Linear system solver (Ax=b)
Krylov subspace solver (KSP)
H. A. Van Der Vorst, BI-CGSTAB: A fast and smoothly convergence variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. Vol. 13, No. 2, pp. 631-644, 1992.
Y. Sadd, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. Vol. 7, No.3, pp. 856-869, 1996.
S. L. Zhang, GPBi-CG: Generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems, SIAM J. Sci. Comput. Vol. 18, No. 2, pp. 537-551, 1997.
P. R. Graves-Morris, A. Salam, Avoiding breakdown in Van der Vorst's method, Numerical Algorithms, Vol. 21, pp. 205-223, 1999.
P. Sonneveld, M. B. van Gijzen, IDR(s): A family of simple and fast algorithm for solving large nonsymmetric systems of linear equations, SIAM J. Sci. Stat. Comput. Vol. 31, pp. 1032-1062, 2008.
Algebraic multigrid method (AMG)
H. D. Sterck, U. M. Yang, J. J. Heys, Reducing complexity in parallel algebraic multigrid preconditioners, SIAM J. Matrix Anal. Appl. Vol. 27, No. 4, pp. 1019-1039, 2006
R. D. Falgout, J. B. Schroder, Non-Galerkin coarse grids for algebraic multigrid, SIAM J. Sci. Comput. Vol. 36, No. 3, pp. C309-C334, 2014
J. Xu, L. Zikatanov, Algebraic multigrid methods, Acta Numerica, Vol. 591-721, 2017
Eigenvalue Solver
Computational Fluid Dynamics (CFD)
Velocity/Pressure coupling algorithm
Scheme development (Dispersion-relation preserving) (DRP)
Finite Element Method (FEM)
English Publications
Chinese Publications
Handouts & Book Chapters
Finite Volume Method (FVM)
Chinese Publications
Handouts & Book Chapters
Isogeometric Analysis (IGA)
Tutorials & Overviews
Thesis (English)
Y. Bazilevs, Isogeometric Analysis of Turbulence and Fluid-Structure Interaction, Doctoral thesis, The University of Texas at Austin 2006
J. A. Cottrell, Isogeometric Analysis and Numerical Modeling of the Fine Scales within the Variational Multiscale Method, Doctoral thesis, The University of Texas at Austin 2007
M. C. Hsu, Fluid–Structure Interaction Analysis of Wind Turbines, University of California, San Diego 2012
Immersed Boundary Method (IBM)
Journal
M. C. Lai, An Immersed Boundary Method with Formal Second-Order Accuracy and Reduced Numerical Viscosity, JCP, Vol. 160, pp. 705-719 2000
P. H. Chiu, A differentially interpolated DFIBM for predicting incompressible NS equations in time varying complex geometries, JCP, pp. 4476-4500 2010
C. Liu, An efficient immersed boundary treatment for complex moving object, JCP, Vol-274, pp 654-680 2014
Documents
My Publications
Journal Papers
Tony W. H. Sheu, Neo S. C. Kao, P. H. Chiu, C. S. Lin, Development of an upwinding scheme through the minimization of modified wavenumber error for the incompressible Navier-Stokes equations, NHTB: Fundamental, Vol. 60, pp. 179-202 2011
Neo S. C. Kao, Tony W. H. Sheu, S. F. Tsai, On a wavenumber optimized streamline upwinding method for solving steady incompressible Navier-Stokes equations, NHTB: Fundamental, Vol. 67, pp. 1-25 2015
Neo S. C. Kao, Tony W. H. Sheu, Development of a finite element flow solver for solving three-dimensional incompressible Navier-Stokes solutions on multiple GPU cards, CAF, Vol. 167, pp. 285-291 2018
Rex K. S. Liu, C. T. Wu, Neo S. C. Kao, Tony W. H. Sheu, An improved mixed Lagrangian-Eulerian (IMLE) method for modelling incompressible Navier-Stokes flows with CUDA programming on multi-GPUs, CAF, Vol. 184, pp. 99-106 2019
Neo S. C. Kao, Rex K. S. Liu, Tony W. H. Sheu, Acceleration of high-order combined compact finite difference scheme for simulating three-dimensional flow and heat transfer problems in GPUs, NHTB: Fundamental, Vol. 78, pp. 265-287 2020