• F. Qi, Y. Liu, Y. Gong, J.-Y. Wang, J. Zhou, R. Chen, R.-S. Huang, X. Wang, L. Luo, and X.-C. Cai, Mixed reality visualization and interactive hemodynamic computation of the human brain, IEEE International Conference on Metaverse Computing, Networking and Applications, (2024).
  • J.-Y. Wang, Y. Gong, J. Zhou, F. Qi, Y. Liu, Z. Cheng, R. Chen, X. Wang, L. Luo, and X.-C. Cai, A collaborative mixed reality platform for the planning of vascular surgery, IEEE International Conference on Metaverse Computing, Networking and Applications, (2024).
  • Y. Jiang, Z. Yan, X. Wang, R. Chen, and X.-C. Cai, A highly parallel algorithm for simulating the elastodynamics of a patient-specific human heart with four chambers using a heterogeneous hyperelastic model, Journal of Computational Physics, 508 (2024), p. 113027.
  • H. Yang, T.-H. Ma, F.-N. Huang, and X.-C. Cai, Nonlinearly preconditioned semismooth Newton algorithms for nonlinear nonsmooth systems, International Journal of Computer Mathematics, 101 (2024), p. 1-22.
  • Y. Liu, F. Qi, and X.-C. Cai, A one-dimensional coarse preconditioner for three-dimensional unsteady incompressible Navier-Stokes flows in patient-specific arteries, SIAM Journal of Scientific Computing, 46 (2024), p. S1-S23.
  • J. Li and X.-C. Cai, Domain decomposed classification algorithms based on linear discriminant analysis: An optimality theory and applications, Neurocomputing, (2024).
  • Y. Liu, F. Qi, and X.-C. Cai, An aneurysm-specific preconditioning technique for the acceleration of Newton-Krylov method with application in the simulation of blood flow, International Journal for Numerical Methods in Biomedical Engineering, (2023).
  • Y. Gong, F. Qi, Y. Liu, J.-Y. Wang, T. Ma, Z. Cheng, Y. Jiang, R. Chen, X. Wang, L. Luo, and X.-C. Cai, An interactive platform for a high performance digital twin of a human heart, IEEE International Conference on Metaverse Computing, Networking and Applications, (2023).
  • S. Li, J. Wang, and X.-C. Cai, A-stable high order block implicit methods for parabolic equations, SIAM J. Num. Anal., (2023).
  • Y. Liu and X.-C. Cai, Two-level additive Schwarz methods for three-dimensional unsteady Stokes flows in patient-specific arteries with parameterized one-dimensional central-line coarse preconditioner, Journal of Computational Physics, 490 (2023), p. 112290.
  • L. Luo and X.-C. Cai, PIN_L: Preconditioned inexact Newton with learning capability for nonlinear system of equations, SIAM J. Sci. Comput., 45 (2023), p. A849-A871.
  • Z. Lin, B. Wu, S. Qin, X. Wang, R. Chen, and X.-C. Cai, Numerical calculation of the portal pressure gradient of the human liver with a domain decomposition method, Domain Decomposition Methods in Science and Engineering XXVI, (2023), p. 161-168.
  • L. Gu, W. Zhang, J. Liu, and X.-C. Cai, Decomposition and preconditioning of deep convolutional neural networks for training acceleration, Domain Decomposition Methods in Science and Engineering XXVI, (2023), p. 153-160.
  • L. Luo, X.-C. Cai, and D.E. Keyes, A parallel adaptive finite element method for modeling a deformable droplet travelling in air, Domain Decomposition Methods in Science and Engineering XXVI, (2023), p. 169-176.
  • S. Laudenschlager and X.-C. Cai, An inner-outer subcycling algorithm for parallel cardiac electrophysiology simulations, International Journal for Numerical Methods in Biomedical Engineering, 39 (2023), p. e3677.
  • S. Qin, R. Chen, B. Wu, and X.-C. Cai, A highly parallel fully implicit domain decomposition method for the simulation of the hemodynamics of a patient-specific artery at the full-body scale, J. Comput. Phys., 472 (2023), p. 111730.
  • L. Gu, W. Zhang, J. Liu, and X.-C. Cai, Decomposition and composition of deep convolutional neural networks and training acceleration via sub-network transfer learning, Electronic Transactions on Numerical Analysis, 56 (2022), pp. 157-186.
  • Z. Yan, Z. Yao, W. Guo, D. Shang, R. Chen, J. Liu, X.-C. Cai, and J. Ge, Impact of the pressure wire on the measured fractional flow reserve and hemodynamics: A combined computational and clinical study, IEEE Transactions on Biomedical Engineering, (2022).
  • Y. Liu, F. Qi, and X.-C. Cai, A one-dimensional coarse preconditioner for three-dimensional unsteady incompressible Navier-Stokes flows in patient-specific arteries, SIAM J. Sci. Comput., (2022).
  • X. Deng, Z.-J. Liao, and X.-C. Cai, An efficient two-level overlapping domain decomposition method for recovering unsteady sources of 3D parabolic problems, Computers & Mathematics with Applications, 111 (2022), p. 98-108.
  • X. Chen and X.-C. Cai, A recycling preconditioning method with auxiliary tip subspace for elastic crack propagation simulation using XFEM, Journal of Computational Physics, 452 (2022), p. 110910.
  • L. Liu, F.-N. Hwang, L. Luo, X.-C. Cai, and D.E. Keyes, A nonlinear elimination preconditioned inexact Newton algorithm, SIAM Journal on Scientific Computing, 44 (2022), p. A1579-A1605.
  • Z. Lin, B. Wu, S. Qin, X. Wang, R. Chen, and X.-C. Cai, Numerical calculation of the portal pressure gradient of the human liver with a domain decomposition method, Proceedings of the 26th International Conference on Domain Decomposition Methods, Springer, (2022).
  • L. Luo, X.-C. Cai, and D.E. Keyes, A parallel adaptive finite element method for modeling a deformable droplet travelling in air, Proceedings of the 26th International Conference on Domain Decomposition Methods, Springer, (2022).
  • L. Gu, W. Zhang, J. Liu, and X.-C. Cai, Decomposition and preconditioning of deep convolutional neural networks for training acceleration, Proceedings of the 26th International Conference on Domain Decomposition Methods, Springer, (2022).
  • Z.-J. Liao, S. Qin, R. Chen, and X.-C. Cai, A parallel domain decomposition method for large eddy simulation of blood flow in human artery with resistive boundary condition, Computers and Fluids, 232 (2022), p. 105201.
  • J. Xie, Z. Cheng, L. Gu, B. Wu, G. Zhang, W. Shiu, R. Chen, Z. Wang, C. Liu, J. Tu, and X.-C. Cai,  Evaluation of cerebrovascular hemodynamics in vascular dementia patients with a new individual computational fluid dynamics algorithm, Comput. Methods Programs Biomed., 213 (2022), p. 106497.
  • Z. Yan, R. Chen, and X.-C. Cai, Large eddy simulation of the wind flow in a realistic full-scale urban community with a scalable parallel algorithm, Comput. Phys. Commun., 270 (2022), p. 108170.
  • L. Gu and X.-C. Cai, Fusing 2D and 3D convolutional neural networks for the segmentation of aorta and coronary arteries from CT images, Artif. Intell. Med., 121 (2021), pp. 102189.
  • S. Qin, B. Wu, J. Liu, W.-S. Shiu, Z. Yan, R. Chen, and X.-C. Cai, Efficient parallel simulation of hemodynamics in patient-specific abdominal aorta with aneurysm, Comput. Biol. Med., 136 (2021), p. 104652.
  • X. Deng, Z.-J. Liao, and X.-C. Cai, A parallel multilevel domain decomposition method for source identification problems governed by elliptic equations, J. Comput. Appl. Math., 392 (2021), p. 113441.
  • Y. Liu and X.-C. Cai, A central-line coarse preconditioner for Stokes flows in artery-like domains, Numer. Algorithm, 1 (2021), pp. 137-160.
  • Z. Lin, R. Chen, B. Gao, S. Qin, B. Wu, J. Liu, and X.-C. Cai, A highly parallel simulation of patient-specific hepatic flows, Inter. J. Numer. Methods Biomed. Eng., (2021), p. e3451.
  • L. Xu, R. Chen, and X.-C. Cai, Parallel finite-volume discrete Boltzmann method for inviscid compressible flows on unstructured grids, Phys. Rev. E, 2 (2021), p. 023306.
  • S. Qin, R. Chen, B. Wu, W.-S. Shiu, and X.-C. Cai, Numerical simulation of blood flows in patient-specific abdominal aorta with primary organs, Biomech. Model. Mechanobiol., (2021), pp. 1-16.
  • L. Luo, X.-C. Cai, and D.E. Keyes, Nonlinear preconditioning strategies for two-phase flows in porous media discretized by a fully implicit discontinuous Galerkin method, SIAM J. Sci. Comput., 0 (2021), pp. S317-S344.
  • J. Li and X.-C. Cai, Summation pollution of principal component analysis and an improved algorithm for location sensitive data, Numer. Linear Algebra Appl., (2021), p. e2370.
  • W. Ma and X.-C. Cai, Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems, Inter. J. High Perf. Comput. Appli., 2 (2020), pp. 121-135.
  • Y. Jiang, R. Chen, and X.-C. Cai, A highly parallel implicit domain decomposition method for the simulation of the left ventricle on unstructured meshes, Comput. Mech., 6 (2020), pp. 1461-1475.
  • R. Chen, B. Wu, Z. Cheng, W.-S. Shiu, J. Liu, L. Liu, Y. Wang, X. Wang, and X.-C. Cai, A parallel non-nested two-level domain decomposition method for simulating blood flows in cerebral artery of stroke patient, Inter. J. Numer. Methods Biomed. Eng., 11 (2020), p. e3392.
  • L. Luo, L. Liu, X.-C. Cai, and D.E. Keyes, Fully implicit hybrid two-level domain decomposition algorithms for two-phase flows in porous media on 3D unstructured grids, J. Comput. Phys., 409 (2020), p. 109312.
  • L. Luo, X.-C. Cai, Z. Yan, L. Xu, and D.E. Keyes, A multilayer nonlinear elimination preconditioned inexact Newton method for steady-state incompressible flow problems in three dimensions, SIAM J. Sci. Comput., 6 (2020), pp. B1404-B1428.
  • L. Luo, W.-S. Shiu, R. Chen, and X.-C. Cai, A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis, J. Comput. Phys., 399 (2019), p. 108926.
  • F. Kong, V. Kheyfets, E. Finol, and X.-C. Cai, Simulation of unsteady blood flows in a patient-specific compliant pulmonary artery with a highly parallel monolithically coupled fluid-structure interaction algorithm, Inter. J. Numer. Methods Biomed. Eng., 7 (2019), p. e3208.
  • S. Li, X. Shao, and X.-C. Cai, Highly parallel space-time domain decomposition methods for parabolic problems, CCF Transactions on High Performance Computing, 1 (2019), pp. 25-34.
  • Z.-J. Liao, R. Chen, Z. Yan, and X.-C. Cai, A parallel implicit domain decomposition algorithm for the large eddy simulation of incompressible turbulent flows on 3D unstructured meshes. Inter. J. Numer. Methods Fluids, 9 (2019), pp. 343-361.
  • R. Chen, J. Huang, and X.-C. Cai, A parallel domain decomposition algorithm for large scale image denoising, Inverse Probl. Imaging, 6 (2019), pp. 1259-1282.
  • S. Gong and X.-C. Cai, A nonlinear elimination preconditioned inexact Newton method for heterogeneous hyperelasticity, SIAM J. Sci. Comput., 5 (2019), pp. S390-S408.
  • R. Chen, Z. Yan, Y. Zhao, and X.-C. Cai, Scalable domain decomposition algorithms for simulation of flows passing full size wind turbine, Commun. Comput. Phys., 5 (2018), pp. 1503-1522.
  • S. Li, X. Shao, and X.-C. Cai, Multilevel space-time additive Schwarz methods for parabolic equations, SIAM J. Sci. Comput., 40 (2018), pp. A3012-A3037.
  • L. Luo, X.-P. Wang, and X.-C. Cai, An efficient finite element method for simulation of droplet spreading on a topologically rough surface, J. Comp. Phys., 349 (2017), pp. 233-252.
  • J. Huang, C. Yang, and X.-C. Cai, A fully implicit method for lattice Boltzmann equations, SIAM J. Sci. Comput., (2015).
  • X. Deng, X.-C. Cai, and J. Zou, A parallel space-time domain decomposition method for some unsteady source inversion problems, Inverse Prob. Imaging, (2015).
  • W.-S. Shiu, F.-N. Hwang, and X.-C. Cai, Parallel domain decomposition method for finite element approximation of 3D non-Newtonian fluids, Int. J. Numer. Methods in Fluids, 78 (2015), pp. 502-520.
  • F.-N. Hwang, Y.-C. Su, and X.-C. Cai, A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation, Computers and Fluids, 110 (2015), pp. 96-107.
  • X. Zheng, C. Yang, X.-C. Cai, and D. Keyes, A parallel domain decomposition based implicit method for the Cahn-Hilliard-Cook phase-field equation with thermal fluctuation in 3D, J. Comput. Phys., 285 (2015), pp. 55-70.
  • C. Cong, X.-C. Cai, and K. Gustafson, Implicit space-time domain decomposition methods for stochastic parabolic partial differential equations, SIAM J. Sci. Comput., 36 (2014), pp. C1-C24.
  • C. Yang and X.-C. Cai, A scalable fully implicit compressible Euler solver for mesoscale nonhydrostatic simulation of atmospheric flows, SIAM J. Sci. Comput., 36 (2014), S23-S47.
  • Y. Wu and X.-C. Cai, A fully implicit domain decomposition based ALE framework for three-dimensional fluid-structure interaction with application in blood flow computation, J. Comput. Phys., 258 (2014), pp. 524-537.
  • Z. Yan, R. Chen, Y. Zhao, and X.-C. Cai, A scalable numerical method for simulating flows around high-speed train under crosswind conditions, Comm. Comput. Phys., 15 (2014), pp. 944-958.
  • R. Chen, Y. Wu, Z. Yan, Y. Zhao, and X.-C. Cai, A parallel domain decomposition method for 3D unsteady incompressible flows at high Reynolds number, J. Sci. Comput., 58 (2014), pp. 275-289.
  • F. Kong and X.-C. Cai, A scalable Schwarz method for 3D linear elasticity problems on domains with complex geometry, SC13, (2013).
  • C. Yang and X.-C. Cai, A scalable implicit solver for phase field drystal simulations, IEEE IPDPS Workshop (2013).
  • H. Yang and X.-C. Cai, Parallel fully implicit two-grid Lagrange-Newton-Krylov-Schwarz methods for distributed control of unsteady incompressible flows, Intern. J. Numer. Methods in Fluids, 72 (2013), pp. 1-21.
  • F.-N. Hwang, X.-C. Cai, Y.-L. Cheng, and C.-W. Tsao, A parallel fully coupled implicit domain decomposition method for numerical simulation of microfluidic mixing in 3D, Intern. J. Comp. Math., 90 (2013), pp. 615-629.
  • R. Chen and X.-C. Cai, Parallel one-shot Lagrange-Newton-Krylov-Schwarz algorithms for shape optimization of steady incompressible flows, SIAM J. Sci. Comput., 34 (2012), pp. B584-B605.
  • H. Yang, E. Prudencio, and X.-C. Cai, Fully implicit Lagrange-Newton-Krylov-Schwarz algorithms for boundary control of unsteady incompressible flows, Int. J. Numer. Meth. Engin., 91 (2012), pp. 644-665.
  • L. Luo, C. Yang, Y. Zhao, and X.-C. Cai, A scalable hybrid algorithm based on domain decomposition and algebraic multigrid for solving partial differential equations on a cluster of CPU/GPUs, Proceedings of 2nd International Workshop on GPUs and Scientific Applications. In conjunction with 2011 International Conference on Parallel Architectures and Compilation Techniques (PACT 2011).
  • Y. Wu and X.-C. Cai, A parallel two-level method for simulating blood flows in branching arteries with the resistive boundary condition, Computers and Fluids, 45 (2011), pp. 92-102.
  • C. Yang and X.-C. Cai, Parallel multilevel methods for implicit solution of shallow water equations with nonsmooth topography on cubed-sphere, J. Comput. Phys., 230 (2011), pp. 2523-2539.
  • X.-C. Cai and X. Li, Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity, SIAM J. Sci. Comput., 33 (2011), pp. 746-762.
  • H. Yang and X.-C. Cai, Parallel two-grid semismooth Newton-Krylov-Schwarz method for nonlinear complementarity problems, J. Sci. Comput., 47 (2011), pp. 258-280.
  • F.-N. Hwang, H.-L. Lin, and X.-C. Cai, Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation, ETNA, 37 (2010), pp. 239-251.
  • H. Yang and X.-C. Cai, Domain decomposition methods for a complementarity problem, Lecture Notes in Computational Science and Engineering, Springer, (2010).
  • S. Liu and X.-C. Cai, Two-level multiplicative domain decomposition algorithm for recovering the Lame coefficient in biological tissues, Lecture Notes in Computational Science and Engineering, Springer, (2010).
  • A. Barker and X.-C. Cai, Two-level Newton and hybrid Schwarz preconditioners for fluid-structure interaction, SIAM J. Sci. Comput., 32 (2010), pp. 2395-2417.
  • A. Barker and X.-C. Cai, Scalable parallel methods for monolithic coupling in fluid-structure interaction with application to blood flow modeling, J. Comput. Phys., 229 (2010), pp. 642-659.
  • C. Yang, J. Cao, and X.-C. Cai, A fully implicit domain decomposition algorithm for shallow water equations on the cubed-sphere, SIAM J. Sci. Comput., 32 (2010), pp. 418-438.
  • X.-C. Cai, S. Liu, and J. Zou, Parallel overlapping domain decomposition methods for coupled inverse elliptic problems, Comm. App. Math. Comp. Sci., 4 (2009), pp. 1-26.
  • X.-C. Cai, Nonlinear overlapping domain decomposition methods, Lecture Notes in Computational Science and Engineering, Springer, 70 (2009), pp. 217-224.
  • A. Barker and X.-C. Cai, NKS for fully coupled fluid-structure interaction with application, Lecture Notes in Computational Science and Engineering, Springer, 70 (2009), pp.275-282.
  • X.-C. Cai, S. Liu, and J. Zou, An overlapping domain decomposition method for parameter identification problems, Lecture Notes in Computational Science and Engineering, U. Langer, M. Discacciati, D.E. Keyes, O.B. Widlund, W. Zulehner (Eds.), Springer, Vol. 60, (2008), pp. 451-458.
  • C. Jin and X.-C. Cai, A preconditioned recycling GMRES solver for stochastic Helmholtz problems, Commun. Comput. Phys., 6 (2009), pp. 342-353.
  • S. Ovtchinnikov, F. Dobrian, X.-C. Cai, and D. Keyes, Additive Schwarz-based fully coupled implicit methods for resistive Hall magnetohydrodynamic problems, J. Comput. Phys., 225 (2007), pp. 1919-1936.
  • C. Jin, X.-C. Cai, and C. Li, Parallel domain decomposition methods for stochastic elliptic equations, SIAM J. Sci. Comput., 29 (2007), pp. 2096-2114.
  • F.-N. Hwang and X.-C. Cai, A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms, Computer Methods in Applied Mechanics and Engineering, 196 (2007), pp. 1603-1611.
  • S. Ovtchinnikov, F. Dobrian, X.-C. Cai, and D. Keyes, Domain-decomposed fully coupled implicit methods for a magnetodydrodynamics problem, Lecture Notes in Computational Science and Engineering, Springer, (2006).
  • E. Prudencio and X.-C. Cai, Parallel multilevel restricted Schwarz preconditioners with pollution removing for PDE-constrained optimization, SIAM J. Sci. Comput., 29 (2007), pp. 964-985.
  • F.-N. Hwang and X.-C. Cai, Parallel fully coupled Schwarz preconditioners for saddle point problems, ETNA, 22 (2006), pp. 146-162.
  • E. Prudencio, R. Byrd, and X.-C. Cai, Parallel full space SQP Lagrange-Newton-Krylov-Schwarz algorithms for PDE-constrained optimization problems, SIAM J. Sci. Comput., 27 (2006), pp. 1305-1328.
  • X.-C. Cai, L. Marcinkowski, and P. Vassilevski, An element agglomeration nonlinear additive Schwarz preconditioned Newton method for unstructured finite element problems, Applications of Mathematics, 50 (2005), pp. 247-275.
  • F.-N. Hwang and X.-C. Cai, A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations, J. Comput. Phys., 204 (2005), pp. 666-691.
  • E. Prudencio, R. Byrd, and X.-C. Cai, Domain decomposition methods for PDE constrained optimization problems, M. Dayde, J. Dongarra, V. Hernandez, and J. Palma, edt., Lecture Notes in Computer Science, Vol 3402, Springer, 2005.
  • S. Ovtchinnikov and X.-C. Cai, One-level Newton-Krylov-Schwarz algorithm for unsteady nonlinear radiation diffusion problem, Numer. Lin. Alg. Applics., 11 (2004), pp. 867-881.
  • F.-N. Hwang and X.-C. Cai, Improving robustness and parallel scalability of Newton method through nonlinear preconditioning, Lecture Notes in Computational Science and Engineering, Vol. 40, R. Kornhuber, R. Hoppe, J. Periaux, O. Pironneau, O. Widlund, J. Xu, eds, Springer, 2004.
  • M. Murillo and X.-C. Cai, A fully implicit parallel algorithm for simulating the nonlinear electrical activity of the heart, Numer. Lin. Alg. Applics., 11 (2004), pp. 261-277.
  • L. Marcinkowski and X.-C. Cai, Parallel performance of some two-level ASPIN algorithms, Lecture Notes in Computational Science and Engineering, Vol. 40, R. Kornhuber, R. Hoppe, J. Periaux, O. Pironneau, O. Widlund, J. Xu, eds, Springer, 2004.
  • X. Yue, F.-N. Hwang, R. Shandas, and X.-C. Cai, Simulation of branching blood flows on parallel computers, Proceedings of Rocky Mountain Bioengineering Symposium, 2004.
  • X.-C. Cai, D. E. Keyes, and L. Marcinkowski, Nonlinear additive Schwarz preconditioners and applications in computational fluid dynamics, International Journal for Numerical Methods in Fluids, 40 (2002), pp. 1463-1470.
  • X.-C. Cai, M. Dryja, and M. Sarkis, Restricted additive Schwarz preconditioners with harmonic overlap for symmetric positive definite linear systems, SIAM J. Numer. Anal., 41 (2003), pp. 1209-1231.
  • X.-C. Cai, D. E. Keyes, and D. P. Young, A nonlinear additive Schwarz preconditioned inexact Newton method for shocked duct flow, Proceedings of the 13th International Conference on Domain Decomposition Methods, Oct. 9-12, 2000, France.
  • X.-C. Cai, M. Dryja, and M. Sarkis, RASHO: A restricted additive Schwarz preconditioner with harmonic overlap, Proceedings of the 13th International Conference on Domain Decomposition Methods, Oct. 9-12, 2000, France.
  • X.-C. Cai and D. E. Keyes, Nonlinearly preconditioned inexact Newton algorithms, SIAM J. Sci. Comput., 24 (2002), pp. 183-200.
  • R. Aitbayev, X.-C. Cai, and M. Paraschivoiu, Parallel two-level methods for three-dimensional transonic compressible flow simulations on unstructured meshes, Proceedings of Parallel CFD’99, 1999.
  • M. Paraschivoiu, X.-C. Cai, M. Sarkis, D. P. Young, and D. Keyes, Multi-domain multi-model formulation for compressible flows: Conservative interface coupling and parallel implicit solvers for 3D unstructured meshes, AIAA Paper 99-0784, 1999.
  • X.-C. Cai, M. Paraschivoiu, and M. Sarkis, An explicit multi-model compressible flow formulation based on the full potential equation and the Euler equations on 3D unstructured meshes, 11th International Conference on Domain Decomposition Methods, C-H. Lai, P. Bjorstad, M. Cross, O. Widlund, eds., 1999.
  • S. Goossens and X.-C. Cai, Lower dimensional interpolation in overlapping composite mesh difference methods, 11th International Conference on Domain Decomposition Methods, C-H. Lai, P. Bjorstad, M. Cross, O. Widlund, eds., 1999.
  • X.-C. Cai, T. Mathew, and M. Sarkis, Maximum norm analysis of overlapping nonmatching grid discretizations of elliptic equations, SIAM J. Numer. Anal., 37 (2000), pp. 1709-1728.
  • X.-C. Cai and J. Zou, Some observations on the $L^2$ convergence of the additive Schwarz preconditioned GMRES method, Numer. Lin. Alg. Applics., 9 (2002), pp. 379-397.
  • X.-C. Cai, M. A. Casarin, Jr., F. W. Elliott, Jr., and, O. B. Widlund, Overlapping Schwarz algorithms for solving Helmholtz’s equation, Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel, C. Farhat and X.-C. Cai, eds., AMS, pp. 437-445, 1998.
  • Y. Wu, X.-C. Cai, and D. E. Keyes, Additive Schwarz methods for hyperbolic equations, Proceedings of the 10th Intl. Conf. on Domain Decomposition Methods, J. Mandel, C. Farhat and X.-C. Cai, eds., AMS, pp. 513–521, 1998.
  • X.-C. Cai, C. Farhat, and M. Sarkis, A minimum overlap restricted additive Schwarz preconditioner and applications in 3D flow simulations, The Tenth International Conference on Domain Decomposition Methods for Partial Differential Equations, J. Mandel, C. Farhat and X.-C. Cai, eds, AMS, 1998.
  • X.-C. Cai and M. Sarkis, A restricted additive Schwarz preconditioner for general sparse linear systems, SIAM J. Sci. Comput., 21 (1999), pp. 792-797.
  • X.-C. Cai, M. Dryja, and M. Sarkis, Overlapping non-matching grid mortar element methods for elliptic problems, SIAM J. Numer. Anal., 36 (1999), pp. 581-606.
  • X.-C. Cai, C. Farhat, and M. Sarkis, Variable degree Schwarz methods for the implicit solution of unsteady compressible Navier-Stokes equations on two-dimensional unstructured meshes, ICASE Report No. 96-48, NASA Langley Research Center, 1996.
  • X.-C. Cai, W. D. Gropp, D. E. Keyes, R. G. Melvin, and D. P. Young, Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation, SIAM J. Sci. Comput., 19 (1998), pp. 246-265.
  • X.-C. Cai, C. Farhat, and M. Sarkis, Schwarz methods for the unsteady compressible Navier-Stokes equations on unstructured meshes, Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds., John Wiley & Sons, Ltd., 1997.
  • X.-C. Cai, D. E. Keyes, and V. Venkatakrishnan, Newton-Krylov-Schwarz: An implicit solver for CFD, Domain Decomposition Methods in Sciences and Engineering, R. Glowinski, J. Periaux, Z. Shi and O. Widlund, eds., John Wiley & Sons, Ltd., 1996.
  • X.-C. Cai and M. Sarkis, Local multiplicative Schwarz algorithms for convection-diffusion equations, East-West J. Numer. Math., 6 (1998).
  • X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri, Parallel implicit methods for aerodynamics, Seventh International Conference on Domain Decomposition Methods for Partial Differential Equations, D. Keyes, J. Xu, eds., AMS, 1994.
  • X.-C. Cai and M. Dryja, Domain decomposition methods for monotone nonlinear elliptic problems, Seventh International Conference on Domain Decomposition Methods for Partial Differential Equations, D. Keyes, J. Xu, eds., AMS, 1994.
  • X.-C. Cai, W. D. Gropp, D. E. Keyes, and M. D. Tidriri, Newton-Krylov-Schwarz methods in CFD, Proceedings of the International Workshop on the Navier-Stokes Equations, Notes in Numerical Fluid Mechanics, R. Rannacher, eds. Vieweg Verlag, Braunschweig, 1994.
  • X.-C. Cai, The use of pointwise interpolation in domain decomposition methods with non-nested meshes, SIAM J. Sci. Comput., 16 (1995), pp. 250-256.
  • X.-C. Cai, A family of overlapping Schwarz algorithms for nonsymmetric and indefinite elliptic problems, in Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering, D. Keyes and Y. Saad and D. Truhlar, eds., SIAM, 1994.
  • X.-C. Cai, W. D. Gropp, and D. E. Keyes, A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems, Numer. Lin. Alg. Applics., 1 (1994), pp. 477-504.
  • X.-C. Cai and Y. Saad, Overlapping domain decomposition algorithms for general sparse matrices, TR 93-027, Army High Performance Computing Research Center, University of Minnesota, 1993.
  • B. Bialecki and X.-C. Cai, $H^1$-norm error bounds for piecewise Hermite bicubic orthogonal spline collocation schemes for elliptic boundary value problems, SIAM J. Numer. Anal., 31 (1994), pp. 1128-1146.
  • X.-C. Cai, Multiplicative Schwarz methods for parabolic problems, SIAM J. Sci. Comput., 15 (1994), pp. 587-603.
  • X.-C. Cai, An optimal two-level overlapping domain decomposition method for elliptic problems in two and three dimensions, SIAM J. Sci. Comput., 14 (1993), pp. 239-247.
  • X.-C. Cai and O. Widlund, Multiplicative Schwarz algorithms for nonsymmetric and indefinite elliptic problems, SIAM J. Numer. Anal., 30 (1993), pp. 936–952.
  • X.-C. Cai and O. Widlund, Domain decomposition algorithms for indefinite elliptic problems, SIAM J. Sci. Stat. Comp., 13 (1992), pp. 243-258.
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