Article
Computer Science, Theory & Methods
Suman Majumder, Yawen Guan, Brian J. Reich, Arvind K. Saibaba
Summary: In this study, we propose a novel approximate inference methodology for analyzing massive spatial datasets using a Gaussian process model. Our method effectively estimates spatial covariance parameters and makes accurate predictions with uncertainty quantification for point-referenced spatial data. It is applicable to various types of observations and covariance functions. Extensive simulation studies and a real data application demonstrate that our method significantly reduces computation time while maintaining scalability.
STATISTICS AND COMPUTING
(2022)
Article
Engineering, Biomedical
Malena Sabate Landman, Ander Biguri, Sepideh Hatamikia, Richard Boardman, John Aston, Carola-Bibiane Schonlieb
Summary: Krylov subspace methods are powerful iterative solvers for linear systems, commonly used in inverse problems. This work aims to bridge the gap between this field and applied medical physics and engineering, by providing a general framework for relevant Krylov subspace methods applied to 3D CT problems. Numerical results in synthetic and real-world CT applications are presented to showcase and compare the different methods.
PHYSICS IN MEDICINE AND BIOLOGY
(2023)
Article
Mathematics, Applied
John W. Pearson, Andreas Potschka
Summary: This paper considers symmetric positive definite preconditioners for multiple saddle-point systems of block tridiagonal form, which can be applied within the MINRES algorithm. The authors describe a preconditioner that yields a preconditioned matrix with only two distinct eigenvalues, 1 and -1, when applied exactly. They discuss the advantages of this approach compared to a more widely studied block diagonal preconditioner, analyze the computational work associated with applying the new preconditioner inexactly, and survey various theoretical results for the block diagonal case. Numerical results confirm the authors' theoretical findings.
IMA JOURNAL OF NUMERICAL ANALYSIS
(2023)
Article
Geochemistry & Geophysics
Jianmei Zhou, Kailiang Lu, Xiu Li, Wentao Liu, Zhipeng Qi, Yanfu Qi
Summary: In this article, a restarting polynomial Krylov method is presented for modeling 3-D large-scale TEM responses. The method utilizes the mimetic finite volume method for spatial discretization and does not require solving large-scale linear equations. It achieves high accuracy and uses limited memory.
IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING
(2022)
Review
Mechanics
R. A. S. Frantz, J. -Ch. Loiseau, J. -Ch. Robinet
Summary: In fluid dynamics, predicting and characterizing bifurcations, from the onset of unsteadiness to the transition to turbulence, is crucial. This review presents a concise theoretical and numerical framework for computing and analyzing stability of high-dimensional systems. The methods discussed are implemented in an open-source toolbox, nekStab, and their accuracy and performance are demonstrated using standard benchmarks.
APPLIED MECHANICS REVIEWS
(2023)
Article
Geosciences, Multidisciplinary
Kailiang Lu, Jianmei Zhou, Xiu Li, Ya'nan Fan, Zhipeng Qi, Huake Cao
Summary: In this paper, the combination of the Shift-and-Invert Krylov (SAI-Krylov) subspace method and the preconditioned conjugate gradient method (PCG) is used to solve the problem of 3D large-scale time-domain transient electromagnetic (TEM) forward modeling. The optimal shift gamma(opt) is selected based on the relationship between the condition number of the coefficient matrix and shift gamma to improve the computation efficiency. The validity and applicability of the proposed method are verified through various models.
JOURNAL OF APPLIED GEOPHYSICS
(2022)
Article
Mathematics, Applied
M. A. Hamadi, K. Jbilou, A. Ratnani
Summary: In this paper, a new block Krylov-type subspace method for model reduction in large scale dynamical systems is proposed. The method projects the initial problem onto a new subspace, generated as a combination of rational and polynomial block Krylov subspaces, and establishes expressions of the error between the original and reduced transfer functions. An adaptive strategy of the interpolation points is presented for constructing the new block Krylov subspace, and the method is shown to be effective in extracting approximate low rank solutions of large-scale Lyapunov equations. Numerical results on benchmark examples confirm the performance of the method compared to other known methods.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Bernhard Beckermann, Alice Cortinovis, Daniel Kressner, Marcel Schweitzer
Summary: This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) subject to low-rank modifications. The analysis shows the usefulness of the derived error bounds for guiding the choice of poles in the rational Krylov method. Additionally, a connection between low-rank updates of the matrix sign function and existing rational Krylov subspace methods is pointed out.
SIAM JOURNAL ON NUMERICAL ANALYSIS
(2021)
Article
Water Resources
Mojtaba Forghani, Yizhou Qian, Jonghyun Lee, Matthew Farthing, Tyler Hesser, Peter K. Kitanidis, Eric F. Darve
Summary: This article presents a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE) to compress bathymetry and flow velocity information, allowing for fast solving of bathymetry inverse problems. By constructing ROMs on a nonlinear manifold and employing a Hierarchical Bayesian setting, variational inference and efficient uncertainty quantification can be achieved using a small number of ROM runs.
ADVANCES IN WATER RESOURCES
(2022)
Article
Mathematics, Applied
Peter Chang-Yi Weng
Summary: The article discusses the solution to the large-scale nonsymmetric algebraic Riccati equation using a structure-preserving doubling algorithm. By applying the appropriate mathematical formulas and sparse plus-low-rank representations, the algorithm achieves a computational complexity of O(n) and essentially quadratic convergence.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
F. Bouyghf, A. Messaoudi, H. Sadok
Summary: In this paper, a comprehensive framework for studying Krylov subspace methods is presented. The mathematical properties of these methods are analyzed, their relationship with other methods is explored, and improvements are proposed. Concrete numerical examples are provided to validate the performance of the algorithms.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Lakhlifa Sadek, Hamad Talibi Alaoui
Summary: This paper proposes two new methods for solving large-scale systems of differential equations based on the Krylov method. The first method obtains the exact solution using the exponential projection technique of the matrix. The second method reduces the problem size and employs different solving approaches, such as Rosenbrock and BDF. Theoretical results and numerical comparisons of the two methods are presented in the paper.
RICERCHE DI MATEMATICA
(2021)
Article
Mathematics, Applied
Viet Q. H. Huynh, Hiroshi Suito
Summary: Recently, a new variant of the BiCGStab method called pipelined BiCGStab has been proposed. It achieves higher scalability and speed-up rates by overlapping the communication phase for inner product computation with matrix-vector computation. Other generalized iteration methods like ssBiCGSafe, BiCGSafe, and GPBi-CG have better convergence behavior than BiCGStab, with ssBiCGSafe being best suited for high-performance computing systems. Inspired by pipelined BiCGStab, we propose pipelined variations of the ss-BiCGSafe method that only require one phase of inner product computation per iteration, showing improved convergence and execution time compared to pipelined BiCGStab and ssBiCGSafe.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Civil
Huiyang Qiu, Rui Hu, Ning Luo, Walter A. Illman, Xiaolan Hou
Summary: This paper compares the performances of travel-time based inversion (TTI) and geostatistical inversion (GI) approaches in hydraulic tomography (HT). The results show that TTI can better reveal the structural features of high-diffusivity zones and requires less data for inverse modeling. On the other hand, GI can estimate parameters throughout the simulation domain, better characterize low-diffusivity zones, and generate the best estimated tomogram for accurate drawdown predictions.
JOURNAL OF HYDROLOGY
(2023)
Article
Acoustics
Hongdong Wang, Jianyao Wang, Zhuyong Liu
Summary: The finite element method is widely used for flexible bodies with contact-impact problems. The partition method effectively reduces the system's degrees of freedom while maintaining accuracy. In the model reduction of contact-impact problems, the Krylov subspace method outperforms the modal truncation method.
JOURNAL OF VIBRATION AND CONTROL
(2022)
Article
Geosciences, Multidisciplinary
Abdullah Cihan, Robin Petrusak, Pramod Bhuvankar, David Alumbaugh, Robert Trautz, Jens T. Birkholzer
Summary: The migration of clay fines in brine-saturated sandstone formations can lead to pore clogging and permeability decline when less saline fluids are injected. Numerical modeling and pressure buildup data suggest that permeability near the injection well can rapidly decrease within the first hour of injection.
Article
Engineering, Chemical
Pramod Bhuvankar, Abdullah Cihan, Jens Birkholzer
Summary: This study investigates mechanisms of permeability impairment caused by low-salinity fluid injection into brine-saturated porous media containing dispersible clays. A computational fluid dynamics model at the pore-scale is used to simulate detachment, migration, and straining of fine particles, showing the impact of salinity and velocity on clay fines concentration and the clogging of narrow pore spaces.
CHEMICAL ENGINEERING SCIENCE
(2022)
Article
Energy & Fuels
Yingqi Zhang, Curtis M. Oldenburg, Quanlin Zhou, Lehua Pan, Barry M. Freifeld, Pierre Jeanne, Veronica Rodriguez Tribaldos, Donald W. Vasco
Summary: Ensuring the safety and integrity of underground gas storage (UGS) infrastructure is crucial for energy reliability in California and worldwide. The Integrated Risk Management and Decision Support System (IRMDSS) combines advanced monitoring and simulation technologies to provide real-time data and simulation tools to UGS operators, alerting them to potential failures, detecting early leakage, and supporting mitigation decision-making to prevent larger failures. The system can analyze temperature and pressure responses to hypothetical leaks, identify gas-water-contact depth, provide early warning signals, estimate leak rates, and support mitigation decisions.
JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING
(2022)
Review
Geochemistry & Geophysics
H. S. Viswanathan, J. Ajo-Franklin, J. T. Birkholzer, J. W. Carey, Y. Guglielmi, J. D. Hyman, S. Karra, L. J. Pyrak-Nolte, H. Rajaram, G. Srinivasan, D. M. Tartakovsky
Summary: Quantitative prediction of phenomena in fractured rock is a major challenge in Earth and Energy Sciences. Recent advances in research have improved understanding and prediction of flow and transport in fractured systems, with applications in various fields.
REVIEWS OF GEOPHYSICS
(2022)
Article
Engineering, Chemical
Boris Faybishenko, Yifeng Wang, Jon Harrington, Elena Tamayo-Mas, Jens Birkholzer, Carlos Jove-Colon
Summary: Understanding gas migration in compacted clay materials is crucial for the design and performance assessment of radioactive waste repositories and other applications. Existing research shows that the complexity of gas migration can be explained using nonlinear dynamics and chaos theory, which helps establish basic principles and predictive models.
TRANSPORT IN POROUS MEDIA
(2022)
Article
Geochemistry & Geophysics
Bin Chen, Quanlin Zhou
Summary: In this study, the thermal fracturing behavior of low-permeability formations was investigated using a plane strain model. It was found that the fracture length increases linearly with the square root of cooling time, and the propagation speed is slower for larger inter-fracture spacing. Both stress interaction and fracture arrest have an effect on the fracture behavior.
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
(2022)
Article
Engineering, Geological
Jens T. Birkholzer, Alexander E. Bond
Summary: The DECOVALEX Project is an international collaboration aimed at advancing the understanding and modeling of coupled THMC processes in geological systems. DECOVALEX-2019, a part of this project, started in 2016 and ended in 2019, involving modeling teams from 13 international partner organizations.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2022)
Article
Environmental Sciences
A. Cihan, C. M. Oldenburg, J. T. Birkholzer
Summary: This study presents a semi-analytical model for studying hydraulic head and brine leakage in multilayered aquifer-aquitard systems with geologic pressure forcing. The results show that even though suitable permeable aquitards can dissipate pressure rapidly, geologic forcing may cause sustained brine leakage into freshwater aquifers through leaky wells.
WATER RESOURCES RESEARCH
(2022)
Article
Environmental Sciences
Lijing Wang, Peter K. Kitanidis, Jef Caers
Summary: Bayesian inversion is commonly used to quantify uncertainty of hydrological variables. This paper proposes a hierarchical Bayesian framework to quantify uncertainty of both global and spatial variables. The authors present a machine learning-based inversion method and a local dimension reduction method to efficiently estimate posterior probabilities and update spatial fields. Using three case studies, they demonstrate the importance of quantifying uncertainty of global variables for predictions and the acceleration effect of the local PCA approach.
WATER RESOURCES RESEARCH
(2022)
Article
Water Resources
Mojtaba Forghani, Yizhou Qian, Jonghyun Lee, Matthew Farthing, Tyler Hesser, Peter K. Kitanidis, Eric F. Darve
Summary: This article presents a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE) to compress bathymetry and flow velocity information, allowing for fast solving of bathymetry inverse problems. By constructing ROMs on a nonlinear manifold and employing a Hierarchical Bayesian setting, variational inference and efficient uncertainty quantification can be achieved using a small number of ROM runs.
ADVANCES IN WATER RESOURCES
(2022)
Article
Environmental Sciences
Xueyuan Kang, Amalia Kokkinaki, Xiaoqing Shi, Hongkyu Yoon, Jonghyun Lee, Peter K. Kitanidis, Jichun Wu
Summary: This study presents a framework that combines a deep-learning-based inversion method with a process-based upscaled model to estimate source zone architecture (SZA) metrics and mass discharge from sparse data. By improving the estimation method, the upscaled model accurately reproduces the concentrations and uncertainties of multistage effluents, providing valuable input for decision making in remediation applications.
WATER RESOURCES RESEARCH
(2022)
Article
Chemistry, Physical
Chun Chang, Sharon Borglin, Chunwei Chou, LianGe Zheng, Yuxin Wu, Timothy J. Kneafsey, Seiji Nakagawa, Marco Voltolini, Jens T. Birkholzer
Summary: A bench-scale experiment was conducted to investigate the behavior of bentonite under high temperatures and its coupled THMC processes. The results showed that the hydration process was axi-symmetrical, but there were density variations and potential risks of sulfate precipitation at high temperatures. These findings provide valuable insights for improving modeling and designing more economical repositories for high-level radioactive waste.
APPLIED CLAY SCIENCE
(2023)
Article
Geochemistry & Geophysics
Louis De Barros, Yves Guglielmi, Frederic Cappa, Christophe Nussbaum, Jens Birkholzer
Summary: Fault slip induced by fluid perturbation in shale formations can impact the integrity of shale caprocks for reservoirs holding buoyant fluids, and a better understanding of these processes is critical for reservoir monitoring. In this study, seismic responses of a shale fault exposed to fluid pressurization during an injection experiment were analyzed. Two types of seismic signals were observed: tremors associated with fluid-induced slip propagation, and micro-earthquakes triggered by stress perturbations. Tremors serve as a more direct observation for fluid-induced slip, providing a useful tool for monitoring fluid leakage and sealing integrity.
GEOPHYSICAL JOURNAL INTERNATIONAL
(2023)
Article
Environmental Sciences
Simon Meunier, Peter K. Kitanidis, Amaury Cordier, Alan M. MacDonald
Summary: This study develops a numerical model to simulate the abstraction capacities of photovoltaic water pumping systems across Africa using openly available data. The model includes realistic geological constraints on pumping depth and sub-hourly irradiance time series. The simulation results show that for much of Africa, groundwater pumping using photovoltaic energy is limited by aquifer conditions rather than irradiance. These findings can help identify regions with high potential for photovoltaic pumping and guide large-scale investments.
COMMUNICATIONS EARTH & ENVIRONMENT
(2023)
Article
Green & Sustainable Science & Technology
Pramod Bhuvankar, Abdullah Cihan, Jens Birkholzer
Summary: It is important to evaluate the risks associated with CO2 leakage in large scale carbon capture and storage (CCS) projects. Leaky wells are considered a major concern for potential CO2 leakage in geologic carbon storage. We present a numerical framework to simulate blowouts of CO2 wells accounting for the supercritical-liquid-gas-solid phase transitions of CO2 during the process. Our simulations show that when the temperature and pressure at the well bottom are significantly lower than the geothermal temperature and hydrostatic pressure at the given depth, CO2 is released as dry ice at the wellhead.
INTERNATIONAL JOURNAL OF GREENHOUSE GAS CONTROL
(2023)