Domain Decomposition Algorithms for Indefinite Elliptic Problems. - Xiao-Chuan Cai; Olof B. Widlund (SIAM J. Sci. Comput., 1992)

Graph Decomposition Techniques for General Sparse Matrices. - Xiao-Chuan Cai; Yousef Saad (PPSC, 1993)

An Optimal Two-Level Overlapping Domain Decomposition Method for Elliptic Problems in Two and Three Dimensions. - Xiao-Chuan Cai (SIAM J. Sci. Comput., 1993)

A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems. - Xiao-Chuan Cai; William D. Gropp; David E. Keyes (Numer. Linear Algebra Appl., 1994)

Multiplicative Schwarz Methods for Parabolic Problems. - Xiao-Chuan Cai (SIAM J. Sci. Comput., 1994)

1. A Family of Overlapping Schwarz Algorithms for Nonsymmetric and Indefinite Elliptic Problems. - Xiao-Chuan Cai (Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering, 1995)

The Use of Pointwise Interpolation in Domain Decomposition Methods with Nonnested Meshes. - Xiao-Chuan Cai (SIAM J. Sci. Comput., 1995)

Overlapping Domain Decomposition Algorithms for General Sparse Matrices. - Xiao-Chuan Cai; Yousef Saad (Numer. Linear Algebra Appl., 1996)

Parallel Newton-Krylov-Schwarz Algorithms for the Transonic Full Potential Equation. - Xiao-Chuan Cai; William D. Gropp; David E. Keyes; Robin G. Melvin; David P. Young (SIAM J. Sci. Comput., 1998)

Parallel Newton-Krylov-Schwarz Method for Solving Nonlinear PDEs on Moving Grids. - Xiao-Chuan Cai; Maria Murillo (PP, 1999)

A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems. - Xiao-Chuan Cai; Marcus Sarkis (SIAM J. Sci. Comput., 1999)

Maximum Norm Analysis of Overlapping Nonmatching Grid Discretizations of Elliptic Equations. - Xiao-Chuan Cai; Tarek P. Mathew; Marcus V. Sarkis (SIAM J. Numer. Anal., 2000)

Parallel Newton-Krylov-Schwarz Method for Solving the Anisotropic Bidomain Equations from the Excitation of the Heart Model. - Maria Murillo; Xiao-Chuan Cai (International Conference on Computational Science (1), 2002)

Some observations on the l2 convergence of the additive Schwarz preconditioned GMRES method. - Xiao-Chuan Cai; Jun Zou (Numer. Linear Algebra Appl., 2002)

Nonlinearly Preconditioned Inexact Newton Algorithms. - Xiao-Chuan Cai; David E. Keyes (SIAM J. Sci. Comput., 2002)

Restricted Additive Schwarz Preconditioners with Harmonic Overlap for Symmetric Positive Definite Linear Systems. - Xiao-Chuan Cai; Maksymilian Dryja; Marcus Sarkis (SIAM J. Numer. Anal., 2003)

A Combined Linear and Nonlinear Preconditioning Technique for Incompressible Navier-Stokes Equations. - Feng-Nan Hwang; Xiao-Chuan Cai (PARA, 2004)

Domain Decomposition Methods for PDE Constrained Optimization Problems. - Ernesto E. Prudencio; Richard H. Byrd; Xiao-Chuan Cai (VECPAR, 2004)

A fully implicit parallel algorithm for simulating the non-linear electrical activity of the heart. - Maria Murillo; Xiao-Chuan Cai (Numer. Linear Algebra Appl., 2004)

One-level Newton-Krylov-Schwarz algorithm for unsteady non-linear radiation diffusion problem. - Serguei Ovtchinnikov; Xiao-Chuan Cai (Numer. Linear Algebra Appl., 2004)

Parallel Full Space SQP Lagrange-Newton-Krylov-Schwarz Algorithms for PDE-Constrained Optimization Problems. - Ernesto E. Prudencio; Richard H. Byrd; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2006)

Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems. - Serguei Ovtchinnikov; Florin Dobrian; Xiao-Chuan Cai; David E. Keyes (J. Comput. Phys., 2007)

Parallel Domain Decomposition Methods for Stochastic Elliptic Equations. - Chao Jin; Xiao-Chuan Cai; Congming Li (SIAM J. Sci. Comput., 2007)

Parallel Multilevel Restricted Schwarz Preconditioners with Pollution Removing for PDE-Constrained Optimization. - Ernesto E. Prudencio; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2007)

A Domain Decomposition Based Parallel Inexact Newton's Method with Subspace Correction for Incompressible Navier-Stokes Equations. - Xiao-Chuan Cai; Xuefeng Li (ICCS (1), 2009)

Scalability Studies of an Implicit Shallow Water Solver for the Rossby-Haurwitz Problem. - Chao Yang 002; Xiao-Chuan Cai (VECPAR, 2010)

Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling. - Andrew T. Barker; Xiao-Chuan Cai (J. Comput. Phys., 2010)

Two-Level Newton and Hybrid Schwarz Preconditioners for Fluid-Structure Interaction. - Andrew T. Barker; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2010)

A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere. - Chao Yang 002; Jianwen Cao 001; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2010)

A parallel well-balanced finite volume method for shallow water equations with topography on the cubed-sphere. - Chao Yang 002; Xiao-Chuan Cai (J. Comput. Appl. Math., 2011)

Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on the cubed-sphere. - Chao Yang 002; Xiao-Chuan Cai (J. Comput. Phys., 2011)

Parallel Two-Grid Semismooth Newton-Krylov-Schwarz Method for Nonlinear Complementarity Problems. - Haijian Yang; Xiao-Chuan Cai (J. Sci. Comput., 2011)

Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity. - Xiao-Chuan Cai; Xuefeng Li (SIAM J. Sci. Comput., 2011)

Special Section: 2010 Copper Mountain Conference. - Ray Tuminaro; Michele Benzi; Xiao-Chuan Cai; Iain Duff; Howard C. Elman; Roland Freund; Kirk E. Jordan; Tim Kelley; David E. Keyes; Misha Elena Kilmer; Sven Leyffer; Tom Manteuffel; et al. (SIAM J. Sci. Comput., 2011)

Numerical Design of an Optimal Bypass for a Partially Blocked Artery. - Rongliang Chen; Xiao-Chuan Cai (IPDPS Workshops, 2012)

Scalable Parallel Algorithms for Boundary Control of Thermally Convective Flows. - Haijian Yang; Xiao-Chuan Cai (IPDPS Workshops, 2012)

A Hybrid Implementation of Two-Level Domain Decomposition Algorithm for Solving Elliptic Equation on CPU/GPUs. - Li Luo 003; Yubo Zhao; Xiao-Chuan Cai (PDCAT, 2012)

Parallel One-Shot Lagrange-Newton-Krylov-Schwarz Algorithms for Shape Optimization of Steady Incompressible Flows. - Rongliang Chen; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2012)

A Scalable Implicit Solver for Phase Field Crystal Simulations. - Chao Yang 002; Xiao-Chuan Cai (IPDPS Workshops, 2013)

A parallel fully coupled implicit domain decomposition method for numerical simulation of microfluidic mixing in 3D. - Feng-Nan Hwang; Xiao-Chuan Cai; Yu-Lun Cheng; Chia-Wen Tsao (Int. J. Comput. Math., 2013)

One-Shot Domain Decomposition Methods for Shape Optimization Problems. - Rongliang Chen; Xiao-Chuan Cai (Domain Decomposition Methods in Science and Engineering XX, 2013)

A Parallel Monolithic Domain Decomposition Method for Blood Flow Simulations in 3D. - Yuqi Wu; Xiao-Chuan Cai (Domain Decomposition Methods in Science and Engineering XX, 2013)

Two-Grid LNKSz for Distributed Control of Unsteady Incompressible Flows. - Haijian Yang; Xiao-Chuan Cai (Domain Decomposition Methods in Science and Engineering XX, 2013)

A Fully Implicit Compressible Euler Solver for Atmospheric Flows. - Chao Yang 002; Xiao-Chuan Cai (Domain Decomposition Methods in Science and Engineering XX, 2013)

A fully implicit domain decomposition based ALE framework for three-dimensional fluid-structure interaction with application in blood flow computation. - Yuqi Wu; Xiao-Chuan Cai (J. Comput. Phys., 2014)

A Parallel Domain Decomposition Method for 3D Unsteady Incompressible Flows at High Reynolds Number. - Rongliang Chen; Yuqi Wu; Zhengzheng Yan; Yubo Zhao; Xiao-Chuan Cai (J. Sci. Comput., 2014)

Parallel Domain Decomposition Methods with Mixed Order Discretization for Fully Implicit Solution of Tracer Transport Problems on the Cubed-Sphere. - Haijian Yang; Chao Yang 002; Xiao-Chuan Cai (J. Sci. Comput., 2014)

Implicit Space-Time Domain Decomposition Methods for Stochastic Parabolic Partial Differential Equations. - Cui Cong; Xiao-Chuan Cai; Karl Gustafson (SIAM J. Sci. Comput., 2014)

A Scalable Fully Implicit Compressible Euler Solver for Mesoscale Nonhydrostatic Simulation of Atmospheric Flows. - Chao Yang 002; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2014)

Two-level space-time domain decomposition methods for unsteady inverse problems. - Xiaomao Deng; Xiao-Chuan Cai; Jun Zou (CoRR, 2015)

A parallel domain decomposition-based implicit method for the Cahn-Hilliard-Cook phase-field equation in 3D. - Xiang Zheng; Chao Yang 002; Xiao-Chuan Cai; David E. Keyes (J. Comput. Phys., 2015)

Convergence Analysis of Two-Level Space-Time Additive Schwarz Method for Parabolic Equations. - Shishun Li; Xiao-Chuan Cai (SIAM J. Numer. Anal., 2015)

A Fully Implicit Method for Lattice Boltzmann Equations. - Jizu Huang; Chao Yang 002; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2015)

Parallel two-level domain decomposition based Jacobi-Davidson algorithms for pyramidal quantum dot simulation. - Tao Zhao; Feng-Nan Hwang; Xiao-Chuan Cai (Comput. Phys. Commun., 2016)

Two-Level Space-Time Domain Decomposition Methods for Three-Dimensional Unsteady Inverse Source Problems. - Xiaomao Deng; Xiao-Chuan Cai; Jun Zou 003 (J. Sci. Comput., 2016)

A Nonlinearly Preconditioned Inexact Newton Algorithm for Steady State Lattice Boltzmann Equations. - Jizu Huang; Chao Yang 002; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2016)

A Highly Scalable Multilevel Schwarz Method with Boundary Geometry Preserving Coarse Spaces for 3D Elasticity Problems on Domains with Complex Geometry. - Fande Kong; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2016)

Nonlinear Preconditioning Techniques for Full-Space Lagrange-Newton Solution of PDE-Constrained Optimization Problems. - Haijian Yang; Feng-Nan Hwang; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2016)

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D. - Fande Kong; Xiao-Chuan Cai (J. Comput. Phys., 2017)

An efficient finite element method for simulation of droplet spreading on a topologically rough surface. - Li Luo 003; Xiao-Ping Wang 002; Xiao-Chuan Cai (J. Comput. Phys., 2017)

A Parallel Finite Element Method for 3D Two-Phase Moving Contact Line Problems in Complex Domains. - Li Luo 003; Qian Zhang 007; Xiao-Ping Wang 002; Xiao-Chuan Cai (J. Sci. Comput., 2017)

Two-Level Space-Time Domain Decomposition Methods for Flow Control Problems. - Haijian Yang; Xiao-Chuan Cai (J. Sci. Comput., 2017)

Simulation of unsteady blood flows in a patient-specific compliant pulmonary artery with a highly parallel monolithically coupled fluid-structure interaction algorithm. - Fande Kong; Vitaly O. Kheyfets; Ender A. Finol; Xiao-Chuan Cai (CoRR, 2018)

Scalability study of an implicit solver for coupled fluid-structure interaction problems on unstructured meshes in 3D. - Fande Kong; Xiao-Chuan Cai (Int. J. High Perform. Comput. Appl., 2018)

Multilevel Space-Time Additive Schwarz Methods for Parabolic Equations. - Shishun Li; Xinping Shao; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2018)

Highly parallel space-time domain decomposition methods for parabolic problems. - Shishun Li; Xinping Shao; Xiao-Chuan Cai (CCF Trans. High Perform. Comput., 2019)

A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis. - Li Luo 003; Wen-Shin Shiu; Rongliang Chen; Xiao-Chuan Cai (J. Comput. Phys., 2019)

基于非结构化网格的高可扩展并行有限体积格子 (Scalable Parallel Finite Volume Lattice Boltzmann Method Based on Unstructured Grid). - Lei Xu; Rongliang Chen; Xiao-Chuan Cai (计算机科学, 2019)

A Nonlinear Elimination Preconditioned Inexact Newton Method for Heterogeneous Hyperelasticity. - Shihua Gong; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2019)

Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids. - Li Luo 003; Lulu Liu; Xiao-Chuan Cai; David E. Keyes (J. Comput. Phys., 2020)

A Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions. - Li Luo 003; Xiao-Chuan Cai; Zhengzheng Yan; Lei Xu; David E. Keyes (SIAM J. Sci. Comput., 2020)

Fusing 2D and 3D convolutional neural networks for the segmentation of aorta and coronary arteries from CT images. - Linyan Gu; Xiao-Chuan Cai (Artif. Intell. Medicine, 2021)

Efficient parallel simulation of hemodynamics in patient-specific abdominal aorta with aneurysm. - Shanlin Qin; Bokai Wu; Jia Liu 017; Wen-Shin Shiu; Zhengzheng Yan; Rongliang Chen; Xiao-Chuan Cai (Comput. Biol. Medicine, 2021)

Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems. - Wenpeng Ma; Xiao-Chuan Cai (Int. J. High Perform. Comput. Appl., 2021)

A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations. - Xiaomao Deng; Zi-Ju Liao; Xiao-Chuan Cai (J. Comput. Appl. Math., 2021)

A central-line coarse preconditioner for Stokes flows in artery-like domains. - Yingzhi Liu; Xiao-Chuan Cai (Numer. Algorithms, 2021)

Summation pollution of principal component analysis and an improved algorithm for location sensitive data. - Jingwei Li; Xiao-Chuan Cai (Numer. Linear Algebra Appl., 2021)

Nonlinear Preconditioning Strategies for Two-Phase Flows in Porous Media Discretized by a Fully Implicit Discontinuous Galerkin Method. - Li Luo 003; Xiao-Chuan Cai; David E. Keyes (SIAM J. Sci. Comput., 2021)

An efficient two-level overlapping domain decomposition method for recovering unsteady sources of 3D parabolic problems. - Xiaomao Deng; Zi-Ju Liao; Xiao-Chuan Cai (Comput. Math. Appl., 2022)

Evaluation of cerebrovascular hemodynamics in vascular dementia patients with a new individual computational fluid dynamics algorithm. - Jian Xie; Zaiheng Cheng; Lihua Gu; Bokai Wu; Gaojia Zhang; Wen-Shin Shiu; Rongliang Chen; Zan Wang; Chang Liu 009; Jie Tu; Xiao-Chuan Cai; Jia Liu 017; et al. (Comput. Methods Programs Biomed., 2022)

Large eddy simulation of the wind flow in a realistic full-scale urban community with a scalable parallel algorithm. - Zhengzheng Yan; Rongliang Chen; Xiao-Chuan Cai (Comput. Phys. Commun., 2022)

A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM. - Xingding Chen; Xiao-Chuan Cai (J. Comput. Phys., 2022)

A Nonlinear Elimination Preconditioned Inexact Newton Algorithm. - Lulu Liu; Feng-Nan Hwang; Li Luo 003; Xiao-Chuan Cai; David E. Keyes (SIAM J. Sci. Comput., 2022)

An Interactive Platform for a High Performance Digital Twin of a Human Heart. - Yujie Gong; Fenfen Qi; Jing-Yuan Wang; Yingzhi Liu; Tianhao Ma; Zaiheng Cheng; Yi Jiang; Rongliang Chen; Xinhong Wang; Li Luo 003; Xiao-Chuan Cai (MetaCom, 2023)

Two-level additive Schwarz methods for three-dimensional unsteady Stokes flows in patient-specific arteries with parameterized one-dimensional central-line coarse preconditioner. - Yingzhi Liu; Xiao-Chuan Cai (J. Comput. Phys., 2023)

A highly parallel fully implicit domain decomposition method for the simulation of the hemodynamics of a patient-specific artery at the full-body scale. - Shanlin Qin; Rongliang Chen; Bokai Wu; Xiao-Chuan Cai (J. Comput. Phys., 2023)

( text{PIN}^{ mathcal L} ) : Preconditioned Inexact Newton with Learning Capability for Nonlinear System of Equations. - Li Luo; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2023)

Impact of Pressure Wire on Fractional Flow Reserve and Hemodynamics of the Coronary Arteries: A Computational and Clinical Study. - Zhengzheng Yan; Zhifeng Yao 002; Weifeng Guo; Dandan Shang; Rongliang Chen; Jia Liu 017; Xiao-Chuan Cai; Junbo Ge (IEEE Trans. Biomed. Eng., 2023)

A-Stable High-Order Block Implicit Methods for Parabolic Equations. - Shishun Li; Jing-Yuan Wang; Xiao-Chuan Cai (SIAM J. Numer. Anal., 2023)

Mixed Reality Visualization and Interactive Hemodynamic Computation of the Human Brain. - Fenfen Qi; Yingzhi Liu; Yujie Gong; Jing-Yuan Wang; Jie Zhou; Rongliang Chen; Ruey-Song Huang; Xinhong Wang; Li Luo 003; Xiao-Chuan Cai (MetaCom, 2024)

A Collaborative Mixed Reality Platform for the Planning of Vascular Surgery. - Jing-Yuan Wang; Yujie Gong; Jie Zhou; Fenfen Qi; Yingzhi Liu; Zaiheng Cheng; Rongliang Chen; Xinhong Wang; Li Luo 003; Xiao-Chuan Cai (MetaCom, 2024)

Nonlinearly preconditioned semismooth Newton algorithms for nonlinear nonsmooth systems. - Haijian Yang; Tianhao Ma; Feng-Nan Hwang; Xiao-Chuan Cai (Int. J. Comput. Math., 2024)

Domain decomposed classification algorithms based on linear discriminant analysis: An optimality theory and applications. - Jingwei Li; Xiao-Chuan Cai (Neurocomputing, 2024)

A highly parallel algorithm for simulating the elastodynamics of a patient-specific human heart with four chambers using a heterogeneous hyperelastic model. - Yi Jiang; Zhengzheng Yan; Xinhong Wang; Rongliang Chen; Xiao-Chuan Cai (J. Comput. Phys., 2024)

A One-Dimensional Coarse Preconditioner for Three-Dimensional Unsteady Incompressible Navier-Stokes Flows in Patient-Specific Arteries. - Yingzhi Liu; Fenfen Qi; Xiao-Chuan Cai (SIAM J. Sci. Comput., 2024)

A computational study of the connection between coronary revascularization and cardio-cerebral hemodynamics. - Zhengzheng Yan; Dandan Shang; Rongliang Chen; Jia Liu 017; Xiao-Chuan Cai (Comput. Methods Programs Biomed., 2025)

A preconditioning method with the Generalized-α time discretization for dynamic crack propagations based on XFEM. - Xingding Chen; Xiao-Chuan Cai (J. Comput. Phys., 2025)

A fully implicit method for numerical simulation of blood flows with incompressible Navier-Stokes equations with slip and penetration boundary conditions. - Xiangdong Zhang; Li Luo; Ye Li; Xiao-Chuan Cai (J. Comput. Phys., 2025)

Multilevel Additive Schwarz Preconditioners for High-Order Block Implicit Methods for Parabolic Equations. - Shishun Li; Lei Xu; Xiao-Chuan Cai (Numer. Linear Algebra Appl., 2025)