Mac Hyman's Selected Papers

Numerical Analysis:

Research Summary

Identifying Gaps in the Spectrum of Self-Adjoint Operators, with M. Hasson and J. Restrepo; to appear in Computers and Mathematics with Applications (2007).

Being sensitive to uncertainty , with L. Arriola; Computing in Science and Engineering; v.9, no.2, p.10-20 (2007).

Applications of Algebraic Topology to Compatible Spatial Discretizations, P.B. Bochev and J.M. Hyman, to appear in the Five-Laboratory Conference on Computational Mathematics proceedings, Vienna, June 2005,, LAUR #05-4619

Principles of Mimetic Discretizations of Differential Operators, Pavel B. Bochev and James M. Hyman, IMA VOLUMES IN MATHEMATICS AND ITS APPLICATIONS; 2006; v.142, p.89-119, LAUR #05-4244

Patch Dynamics for Multiscale Problems, J.M. Hyman, Computing in Science and Engineering, May-June 2005; Vol. 7, no. 3, p. 22-28, LAUR #05-2277

Brouwer's Law: Optimal Multistep Integrators for Celestial Mechanics, K.R Grazier, W.I. Newman, David J. Goldstein, James M. Hyman, Philip W. Sharp, LAUR #04-6861

A numerical study of the exact evolution equations for surface waves in water of finite depth, Yi A. Li, and J.M. Hyman, W.Y Choi, Studies in Applied Mathematics, v. 113, no. 3, p. 303-324 (2004)

Equation-free, coarsegrained multiscale computation:enabling microscopic simulators to perform system-level analysis, I Kevrekidis, C. Gear, J. Hyman, Kevrekidis P., O. Runborg, and K. Theodoropoulos, Communications in Mathematical Sciences 1 (2003), no. 4, 715-762

Computer arithmetic for probability distribution variables, W. Li, and J.M. Hyman, Reliability Engineering and System Safety, 85 (2004) pp. 191-209.

An adaptive moving mesh method with static rezoning for partial differential equations, S. Li, J.M. Hyman, L.R. Petzold, Computers and Mathematics with Applications; November/December 2003; v.46, no.10, p.1511-1524

The Convergance of Mimetic Discretization for Rough Grids, J.M. Hyman and S. Steinberg, LA-UR-01-2434 (2003)

Solution Adapted Mesh Refinement and Sensitivity Analysis for Parabolic Partial Differential Equation Systems, S. Li, L. Petzold, and J.M. Hyman (2002)

Mimetic finite difference methods for diffusion equations, J. Hyman, J. Morel, M. Shashkov, S. Steinberg, COMPUTATIONAL GEOSCIENCES; 2002; v.6, no.3-4, p.333-352

Mimetic Finite Difference Methods for Maxwell's Equations and the Equations of Magnetic Diffusion   J. M. Hyman and M. Shashkov,Prog. in Electromagnetic Research, PIER Vol. 32, (2001), 89-121. Los Alamos Report (ps)

Mimetic Finite Difference Operators for Second-Order Tensors on Unstructured Grids   J. C. Campbell, J. M. Hyman, and M. J. Shashkov, to appear Computers Math. with Applications (2001).

Fourth and Sixth-Order Conservative Finite Difference Approximations of the Divergence and Gradient   J. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, Applied Numerical Analysis 37, (2001), 171-187, Los Alamos Report (ps)

The Effect of Inner Products for Discrete Vector Fields on the Accuracy of Mimetic Finite Difference Methods   J. M. Hyman, M. Shashkov and S. Steinberg, Los Alamos Report (2000)

An Algorithm to Align a Quadrilateral Grid with Internal Boundaries   J. M. Hyman, S. Li, P. Knupp and M. Shashkov, J. Comp. Physics, v. 163(#1) (2000), pp. 133-149, Los Alamos Report LA-UR-98-5461 (ps)

An Algorithm to Align a Quadrilateral Grid with Internal Boundaries   J. M. Hyman, S. Li, P. Knupp and M. Shashkov, Los Alamos Report LA-UR-98-5460 (ps)

The Orthogonal Decomposition Theorems for Mimetic Finite Difference Methods,   J. M. Hyman and M. Shashkov, SIAM Journal on Numerical Analysis, v. 36(#3) pp. 788-818, (1999)Los Alamos Report (ps)

Mimetic Discretizations for Maxwell's Equations   J. Hyman and M. Shashkov, Journal of Computational Physics, 151, No. 2, 881-909 (1999), Los Alamos Report (ps)

The Approximation of Boundary Conditions for Mimetic Finite Difference Methods,J. M. Hyman and M. Shashkov, Computers & Mathematics with Applications, Vo. 36, No. 5, 79-99, (1998) Los Alamos Report (ps)

Mimetic Discretizations for Maxwell's Equations and the Equations of Magnetic Diffusion   J. M. Hyman and M. Shashkov, in J. A. DeSanto, ed., Mathematical and and Numerical Aspects of Wave Propagations, (SIAM, Philadelphia, (1998)) 561-563, Proc. of the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Golden, Colorado, June 1-5, (1998), Extended Los Alamos Report (ps)

The Black Box Multigrid Numerical Homogenization Algorithm,   J. D. Moulton, J. E. Dendy, and J. M. Hyman, Journal of Computational Physics, 141 (1998), 1-29, (pdf) Los Alamos Report (ps)

The Numerical Solution of Diffusion Problems in Strongly Heterogeneous Non-Isotropic Materials,   J. Hyman, M. Shashkov and S. Steinberg, Journal of Computational Physics, 132, pp. 130-148, (1997).

Natural Discretizations for the Divergence, Gradient, and Curl on Logically Rectangular Grids,   J. M. Hyman and M. Shashkov, International Journal of Computers & Mathematics with Applications, Vol. 33, No. 4, (1997), pp. 81-104.

Adjoint Operators for the Natural Discretizations of the Divergence, Gradient and Curl on Logically Rectangular Grids,  J. M. Hyman and M. Shashkov, Applied Numerical Mathematics 25 (1997) 413-442. Los Alamos Report (ps)

The Numerical Solution of Diffusion Problems in Strongly Heterogeneous Non-Isotropic Materials,   J. M. Hyman, M. Shashkov, and S. Steinberg (1996)

The Sensitivity and Accuracy of Fourth Order Finite-Difference Schemes on Nonuniform Grids in One Dimension,  J. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg, An International Journal of Computers & Mathematics with Applications, Vol. 30, No. 8, pp. 41-55, (1995). (pdf)

High-Order Mimetic Finite Difference Methods on Nonuniform Grids, in ICOSAHOM-95,   J. Castillo, J. M. Hyman, M. Shashkov and S. Steinberg,Proc. of the Third International Conference on Spectral and High Order Methods, Houston, Texas, 5-9 June (1995). Special Issue of Houston Journal of Mathematics, eds. A.V. Ilin and L. R. Scott, 1995, pp. 347-361. (ps)

High Order Finite Volume Approximations of Differential Operators on Nonuniform Grids,   J. M. Hyman, R. J. Knapp and J. C. Scovel, Physica D, 60 (1992) pp. 112-138.

Inner Products for Discrete Vector Fields and Accuracy of Mimetic Finite Difference Methods,   J. M. Hyman, M. Shashkov, and S. Steinberg (1991)

Nonnegativity-, Monotonicity-, or Convexity-Preserving Cubic and Quintic Hermite Interpolation, with R. L. Dougherty and A. S. Edelman, Math. Comp. 52, No.186 (1989), pp. 471-494.

Deriving Mimetic Difference Aproximations to Differential Operators Using Algebraic Topology, James M. Hyman and James C. Scovel, Math. Comp. 52, No.186 (1989), pp. 471-494.

Numerical Methods for Tracking Interfaces, J. M. Hyman, Physica D (1984), pp. 396-407.

High-Order Sparse Factorization Methods for Elliptic Boundary Value Problem, J.M. Hyman and T.A. Manteuffel, Advances in Computer Methods for Partial Differential Equations - V (1979), pp. 551-555.

Self-Adjusting Grid for One-Dimensional Hyperbolic Conservation Laws,   A. Harten and J. M. Hyman, J. Comp. Phys. 50, No. 2, (May 1983), pp. 235-269.

Accurate Monotonicity Preserving Cubic Interpolation,   J. M. Hyman, Society of Industrial and Applied Mathematics Journal of Scientific and Statistical Computing, 4, No. 4, (December 1983) pp. 645-654.

Numerical Methods for Nonlinear Differential Equations, James M. Hyman, Nonlinear Problems: Presernt and Future, A.R. Bishop, D.K. Campbell, B. Nicolaenko (eds.) North-Holland Publishing Company, (1982)

The Numerical Differentiation of Discrete Functions Using Polynomial Interpolation Methods, with B. Larrouturou, Appl. Math and Comp., Vols. 10--11; reprinted in Numerical Grid Generation, J. F. Thompson, Ed., Elsevier North-Holland, New York (1982), pp. 487-506.

A Method of Lines Approach to the Numerical Solution of Conservation Laws, J.M. Hyman, Advances in Computer Methods for Partial Differential Equations - III (1979), pp. 313-321.

Periodic Solutions of a Logistic Difference Equation,   F.C. Hoppensteadt and J.M. Hyman, SIAM Appl. Math. 32, No. 1, (1977).

Finite Difference Approximations and Entropy Conditions for Shocks,   A. Harten, J. M. Hyman, and P. D. Lax, Comm. on Pure and Appl. Math. 29, pp. 297-322 (1976).



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