A103
View details for DOI 10.1137/11085774X
View details for Web of Science ID 000315575000004
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Accuracy in One-way and Two-way Algorithms for Computing Desired Entries in the Inverse of Sparse Matrices
11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM)
AMER INST PHYSICS. 2013: 1501–1504
View details for DOI 10.1063/1.4825806
View details for Web of Science ID 000331472800355
- Task-based FMM for multicore architectures 2013
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An\ mathcal O (N\ log N) Fast Direct Solver for Partial Hierarchically Semi-Separable Matrices
Journal of Scientific Computing
2013; 57 (3): 477-501
View details for DOI 10.1007/s10915-013-9714-z
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Fast Algorithms for Bayesian Inversion
Computational Challenges in the Geosciences
2013; 156: 101-142
View details for DOI 10.1007/978-1-4614-7434-0_5
- Task-based Parallelization of the Fast Multipole Method on NVIDIA GPUs and Multicore Processors 2013
- Optimizing the Black-box FMM for Smooth and Oscillatory Kernels 2013
- Composition and reuse with compiled domain-specific languages 2013
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Folding Proteins at 500 ns/hour with Work Queue.
Proceedings ... IEEE International Conference on eScience. IEEE International Conference on eScience
2012; 2012: 1-8
Abstract
Molecular modeling is a field that traditionally has large computational costs. Until recently, most simulation techniques relied on long trajectories, which inherently have poor scalability. A new class of methods is proposed that requires only a large number of short calculations, and for which minimal communication between computer nodes is required. We considered one of the more accurate variants called Accelerated Weighted Ensemble Dynamics (AWE) and for which distributed computing can be made efficient. We implemented AWE using the Work Queue framework for task management and applied it to an all atom protein model (Fip35 WW domain). We can run with excellent scalability by simultaneously utilizing heterogeneous resources from multiple computing platforms such as clouds (Amazon EC2, Microsoft Azure), dedicated clusters, grids, on multiple architectures (CPU/GPU, 32/64bit), and in a dynamic environment in which processes are regularly added or removed from the pool. This has allowed us to achieve an aggregate sampling rate of over 500 ns/hour. As a comparison, a single process typically achieves 0.1 ns/hour.
View details for DOI 10.1109/eScience.2012.6404429
View details for PubMedID 25540799
View details for PubMedCentralID PMC4273313
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Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics
OIL & GAS SCIENCE AND TECHNOLOGY-REVUE D IFP ENERGIES NOUVELLES
2012; 67 (5): 857-875
View details for DOI 10.2516/ogst/2012064
View details for Web of Science ID 000314141700010
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Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation
JOURNAL OF COMPUTATIONAL PHYSICS
2012; 231 (4): 1175-1196
View details for DOI 10.1016/j.jcp.2011.09.027
View details for Web of Science ID 000300462100005
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Extension and optimization of the FIND algorithm: Computing Green's and less-than Green's functions
JOURNAL OF COMPUTATIONAL PHYSICS
2012; 231 (4): 1121-1139
View details for DOI 10.1016/j.jcp.2011.05.027
View details for Web of Science ID 000300462100003
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Optimizing the multipole-to-local operator in the fast multipole method for graphical processing units
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2012; 89 (1): 105-133
View details for DOI 10.1002/nme.3240
View details for Web of Science ID 000298589300005
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Time integrators based on approximate discontinuous Hamiltonians
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2012; 89 (1): 71-104
View details for DOI 10.1002/nme.3236
View details for Web of Science ID 000298589300004
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Fast Multipole Method Using the Cauchy Integral Formula
Workshop on Numerical Analysis and Multiscale Computations
SPRINGER-VERLAG BERLIN. 2012: 127–144
View details for DOI 10.1007/978-3-642-21943-6_6
View details for Web of Science ID 000310180800006
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Folding Proteins at 500 ns/hour with Work Queue
IEEE 8th International Conference on E-Science (e-Science)
IEEE. 2012
View details for Web of Science ID 000315360600019
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Optimization of the parallel black-box fast multipole method on CUDA
Innovative Parallel Computing (InPar)
2012: 1 - 14
View details for DOI 10.1109/InPar.2012.6339607
- Poster: Matrices over Runtime Systems at Exascale 2012
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Folding Proteins at 500 ns/hour with Work Queue
2012
View details for DOI 10.1109/eScience.2012.6404429
- EFFICIENT DATA ASSIMILATION TOOL IN CONJUNCTION WITH TOUGH2 FOR CO2 MONITORING 2012
- Matrices Over Runtime Systems at Exascale 2012
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Matrices Over Runtime Systems @ Exascale
25th ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis (SC)
IEEE. 2012: 1330–1331
View details for Web of Science ID 000320824300158
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Assembly of finite element methods on graphics processors
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2011; 85 (5): 640-669
View details for DOI 10.1002/nme.2989
View details for Web of Science ID 000286775000007
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The fast multipole method on parallel clusters, multicore processors, and graphics processing units
COMPTES RENDUS MECANIQUE
2011; 339 (2-3): 185-193
View details for DOI 10.1016/j.crme.2010.12.005
View details for Web of Science ID 000287768400012
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Liszt: a domain specific language for building portable mesh-based PDE solvers
2011
View details for DOI 10.1145/2063384.2063396
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Generalized Fast Multipole Method
9th World Congress on Computational Mechanics/4th Asian Pacific Congress on Computational Mechanics
IOP PUBLISHING LTD. 2010
View details for DOI 10.1088/1757-899X/10/1/012230
View details for Web of Science ID 000290445000231
- The CUDA codes to perform M2L operation in FMM 2010
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Generalized fast multipole method
2010
View details for DOI 10.1088/1757-899X/10/1/012230
- An implementation of low-frequency fast multipole BIEM for Helmholtz'equation on GPU 2010
- Application of assembly of finite element methods on graphics processors for real-time elastodynamics GPU Computing Gems edited by Hwu, Wen-mei, W. Elsevier. 2010: 1
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Introduction to Assembly of Finite Element Methods on Graphics Processors
9th World Congress on Computational Mechanics/4th Asian Pacific Congress on Computational Mechanics
IOP PUBLISHING LTD. 2010
View details for DOI 10.1088/1757-899X/10/1/012009
View details for Web of Science ID 000290445000010
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The black-box fast multipole method
JOURNAL OF COMPUTATIONAL PHYSICS
2009; 228 (23): 8712-8725
View details for DOI 10.1016/j.jcp.2009.08.031
View details for Web of Science ID 000271671100011
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A hybrid method for the parallel computation of Green's functions
JOURNAL OF COMPUTATIONAL PHYSICS
2009; 228 (14): 5020-5039
View details for DOI 10.1016/j.jcp.2009.03.035
View details for Web of Science ID 000267846500005
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Computing generalized Langevin equations and generalized Fokker-Planck equations
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2009; 106 (27): 10884-10889
Abstract
The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
View details for DOI 10.1073/pnas.0902633106
View details for Web of Science ID 000267796100005
View details for PubMedID 19549838
View details for PubMedCentralID PMC2708778
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High-ionic-strength electroosmotic flows in uncharged hydrophobic nanochannels
JOURNAL OF COLLOID AND INTERFACE SCIENCE
2009; 330 (1): 194-200
Abstract
We report molecular dynamics simulation results of high-ionic-strength electroosmotic flows inside uncharged nanochannels. The possibility of this unusual electrokinetic phenomenon has been discussed by Dukhin et al. [A. Dukhin, S. Dukhin, P. Goetz, Langmuir 21 (2005) 9990]. Our computed velocity profiles clearly indicate the presence of a net flow with a maximum velocity around 2 m/s. We found the apparent zeta potential to be -29.7+/-6.8 mV, using the Helmholtz-Smoluchowski relation and the measured mean velocity. This value is comparable to experimentally measured values in Dukhin et al. and references therein. We also investigate the orientations of water molecules in response to an electric field by computing polarization density. Water molecules in the bulk region are oriented along the direction of the external electric field, while their near-wall orientation shows oscillations. The computation of three-dimensional density distributions of sodium and chloride ions around each individual water molecule show that chloride ions tend to concentrate near a water molecule, whereas sodium ions are diffusely distributed.
View details for DOI 10.1016/j.jcis.2008.10.029
View details for Web of Science ID 000262229700028
View details for PubMedID 19007939
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Optimization of the FIND Algorithm to Compute the Inverse of a Sparse Matrix
13th International Workshop on Computational Electronics
IEEE. 2009: 285–288
View details for Web of Science ID 000272988200074
- Concentration distributions of arbitrary shaped particles in microfluidic channel flows Bulletin of the American Physical Society 2009; 54 (19)
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Optimization of the FIND algorithm to compute the inverse of a sparse matrix
2009
View details for DOI 10.1109/IWCE.2009.5091136
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Computing generalized Langevin equations and generalized Fokker–Planck equations
edited by Chorin, Alexandre, J.
2009
View details for DOI 10.1073/pnas.0902633106
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Large calculation of the flow over a hypersonic vehicle using a GPU
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (24): 10148-10161
View details for DOI 10.1016/j.jcp.2008.08.023
View details for Web of Science ID 000261207600009
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Computing entries of the inverse of a sparse matrix using the FIND algorithm
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (22): 9408-9427
View details for DOI 10.1016/j.jcp.2008.06.033
View details for Web of Science ID 000260645700006
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Fast electrostatic force calculation on parallel computer clusters
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (19): 8551-8567
View details for DOI 10.1016/j.jcp.2008.06.016
View details for Web of Science ID 000259753700005
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Stability of asynchronous variational integrators
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (18): 8367-8394
View details for DOI 10.1016/j.jcp.2008.05.017
View details for Web of Science ID 000258972000007
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Adaptive biasing force method for scalar and vector free energy calculations
JOURNAL OF CHEMICAL PHYSICS
2008; 128 (14)
Abstract
In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in N-acetylalanyl-N'-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.
View details for DOI 10.1063/1.2829861
View details for Web of Science ID 000255470300020
View details for PubMedID 18412436
- A black-box Fast Multipole Method 2008
- BIRS 08w5074: Mathematical and numerical methods for free energy calculations in molecular systems 2008
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Fast inverse using nested dissection for NEGF
JOURNAL OF COMPUTATIONAL ELECTRONICS
2007; 6 (1-3): 187-190
View details for DOI 10.1007/s10825-006-0112-8
View details for Web of Science ID 000208473600045
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Stability of asynchronous variational integrators
21st International Workshop on Principles of Advanced and Distributed Simulation (PADS 2007)
IEEE COMPUTER SOC. 2007: 38–44
View details for Web of Science ID 000248079800006
- Thermodynamic integration using constrained and unconstrained dynamics Free Energy Calculations 2007; 86: 119-170
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The effect of stratification on the wave number selection in the instability of sedimenting spheroids
PHYSICS OF FLUIDS
2006; 18 (12)
View details for DOI 10.1063/1.2396913
View details for Web of Science ID 000243158200003
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Stabilization of a suspension of sedimenting rods by induced-charge electrophoresis
PHYSICS OF FLUIDS
2006; 18 (12)
View details for DOI 10.1063/1.2404948
View details for Web of Science ID 000243158200013
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Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions
JOURNAL OF FLUID MECHANICS
2006; 563: 223-259
View details for DOI 10.1017/S0022112006001376
View details for Web of Science ID 000241085500011
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Effect of flexibility on the shear-induced migration of short-chain polymers in parabolic channel flow
JOURNAL OF FLUID MECHANICS
2006; 557: 297-306
View details for DOI 10.1017/S0022112006000243
View details for Web of Science ID 000238820700013
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Molecular dynamics simulation of electro-osmotic flows in rough wall nanochannels
PHYSICAL REVIEW E
2006; 73 (5)
Abstract
We performed equilibrium and nonequilibrium molecular dynamics simulation to study electro-osmotic flows inside charged nanochannels with different types of surface roughness. We modeled surface roughness as a sequence of two-dimensional subnanoscale grooves and ridges (step function-type roughness) along the flow direction. The amplitude, spatial period, and symmetry of surface roughness were varied. The amplitude of surface roughness was on the order of the Debye length. The walls have uniform negative charges at the interface with fluids. We included only positive ions (counterions) for simplicity of computation. For the smooth wall, we compared our molecular dynamics simulation results to the well-known Poisson-Boltzmann theory. The density profiles of water molecules showed "layering" near the wall. For the rough walls, the density profiles measured from the wall are similar to those for the smooth wall except near where the steps are located. Because of the layering of water molecules and the finite size effect of ions and the walls, the ionic distribution departs from the Boltzmann distribution. To further understand the structure of water molecules and ions, we computed the polarization density. Near the wall, its z component dominates the other components, indicating the preferred orientation ("ordering") of water molecules. Especially, inside the groove for the rough walls, its maximum is 10% higher (stronger ordering) than for the smooth wall. The dielectric constant, computed with a Clausius-Mosotti-type equation, confirmed the ordering near the wall and the enhanced ordering inside the groove. The residence time and the diffusion coefficient, computed using the velocity autocorrelation function, showed that the diffusion of water and ions along the direction normal to the wall is significantly reduced near the wall and further decreases inside the groove. Along the flow direction, the diffusion of water and ions inside the groove is significantly lowered while it is similar to the bulk value elsewhere. We performed nonequilibrium molecular dynamics simulation to compute electro-osmotic velocities and flow rates. The velocity profiles correspond to those for overlapped electric double layers. For the rough walls, velocity inside the groove is close to zero, meaning that the channel height is effectively reduced. The flow rate was found to decrease as the period of surface roughness decreases or the amplitude of surface roughness increases. We defined the zeta potential as the electrostatic potential at the location of a slip plane. We computed the electrostatic potential with the ionic distribution and the dielectric constant both from our molecular dynamics simulation. We estimated the slip plane from the velocity profile. The zeta potential showed the same trend as the flow rate: it decreases with an increasing amplitude and a decreasing period of surface roughness.
View details for DOI 10.1103/PhysRevE.73.051203
View details for Web of Science ID 000237951300019
View details for PubMedID 16802924
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The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation
JOURNAL OF FLUID MECHANICS
2006; 553: 347-388
View details for DOI 10.1017/S0022112006009025
View details for Web of Science ID 000237366800015
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Numerical Methods for Calculating the Potential of Mean Force
New Algorithms for Macromolecular Simulation
2006; 49: 213-249
View details for DOI 10.1007/3-540-31618-3_13
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A Bayesian approach to calculating free energies in chemical and biological systems
26th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
AMER INST PHYSICS. 2006: 23–30
View details for Web of Science ID 000244484400003
- Stratification and wavenumber selection in the instability of sedimenting spheroids 2006
- The Dynamics of Rodlike Particles under Sedimentation and Induced-Charge Electrophoresis 2006
- Adaptive Biasing Force Method for Vector Free Energy Calculations 2006
- Electric Double Layer Structures near Rough Surfaces: Molecular Dynamics Simulation Bulletin of the American Physical Society 2006
- Fast Inverse using Nested Dissection for the Non Equilibrium Green's Function 11th International Workshop on Computational Electronics 2006
- Effect of flexibility on the shear-induced migration of short polymers in parabolic channel flow 2006
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A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers
PHYSICS OF FLUIDS
2005; 17 (3)
View details for DOI 10.1063/1.1862262
View details for Web of Science ID 000227372600031
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Interactions of wall roughness and electroosmotic flows inside nanochannels
3rd International Conference on Microchannels and Minichannels
AMER SOC MECHANICAL ENGINEERS. 2005: 641–645
View details for Web of Science ID 000243025800091
- Concentration fluctuations in dilute suspensions of orientable and deformable particles under sedimentation 2005
- Hydrodynamic interactions in colloidal dispersions of conducting rods under induced-charge electrophoresis 2005
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Induced-charge electrophoresis in suspensions of rodlike particles: Theory and simulations
ASME International Mechanical Engineering Congress and Exposition
AMER SOC MECHANICAL ENGINEERS. 2005: 251–256
View details for Web of Science ID 000243038600033
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Microstructure in the sedimentation of anisotropic and deformable particles
ASME International Mechanical Engineering Congress and Exposition
AMER SOC MECHANICAL ENGINEERS. 2005: 797–803
View details for Web of Science ID 000243038600101
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Efficient fast multipole method for low-frequency scattering
JOURNAL OF COMPUTATIONAL PHYSICS
2004; 197 (1): 341-363
View details for DOI 10.1016/j.jcp.2003.12.002
View details for Web of Science ID 000221833000016
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A fast multipole method for Maxwell equations stable at all frequencies
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
2004; 362 (1816): 603-628
Abstract
The solution of Helmholtz and Maxwell equations by integral formulations (kernel in exp(i kr)/r) leads to large dense linear systems. Using direct solvers requires large computational costs in O(N(3)). Using iterative solvers, the computational cost is reduced to large matrix-vector products. The fast multipole method provides a fast numerical way to compute convolution integrals. Its application to Maxwell and Helmholtz equations was initiated by Rokhlin, based on a multipole expansion of the interaction kernel. A second version, proposed by Chew, is based on a plane-wave expansion of the kernel. We propose a third approach, the stable-plane-wave expansion, which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the plane-wave expansion. The computational complexity is Nlog N as with the other methods.
View details for DOI 10.1098/rsta.2003.1337
View details for Web of Science ID 000220407200010
View details for PubMedID 15306510
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Assessing the efficiency of free energy calculation methods
JOURNAL OF CHEMICAL PHYSICS
2004; 120 (8): 3563-3578
Abstract
The efficiencies of two recently developed methods for calculating free energy changes along a generalized coordinate in a system are discussed in the context of other, related approaches. One method is based on Jarzynski's identity [Phys. Rev. Lett. 78, 2690 (1997)]. The second method relies on thermodynamic integration of the average force and is called the adaptive biasing force method [Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)]. Both methods are designed such that the system evolves along the chosen coordinate(s) without experiencing free energy barriers and they require calculating the instantaneous, unconstrained force acting on this coordinate using the formula derived by Darve and Pohorille. Efficiencies are analyzed by comparing analytical estimates of statistical errors and by considering two numerical examples-internal rotation of hydrated 1,2-dichloroethane and transfer of fluoromethane across a water-hexane interface. The efficiencies of both methods are approximately equal in the first but not in the second case. During transfer of fluoromethane the system is easily driven away from equilibrium and, therefore, the performance of the method based on Jarzynski's identity is poor.
View details for DOI 10.1063/1.1642607
View details for Web of Science ID 000189139700006
View details for PubMedID 15268518
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Calculating transport properties of nanodevices
Conference on Nanosensing
SPIE-INT SOC OPTICAL ENGINEERING. 2004: 452–463
View details for DOI 10.1117/12.571494
View details for Web of Science ID 000226789700046
- Computing flow rate of electroosmotic flows in nanochannels with different wall roughness The Smithsonian/NASA Astrophysics Data System 2004
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Calculating transport properties of nanodevices
2004
View details for DOI 10.1117/12.571494
- Dynamic Simulations of Sedimenting Fibers with Fast Fourier Transform Acceleration Abstracts of the Papers 2004
- Pattern formation in sedimenting suspensions of spheroids 2004
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Analysis and performance results of a molecular modeling application on Merrimac
2004
View details for DOI 10.1109/SC.2004.69
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Fast multipole method for low-frequency electromagnetic scattering
2nd MIT Conference on Computational Fluid and Solid Mechanics
ELSEVIER SCIENCE BV. 2003: 1299–1302
View details for Web of Science ID 000184938200317
- Unfolding of proteins: Thermal and mechanical unfolding 2003
- Surface tension evaluation in lennard-jones fluid system with untruncated potentials 2003
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Calculating free energies using a scaled-force molecular dynamics algorithm
MOLECULAR SIMULATION
2002; 28 (1-2): 113-144
View details for DOI 10.1080/08927020290004412
View details for Web of Science ID 000176122400009
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Calculating free energies using average force
JOURNAL OF CHEMICAL PHYSICS
2001; 115 (20): 9169-9183
View details for Web of Science ID 000172129300010
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The fast multipole method I: error analysis and asymptotic complexity
SIAM JOURNAL ON NUMERICAL ANALYSIS
2000; 38 (1): 98-128
View details for Web of Science ID 000088263500006
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The fast multipole method: Numerical implementation
JOURNAL OF COMPUTATIONAL PHYSICS
2000; 160 (1): 195-240
View details for Web of Science ID 000086782500010
- Méthodes multipôles rapides: Résolution des équations de Maxwell par formulations intégrales 1999; 133 ( 99 PA06 6598): 228
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Advanced structured-unstructured solver for electromagnetic scattering from multimaterial objects
1997
View details for DOI 10.2514/6.1997-863
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Fast-multipole method: a mathematical study
Comptes Rendus de l'Académie des Sciences-Series I-Mathematics
1997; 325 (9): 1037–1042
View details for DOI http://dx.doi.org/10.1016/S0764-4442(97)89101-X
- THE MULTISTEP FAST MULTIPOLE METHOD: ALGORITHM AND ERROR ESTIMATION 1997
- SOLVING THE SCALAR WAVE EQUATION VIA A DIRECTIONAL FAST MULTIPOLE METHOD
- A KALMAN FILTER POWERED BY H-MATRICES FOR QUASI-CONTINUOUS DATA ASSIMILATION PROBLEMS
- Concentration fluctuations in the dilute sedimentation of anisotropic particles 15th US National Congress
- CFD for Blood Transfusions on the Battlefield and Inhalation of Toxic Agents in the Lung
- Dynamic simulations of the instability of sedimenting fibers