FOSLS

  • Multilevel projection methods for first-order system least squares.
    On some applications of a general multigrid methodology for reformulating PDEs as well-posed minimization problems. 
    T. Manteuffel and S. McCormick, 
    Procs. ASME, Fluids. Eng. Div. Summer Meeting, Lake Tahoe, June 9-23, 1994. 

  • First-order system least squares for second-order elliptic problems with discontinuous coefficients.
    On applying the fosls approach to problems where the coefficients may have large jump discontinuities. T. Manteuffel, S. McCormick, J. Morel, and G. Yang, 
    Proc. 7th Copper Mountain Conferrence on Multigrid Methods, , Copper Mountain, CO, April 3-7, 1995, NASA Conference Pub.No. 3339 , part 2, pp. 551. 
     
  • First-order system least squares for second-order partial differential equations: part I .
    On a theoretical foundation for fosls, a general approach to the well-posed formulation of PDEs as minimization problems; here we develop fosls for general convection-diffusion-reaction equations and show ellipticity in a div-like norm. 
    Z. Cai, R. Lazarov, T. Manteuffel and S. McCormick, 
    SIAM J. Num. Anal., Vol. 31, No. 6, pp. 1785-1802 (1994). 
     
  • First-order system least squares for vorticity form of the Stokes equations, with application to linear elasticity.
    On applying the fosls approach to Stokes equations in vorticity form, again generalized by a pressure- perturbed continuity equation to include linear elasticity; here we obtain only a weaker norm equivalence for a combined inverse norm and L2 norm functional. 
    Z. Cai, T. Manteuffel and S. McCormick, 
    E.T.N.A., Vol. 3, pp. 150-159, (1997). 
     
  • First-order System Least Squares for Second-Order Partial Differential Equations: Part II.
    On applying the fosls approach to convection-diffusion-reaction equations augmented by curl equations that yield full H1 ellipticity. 
    Z. Cai, T.A. Manteuffel and S. McCormick, 
    SIAM J. Numer. Anal., Vol. 34, No. 2, (1997).
     
  • First-order system least squares for Stokes equations, with application to linear elasticity.
    On applying the fosls approach to Stokes equations, generalized by a pressure-perturbed continuity equation to include linear elasticity; we develop a minimization formulation that is fully elliptic in the H1 sense in each variable. 
    Z. Cai, T.A. Manteuffel and S. McCormick, 
    SIAM J. Numer. Anal., Vol. 34, No. 5, pp. 1727-1741 (1997). 
     
  • Local error estimates and adaptive refinement for first-order system least squares (FOSLS) .
    by M. Berndt, T. Manteuffel, and S. McCormick, 
    E.T.N.A. Vol. 6, pp. 35-43 (1998). 
     
  • First-order System Least-squares for Planar Linear Elasticity: Pure Traction Problem.
    A proof of H1 ellipticity for a fosls formulation of planar linear elasticity with traction boundary conditions. 
    Z. Cai, T.A. Manteuffel, S.F. McCormick and S. V. Parter, 
    SIAM J. Numer. Anal., Vol. 35, No. 1, pp. 320-335 (1998). 
     
  • Least-squares finite-element solution of the neutron transport equation in diffusive regimes.
    A scaled functional is developed and shown to be V-elliptic in a special norm independent of cross-section parameters. Numerical results are presented for slab geometry. 
    T.A. Manteuffel and Klaus Ressel, 
    SIAM J. Numer. Anal., Vol. 35, No. 2, pp. 806 ? 835 (1998). 
     
  • First-order system least squares (FOSLS) for convection-diffusion problems: numerical results.
    fosls formulation for a transformed problem is developed and is shown to be V-elliptic uniformly in the convection parameters. Numerical results are presented. 
    J.-M. Fiard, T.A. Manteuffel and S. McCormick, 
    SIAM J. Sci. Comp., Vol. 19, No. 6, pp. 1958-1979 (1998). 
     
  • Analysis of velocity-flux first-order system least-squares principles for the Navier-Stokes equations: Part I.
    A standard norm fosls formulation for Navier-stokes equations is developed and shown to be H1-elliptic sufficiently close to the solution. Numerical solution schemes are presented. 
    P. Bochev, Z. Cai, T.A. Manteuffel and S. McCormick, 
    SIAM J. Numer. Anal., Vol. 35, No. 3, pp 990 - 1009 (1998). 
     
  • Analysis of velocity-flux least-squares principles for the Navier-Stokes equations: Part II.
    A dual norm fosls formulation is developed and shown to be L2-elliptic sufficiently close to the solution. Numerical solution techniques are presented. 
    P. Bochev, Z. Cai, T.A. Manteuffel and S. McCormick, 
    SIAM J. Numer. Anal., Vol. 36, No. 4, pp 1125-1144 (1999). 
     
  • A boundary functional for the least-squares finite element solution of the neutron transport equation.
    A scaled functional together with a boundary functional is developed. Trace theorems are proven and the functional is shown to be V-elliptic in a special norm independent of problem parameters. 
    T. A. Manteuffel, K.J. Ressel and G. Starke, 
    SIAM J. Numer. Anal., Vol. 37, No. 2, pp. 556-586 (2000). 
     
  • First-order system least squares for the Stokes and elasticity equations: further results.
    Further results, including proof of ellipticity with mixed boundary conditions and certain dual norms, is presented. 
    Z. Cai, C.-O. Lee, T. A. Manteuffel, and S. F. McCormick, 
    SIAM J. Sci. Comp., Vol. 21, No. 5, pp. 1728-1739 (2000). 
     
  • First-order system least-squares (FOSLS) for the Helmholtz equation.
    fosls formulation for the Helmholtz equation is described and a multilevel algorithm for the solution of the resulting linear sysem is developed. 
    B. Lee, T. A. Manteuffel, S. F. McCormick, and J. Ruge, 
    SIAM J. Sci. Comp., Vol. 21, No. 5, pp. 1927-1949 (2000) 
     
  • First-order system least squares for planar linear elasticity: numerical results.
    A multigrid algorithm is developed and numerical results are presented. 
    Z. Cai, C.-O. Lee, and T.Manteuffel, and S. F. McCormick, 
    SIAM J. Sci. Comp., Vol. 21, No. 5, p. 1706-1727 (2000). 
     
  • Improved discretization error estimates for first-order system least squares (FOSLS).
    by T. Manteuffel, S. McCormick, and C. Pflaum, 
    Math. Comp., submitted. 
     
  • First-order system LL* (FOSLL*): scalar elliptic partial differential equations.
    by Z. Cai, T. Manteuffel, and S. McCormick, 
    SIAM J. Num. Anal., submitted. 
     
  • First-order system least squares (FOSLS) for spatial linear elasticity: pure traction.
    by S.-D. Kim, T. Manteuffel, and S. McCormick, 
    SIAM J. Num. Anal. ,Vol. 38, No. 5, pp. 1454-1482 (2001).

Multigrid

  • Multilevel projection methods for first-order system least squares.
    On some applications of a general multigrid methodology for reformulating PDEs as well-posed minimization problems. 
    T. Manteuffel and S. McCormick, 
    Procs. ASME, Fluids. Eng. Div. Summer Meeting, Lake Tahoe, June 9-23, 1994. 
     
  • A fast multigrid algorithm for isotropic transport problems, part I: pure scattering.
    On applying the fosls approach to transport problems for the case of pure scattering. T. Manteuffel, S. McCormick, J. Morel, S. Oliviera, and G. Yang, 
    SIAM J. Sci. Comp., Vol. 16, No. 3, pp. 601-635, (1995). 
     
  • A fast multigrid algorithm for isotropic transport problems, part II: with absorption.
    On applying the fosls approach to transport problems for the case of absorption. T. Manteuffel, S. McCormick, J. Morel, and G. Yang, 
    SIAM J. Sci. Comp., Vol. 17, No. 6, pp. 1449 - 1474, (1996). 
     
  • Robustness and scalability of algebraic multigrid (AMG) .
    by A. Cleary, R. Falgout, V. Henson, J. Jones, T. Manteuffel, S. McCormick, G. Miranda, and J. Ruge, 
    SIAM J. Sci. Comp., to appear. 
     
  • Algebraic multigrid based on element interpolation (AMGe) .
    by M. Brezina, A. Cleary, R. Falgout, V. Henson, J. Jones, T. Manteuffel, S. McCormick, and J. Ruge, 
    SIAM J. Sci. Comp., to appear.

Transport

  • A fast multigrid algorithm for isotropic transport problems, part I: pure scattering.
    On applying the fosls approach to transport problems for the case of pure scattering. 
    T. Manteuffel, S. McCormick, J. Morel, S. Oliviera, and G. Yang, 
    SIAM J. Sci. Comp., Vol. 16, No. 3, pp. 601-635, (1995). 
  • A fast multigrid algorithm for isotropic transport problems, part II: with absorption.
    On applying the fosls approach to transport problems for the case of absorption. 
    T. Manteuffel, S. McCormick, J. Morel, and G. Yang, 
    SIAM J. Sci. Comp., Vol. 17, No. 6, pp. 1449 - 1474, (1996).
     
  • Least-squares finite-element solution of the neutron transport equation in diffusive regimes.
    A scaled functional is developed and shown to be V-elliptic in a special norm independent of cross-section parameters. Numerical results are presented for slab geometry. 
    T.A. Manteuffel and Klaus Ressel, 
    SIAM J. Numer. Anal., Vol. 35, No. 2, pp. 806 ? 835 (1998). 
     
  • A boundary functional for the least-squares finite element solution of the neutron transport equation.
    A scaled functional together with a boundary functional is developed. Trace theorems are proven and the functional is shown to be V-elliptic in a special norm independent of problem parameters. 
    T. A. Manteuffel, K.J. Ressel and G. Starke, 
    SIAM J. Numer. Anal., Vol. 37, No. 2, pp. 556-586 (2000).

Iterative

  • On the Roots of the Orthogonal Polynomials and Residual Polynomials Associated with a Conjugate Gradient Method.
    T. A. Manteuffel and J.S. Otto, 
    Journal of Numerical Linear Algebra, Vol. 1 (5), pp. 449 - 475, (1994). >
  • Estimating the Spectrum of a Matrix Using the Roots of the Polynomials Associated with the QMR Iteration.
    T. Barth and T. A. Manteuffel, 
    Center for Computational Mathematics Report, University of Colorado at Denver, March, 1993.
  • Variable Metric Conjugate Gradient Methods.
    T. Barth and T. A. Manteuffel, 
    Proceedings of the 10th International Symposium on Matrix Analysis and Parallel Computing, Keio University, Yokohama, Japan, March 14-16, 1994. 
  • Conjugate Gradient Algorithms Using Multiple Recursions.
    T. Barth and T. A. Manteuffel, 
    Proceedings of the Workshop on Conjugate Gradient Methods, University of Washington, Seattle, WA, July 9-14, 1995. 
  • Adaptive $K$-step Iterative Methods for Nonsymmetric Systems of Linear Equations.
    T. A. Manteuffel, G. Starke and R. S. Varga, 
    Electr. Trans. Numer. Anal., Vol. 3, pp 50-65, (1995). 
  • Minimal Residual Method Stronger Than Polynomial Preconditioning.
    V. Faber, W. Joubert, E. Knill and T. A. Manteuffel, 
    SIAM J. Mat. Anal., Vol. 17, No. 4 (1996). 
     
  • On Hybrid Iterative Methods for Nonsymmetric Systems of Linear Equations.
    T. A. Manteuffel and G. Starke 
    Numerische Math., (1996).