Thomas A. Manteuffel

发表

Special Issue on Iterative Methods in Numerical Linear Algebra

Thomas A. Manteuffel, 1996, SIAM J. Sci. Comput..

Automatic Construction of Sparse Preconditioners for High-Order Finite Element Methods

Thomas A. Manteuffel, Marian Brezina, Travis M. Austin, 2011 .

Parallel-In-Time For Moving Meshes

Thomas A. Manteuffel, Robert D. Falgout, Jacob B. Schroder, 2016 .

First-Order System Least Squares for Incompressible Resistive Magnetohydrodynamics

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2010, SIAM J. Sci. Comput..

Adaptive Smoothed Aggregation (αSA)

Thomas A. Manteuffel, Robert D. Falgout, Scott P. MacLachlan, 2004, SIAM J. Sci. Comput..

Constrained Optimization for Liquid Crystal Equilibria

Thomas A. Manteuffel, Scott P. MacLachlan, J. H. Adler, 2016, SIAM J. Sci. Comput..

Echocardiographic particle imaging velocimetry data assimilation with least square finite element methods

Thomas A. Manteuffel, Jeffrey J. Heys, Marek Belohlavek, 2014, Comput. Math. Appl..

Multilevel First-Order System Least Squares for Elliptic Grid Generation

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2003, SIAM J. Numer. Anal..

First-Order System Least Squares (FOSLS) for Convection-Diffusion Problems: Numerical Results

Thomas A. Manteuffel, Stephen F. McCormick, Jean Michel Fiard, 1998, SIAM J. Sci. Comput..

A Least-Squares Finite Element Method for the Linear Boltzmann Equation with Anisotropic Scattering

Thomas A. Manteuffel, Travis M. Austin, 2006, SIAM J. Numer. Anal..

A Boundary Functional for the Least-Squares Finite- Element Solution of Neutron Transport Problems

Thomas A. Manteuffel, Gerhard Starke, Klaus J. Ressel, 1999, SIAM J. Numer. Anal..

First-Order System Least-Squares for the Helmholtz Equation

Thomas A. Manteuffel, Barry Lee, Stephen F. McCormick, 1999, SIAM J. Sci. Comput..

Least-Squares Finite Element Methods for Quantum Electrodynamics

Thomas A. Manteuffel, Stephen F. McCormick, Christian Ketelsen, 2010, SIAM J. Sci. Comput..

Numerical Methods for Gremban's Expansion of Signed Graphs

Thomas A. Manteuffel, Alyson Fox, Geoffrey Sanders, 2017, SIAM J. Sci. Comput..

Nonsymmetric Algebraic Multigrid Based on Local Approximate Ideal Restriction (ℓAIR)

Thomas A. Manteuffel, John W. Ruge, Ben S. Southworth, 2017, SIAM J. Sci. Comput..

Reduction-based Algebraic Multigrid for Upwind Discretizations

Thomas A. Manteuffel, John W. Ruge, Ben S. Southworth, 2017 .

FOSLL* for Nonlinear Partial Differential Equations

Thomas A. Manteuffel, Eunjung Lee, Chad R. Westphal, 2015, SIAM J. Sci. Comput..

Relaxation‐corrected bootstrap algebraic multigrid (rBAMG)

Thomas A. Manteuffel, Stephen F. McCormick, Marian Brezina, 2012, Numer. Linear Algebra Appl..

On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method

Thomas A. Manteuffel, James S. Otto, T. Manteuffel, 1994, Numer. Linear Algebra Appl..

Robustness and Scalability of Algebraic Multigrid

Van Emden Henson, Thomas A. Manteuffel, Robert D. Falgout, 1999, SIAM J. Sci. Comput..

A Comparison of Finite Element Spaces for H(div) Conforming First-Order System Least Squares

Thomas A. Manteuffel, Steffen Münzenmaier, Christopher A. Leibs, 2017, SIAM J. Sci. Comput..

Seventh Copper Mountain Conference on Multigrid Methods

Thomas A. Manteuffel, Craig C. Douglas, N. Duane Melson, 2019 .

An Efficiency-Based Adaptive Refinement Scheme Applied to Incompressible, Resistive Magnetohydrodynamics

Lei Tang, Thomas A. Manteuffel, Stephen F. McCormick, 2009, LSSC.

An alternative least-squares formulation of the Navier-Stokes equations with improved mass conservation

Thomas A. Manteuffel, Jeffrey J. Heys, Stephen F. McCormick, 2007, J. Comput. Phys..

FOSLL∗ Method for the Eddy Current Problem with Three-Dimensional Edge Singularities

Thomas A. Manteuffel, Eunjung Lee, T. Manteuffel, 2007, SIAM J. Numer. Anal..

Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

Thomas A. Manteuffel, Stephen F. McCormick, A. L. Codd, 2003, SIAM J. Numer. Anal..

Enhanced Mass Conservation in Least-Squares Methods for Navier-Stokes Equations

Thomas A. Manteuffel, Jeffrey J. Heys, Stephen F. McCormick, 2009, SIAM J. Sci. Comput..

The Sixth Copper Mountain Conference on Multigrid Methods, part 2

Thomas A. Manteuffel, S. F. McCormick, N. Duane Melson, 1993 .

A generalized eigensolver based on smoothed aggregation (GES-SA) for initializing smoothed aggregation (SA) multigrid

Panayot S. Vassilevski, Thomas A. Manteuffel, Stephen F. McCormick, 2008, Numer. Linear Algebra Appl..

First-Order System Least Squares For Linear Elasticity: Numerical Results

Thomas A. Manteuffel, Stephen F. McCormick, Chang-Ock Lee, 1999, SIAM J. Sci. Comput..

Mixed (LL∗)−1 and LL∗ least‐squares finite element methods with application to linear hyperbolic problems

Thomas A. Manteuffel, Delyan Kalchev, Steffen Münzenmaier, 2018, Numer. Linear Algebra Appl..

A Fluidity-Based First-Order System Least-Squares Method for Ice Sheets

Thomas A. Manteuffel, Jeffery Allen, Harihar Rajaram, 2017, SIAM J. Sci. Comput..

Special Section: 2010 Copper Mountain Conference

Misha Elena Kilmer, Sven Leyffer, David E. Keyes, 2011, SIAM J. Sci. Comput..

Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I

Thomas A. Manteuffel, Stephen F. McCormick, Markus Berndt, 2005, SIAM J. Numer. Anal..

Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part II

Thomas A. Manteuffel, Stephen F. McCormick, Markus Berndt, 2005, SIAM J. Numer. Anal..

A Fast Multigrid Algorithm for Isotropic Transport Problems I: Pure Scattering

G. Yang, Thomas A. Manteuffel, Stephen F. McCormick, 1995, SIAM J. Sci. Comput..

Parallel adaptive mesh refinement for first-order system least squares

Lei Tang, Thomas A. Manteuffel, Jose Garcia, 2012, Numer. Linear Algebra Appl..

Special Section on Iterative Methods in Numerical Linear Algebra

Thomas A. Manteuffel, Stephen F. McCormick, 1994, SIAM J. Scientific Computing.

Weighted-Norm First-Order System Least-Squares (FOSLS) for Div/Curl Systems with Three Dimensional Edge Singularities

Thomas A. Manteuffel, Eunjung Lee, Chad R. Westphal, 2008, SIAM J. Numer. Anal..

A Least-Squares Finite Element Method Based on the Helmholtz Decomposition for Hyperbolic Balance Laws pdf

Thomas A. Manteuffel, Delyan Z. Kalchev, 2019, ArXiv.

First-Order System Least Squares (FOSLS) for Spatial Linear Elasticity: Pure Traction

Thomas A. Manteuffel, Stephen F. McCormick, Sang Dong Kim, 2000, SIAM J. Numer. Anal..

Preconditioning Second-Order Elliptic Operators: Experiment and Theory

Thomas A. Manteuffel, Wayne Joubert, Seymour V. Parter, 1992, SIAM J. Sci. Comput..

On Mass-Conserving Least-Squares Methods

Thomas A. Manteuffel, Jeffrey J. Heys, Stephen F. McCormick, 2006, SIAM J. Sci. Comput..

A Fast Multigrid Algorithm for Isotropic Transport Problems. II: With Absorption

G. Yang, Thomas A. Manteuffel, Stephen F. McCormick, 1996, SIAM J. Sci. Comput..

Algebraic Multigrid for Markov Chains

Thomas A. Manteuffel, Hans De Sterck, Stephen F. McCormick, 2010, SIAM J. Sci. Comput..

Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations

Lei Tang, Thomas A. Manteuffel, Stephen F. McCormick, 2011, SIAM J. Sci. Comput..

An energy‐based AMG coarsening strategy

Thomas A. Manteuffel, Scott P. MacLachlan, Stephen F. McCormick, 2006, Numer. Linear Algebra Appl..

Spectral AMGe (ρAMGe)

Panayot S. Vassilevski, Thomas A. Manteuffel, Robert D. Falgout, 2003, SIAM J. Sci. Comput..

First-order system least squares and the energetic variational approach for two-phase flow

Ludmil T. Zikatanov, Thomas A. Manteuffel, Chun Liu, 2010, J. Comput. Phys..

Towards Adaptive Smoothed Aggregation (AlphaSA) for Nonsymmetric Problems

Thomas A. Manteuffel, Stephen F. McCormick, Marian Brezina, 2010, SIAM J. Sci. Comput..

Adaptive Algebraic Multigrid

Thomas A. Manteuffel, Robert D. Falgout, Scott P. MacLachlan, 2005, SIAM J. Sci. Comput..

Nested Iteration and First-Order Systems Least Squares for a Two-Fluid Electromagnetic Darwin Model

Thomas A. Manteuffel, Christopher A. Leibs, 2015, SIAM J. Sci. Comput..

Introduction

Gene H. Golub, Thomas A. Manteuffel, G. Golub, 1992, SIAM J. Matrix Anal. Appl..

First-Order System Least Squares for the Stokes and Linear Elasticity Equations: Further Results

Thomas A. Manteuffel, Stephen F. McCormick, Chang-Ock Lee, 2000, SIAM J. Sci. Comput..

Smoothed aggregation algebraic multigrid for stochastic PDE problems with layered materials

Thomas A. Manteuffel, Stephen F. McCormick, Marian Brezina, 2014, Numer. Linear Algebra Appl..

Smoothed Aggregation Multigrid for Markov Chains

Thomas A. Manteuffel, Hans De Sterck, Stephen F. McCormick, 2010, SIAM J. Sci. Comput..

A Technique for Accelerating the Convergence of Restarted GMRES

Elizabeth R. Jessup, Thomas A. Manteuffel, Allison H. Baker, 2005, SIAM J. Matrix Anal. Appl..

A Moment-Parity Multigrid Preconditioner for the First-Order System Least-Squares Formulation of the Boltzmann Transport Equation

Thomas A. Manteuffel, Barry Lee, Peter N. Brown, 2003, SIAM J. Sci. Comput..

Adaptive reduction‐based AMG

Thomas A. Manteuffel, Scott P. MacLachlan, Stephen F. McCormick, 2006, Numer. Linear Algebra Appl..

A robust multilevel approach for minimizing H(div)-dominated functionals in an H1-conforming finite element space

Thomas A. Manteuffel, Stephen F. McCormick, Travis M. Austin, 2004, Numer. Linear Algebra Appl..

First-Order System Least Squares and Electrical Impedance Tomography

Thomas A. Manteuffel, Stephen F. McCormick, H. R. MacMillan, 2004, SIAM J. Numer. Anal..

A Root-Node-Based Algebraic Multigrid Method

Thomas A. Manteuffel, Jacob B. Schroder, Ben S. Southworth, 2016, SIAM J. Sci. Comput..

Top-level acceleration of adaptive algebraic multilevel methods for steady-state solution to Markov chains

Thomas A. Manteuffel, Hans De Sterck, Killian Miller, 2011, Adv. Comput. Math..

Advances in implementation, theoretical motivation, and numerical results for the nested iteration with range decomposition algorithm pdf

Thomas A. Manteuffel, Wayne Mitchell, 2018, Numer. Linear Algebra Appl..

First-Order System LL* (FOSLL*) for General Scalar Elliptic Problems in the Plane

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2005, SIAM J. Numer. Anal..

A low-communication, parallel algorithm for solving PDEs based on range decomposition

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2017, Numer. Linear Algebra Appl..

First-Order System \CL\CL* (FOSLL*): Scalar Elliptic Partial Differential Equations

Thomas A. Manteuffel, Stephen F. McCormick, Zhiqiang Cai, 2001, SIAM J. Numer. Anal..

Range Decomposition: A Low Communication Algorithm for Solving PDEs on Massively Parallel Machines

Thomas A. Manteuffel, 2016 .

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

Thomas A. Manteuffel, Marian Brezina, Travis M. Austin, 2012, J. Comput. Phys..

Island Coalescence Using Parallel First-Order System Least Squares on Incompressible Resistive Magnetohydrodynamics

Lei Tang, Thomas A. Manteuffel, Stephen F. McCormick, 2013, SIAM J. Sci. Comput..

Finite element methods for quantum electrodynamics using a Helmholtz decomposition of the gauge field

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2010, Numer. Linear Algebra Appl..

Special Section on Iterative Methods in Numerical Linear Algebra

Thomas A. Manteuffel, Stephen F. McCormick, 1994, SIAM J. Sci. Comput..

First-Order System Least Squares for Geometrically Nonlinear Elasticity

Thomas A. Manteuffel, Stephen F. McCormick, Chad R. Westphal, 2006, SIAM J. Numer. Anal..

Algebraic multigrid for directed graph Laplacian linear systems (NS‐LAMG)

Thomas A. Manteuffel, Alyson Fox, T. Manteuffel, 2018, Numer. Linear Algebra Appl..

A Parallel Version of a Multigrid Algorithm for Isotropic Transport Equations

G. Yang, Thomas A. Manteuffel, Stephen F. McCormick, 1994, SIAM J. Sci. Comput..

Projection Multilevel Methods for Quasilinear Elliptic Partial Differential Equations: Theoretical Results

Thomas A. Manteuffel, Stephen F. McCormick, Oliver Röhrle, 2006, SIAM J. Numer. Anal..

Convergence in Norm of Nonsymmetric Algebraic Multigrid

Thomas A. Manteuffel, Ben S. Southworth, T. Manteuffel, 2018, SIAM J. Sci. Comput..

Algebraic Multigrid Domain and Range Decomposition (AMG-DD/AMG-RD)

Randolph E. Bank, Thomas A. Manteuffel, Robert D. Falgout, 2015, SIAM J. Sci. Comput..

Enhancing Least-Squares Finite Element Methods Through a Quantity-of-Interest

Lei Tang, Thomas A. Manteuffel, Eric C Cyr, 2014, SIAM J. Numer. Anal..

Projection Multilevel Methods for Quasilinear Elliptic Partial Differential Equations: Numerical Results

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2006, SIAM J. Numer. Anal..

Efficiency‐based h‐ and hp‐refinement strategies for finite element methods

Lei Tang, Thomas A. Manteuffel, Hans De Sterck, 2008, Numer. Linear Algebra Appl..

Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking

Thomas A. Manteuffel, Hans De Sterck, Stephen F. McCormick, 2008, SIAM J. Sci. Comput..

Special Issue on Iterative Methods in Numerical Linear Algebra

Thomas A. Manteuffel, Linda R. Petzold, 1992, SIAM J. Sci. Comput..

Weighted least-squares finite elements based on particle imaging velocimetry data

Thomas A. Manteuffel, Jeffrey J. Heys, Stephen F. McCormick, 2010, J. Comput. Phys..

Algebraic Multigrid Based on Element Interpolation (AMGe)

Thomas A. Manteuffel, Robert D. Falgout, Jim E. Jones, 2000, SIAM J. Sci. Comput..

Weighted-Norm First-Order System Least Squares (FOSLS) for Problems with Corner Singularities

Thomas A. Manteuffel, Eunjung Lee, Chad R. Westphal, 2006, SIAM J. Numer. Anal..

An Upper Bound on the Diameter of a Graph from Eigenvalues Associated with its Laplacian

Fan Chung Graham, Thomas A. Manteuffel, Vance Faber, 1994, SIAM J. Discret. Math..

Improved discretization error estimates for first-order system least squares

Thomas A. Manteuffel, Stephen F. McCormick, Christoph Pflaum, 2003, J. Num. Math..

Exploring basal sliding with a fluidity-based, ice-sheet model using FOSLS

Thomas A. Manteuffel, Jeffery Allen, Harihar Rajaram, 2018, Numer. Linear Algebra Appl..

Adaptive Smoothed Aggregation (AlphaSA) Multigrid

Thomas A. Manteuffel, Robert D. Falgout, Scott P. MacLachlan, 2005, SIAM Rev..

First‐order system least squares for the Oseen equations

Thomas A. Manteuffel, Stephen F. McCormick, Chang-Ock Lee, 2006, Numer. Linear Algebra Appl..

Operator‐based interpolation for bootstrap algebraic multigrid

Thomas A. Manteuffel, Stephen F. McCormick, Minho Park, 2010, Numer. Linear Algebra Appl..

Parallel efficiency-based adaptive local refinement

Lei Tang, Thomas A. Manteuffel, Stephen F. McCormick, 2010 .

Least-Squares Finite Element Discretization of the Neutron Transport Equation in Spherical Geometry

Thomas A. Manteuffel, Jacob B. Schroder, Christian Ketelsen, 2015, SIAM J. Sci. Comput..

First-Order System Least Squares for Incompressible Resistive Magnetohydrodynamics

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2010, SIAM J. Sci. Comput..

A Comparison of Adaptive Chebyshev and Least Squares Polynomial Preconditioning for Hermitian Positive Definite Linear Systems

Thomas A. Manteuffel, Steven F. Ashby, James S. Otto, 1992, SIAM J. Sci. Comput..

Further results on error estimators for local refinement with first-order system least squares (FOSLS)

Thomas A. Manteuffel, Stephen F. McCormick, John W. Ruge, 2010, Numer. Linear Algebra Appl..

Multigrid Reduction in Time for Nonlinear Parabolic Problems: A Case Study

Thomas A. Manteuffel, Robert D. Falgout, Jacob B. Schroder, 2017, SIAM J. Sci. Comput..

Numerical Conservation Properties of H(div)-Conforming Least-Squares Finite Element Methods for the Burgers Equation

Thomas A. Manteuffel, Hans De Sterck, Stephen F. McCormick, 2005, SIAM J. Sci. Comput..

Mixed $(\mathcal{L}\mathcal{L}^*)^{-1}$ and $\mathcal{L}\mathcal{L}^*$ least-squares finite element methods with application to linear hyperbolic problems

Thomas A. Manteuffel, Delyan Z. Kalchev, Steffen Munzenmaier, 2020 .

Minimal Residual Method Stronger than Polynomial Preconditioning

Thomas A. Manteuffel, Emanuel Knill, Wayne Joubert, 1996, SIAM J. Matrix Anal. Appl..

Least-Squares Finite Element Methods and Algebraic Multigrid Solvers for Linear Hyperbolic PDEs

Thomas A. Manteuffel, Hans De Sterck, Stephen F. McCormick, 2004, SIAM J. Sci. Comput..

On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

Thomas A. Manteuffel, Vance Faber, Seymour V. Parter, 1990 .

Iterative schemes for the neutron diffusion equation

Gumersindo Verdú, Thomas A. Manteuffel, Rafael Bru, 2002 .

Algebraic elimination of slide surface constraints in implicit structural analysis

Thomas A. Manteuffel, Charles Tong, Edmond Chow, 2003 .

Adaptive -step iterative methods for nonsymmetric systems of linear equations.

Thomas A. Manteuffel, Richard S. Varga, Gerhard Starke, 1995 .

Least-Squares Finite-Element Solution of the Neutron Transport Equation in Diffusive Regimes

Thomas A. Manteuffel, Klaus J. Ressel, T. Manteuffel, 1998 .

First-Order System Least Squares (FOSLS) for Planar Linear Elasticity: Pure Traction Problem

Thomas A. Manteuffel, Stephen F. McCormick, Zhiqiang Cai, 1998 .

Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I

Pavel B. Bochev, Thomas A. Manteuffel, Stephen F. McCormick, 1998 .

Extending the applicability of multigrid methods

Ludmil T. Zikatanov, Jinchao Xu, Thomas A. Manteuffel, 2006 .

On the efficient numerical solution of systems of second order boundary value problems

Thomas A. Manteuffel, Andrew B. White, 1986 .

First-order system least squares (FOSLS) for coupled fluid-elastic problems

Thomas A. Manteuffel, Jeffrey J. Heys, John W. Ruge, 2004 .

Adaptive Algebraic Multigrid Methods

Thomas A. Manteuffel, Robert D. Falgout, Scott P. MacLachlan, 2004 .

On hybrid iterative methods for nonsymmetric systems of linear equations

Thomas A. Manteuffel, Gerhard Starke, T. Manteuffel, 1996 .

LOCAL ERROR ESTIMATES AND ADAPTIVE REFINEMENT FOR FIRST-ORDER SYSTEM LEAST SQUARES (FOSLS)

Thomas A. Manteuffel, Stephen F. McCormick, Markus Berndt, 1997 .

Efficiency-based local adaptive refinement for fosls finite elements

Thomas A. Manteuffel, Josh W. Nolting, 2008 .

Orthogonal error methods

Thomas A. Manteuffel, Vance Faber, T. Manteuffel, 1987 .

A calculus of difference schemes for the solution of boundary-value problems on irregular meshes

Thomas A. Manteuffel, Andrew B. White, 1992 .

Multilevel methods for transport equations in diffusive regimes

Thomas A. Manteuffel, Klaus J. Ressel, 1993 .

Improved discretization error estimates for first-order system least squares

Thomas A. Manteuffel, Stephen F. McCormick, Christoph Pflaum, 2003 .

An Interval Analysis Approach to Rank Determination in Linear Least Squares Problems

Thomas A. Manteuffel, T. Manteuffel, 1981 .

Efficiency-based hand hp-refinement strategies for finite element methods

Thomas A. Manteuffel, Stephen F. McCormick, H. De Sterck, 2007 .

Algebraic multigrid for higher-order finite elements

Thomas A. Manteuffel, Jeffrey J. Heys, Luke N. Olson, 2005 .

Asymptotic behavior of singular values and singular functions of certain convolution operators

Thomas A. Manteuffel, Vance Faber, Andrew B. White, 1986 .

Multigrid Reduction in Time for Nonlinear Parabolic Problems

Thomas A. Manteuffel, Robert D. Falgout, Jacob B. Schroder, 2016 .

An analysis of block successive overrelaxation for a class of matrices with complex spectra

Thomas A. Manteuffel, R. C. Y. Chin, 1988 .

ADI as a preconditioning for solving the convection-diffusion equation

Thomas A. Manteuffel, John de Pillis, Raymond C. Y. Chin, 1984 .

Optimal equivalent preconditioners

Thomas A. Manteuffel, James S. Otto, 1993 .

The numerical solution of second-order boundary value problems on nonuniform meshes

Thomas A. Manteuffel, Andrew B. White, T. Manteuffel, 1986 .

Analysis of Velocity-Flux Least-Squares Principles for the Navier--Stokes Equations: Part II

Pavel B. Bochev, Thomas A. Manteuffel, Stephen F. McCormick, 1999 .

Preconditioning and Boundary Conditions

Thomas A. Manteuffel, Seymour V. Parter, T. Manteuffel, 2015 .

Preconditioning and boundary conditions without H 2 estimates: L 2 condition numbers and the distribution of the singular values

Thomas A. Manteuffel, Charles I. Goldstein, Seymour V. Parter, 1993 .