PUBLICATIONS

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Dr. Graeme Fairweather, Professor and Head
Mathematical and Computer Sciences
Colorado School of Mines
Book and Book Contributions

• Finite Element Galerkin Methods for Differential Equations, Lecture Notes in Pure and Applied Mathematics, Volume 34, Marcel Dekker, New York, 1978, 280 pages.
• A. R. Mitchell: Some Biographical and Mathematical Notes, in Numerical Analysis A. R. Mitchell 75th Birthday Volume, D. F. Griffiths and G. A. Watson, editors, World Scientific London, 1996, pp. 1-8, (with D. F. Griffiths, G. A. Watson and J. D. Lambert).
• Preface, Interactive Mathematics Program Year 3, Key Curriculum Press, Berkeley, California, 1999.

Edited Conference Proceedings

• Numerical Integration: Recent Developments, Software and Applications, Proceedings of the NATO Advanced Research Workshop, Dalhousie University, Halifax, Nova Scotia, August 11-15, 1986, D. Reidel Publishing Company, Dordrecht, The Netherlands, 1987, 394 pages, (co-edited with P. Keast).
• Proceedings of the Workshop on the Method of Lines for Time Dependent Problems, University of Kentucky, 1995, Appl. Numer. Math., 20(1-2), 1996, 244 pages, (co-edited with I. Gladwell).
• Proceedings of the NSF/CBMS Regional Workshop on Hamiltonian Differential Equations, Colorado School of Mines, 1997, Appl. Numer. Math., 29, 1999, 165 pages, (co-edited with I. Gladwell, B. Leimkuhler, E. S. Van Vleck).

Refereed Papers

• Improved forms of the alternating direction methods of Douglas, Peaceman and Rachford for solving parabolic and elliptic equations, Numer. Math., 6(1964), 285-292, (with A. R. Mitchell).
• A generalized alternating direction method of Douglas-Rachford type for solving the biharmonic equation, Comput. J., 7(1964), 242-245, (with A. R. Mitchell).
• A new alternating direction method for parabolic equations in three space variables, J. Soc. Indust. Appl. Math., 13(1965), 957-965, (with A. R. Mitchell).
• A high accuracy alternating direction method for the wave equation, J. Inst. Math. Appl., 1(1965), 309-316, (with A. R. Mitchell).
• Some computational results of an improved ADI method for the Dirichlet problem, Comput. J., 9(1966), 298-303, (with A. R. Mitchell).
• Some stable difference approximations to a fourth order parabolic differential equation, Math. Comp., 10(1967), 1-11, (with A. R. Gourlay).
• Some high accuracy difference schemes with a splitting operator for equations of parabolic and elliptic type, Numer. Math., 10(1967), 56-66, (with A. R. Gourlay and A. R. Mitchell).
• A new computational procedure for A.D.I. methods, SIAM J. Numer. Anal., 4(1967), 163-170, (with A. R. Mitchell).
• A note on a generalization of a method of Douglas, Math. Comp., 23(1969), 407-409.
• Modified Romberg Quadrature, Algorithm 351, Comm. ACM, 12(1969), 324-325.
• On the eigenvalues and eigenvectors of a class of Hessenberg matrices, SIAM Rev., 13(1971), 220-221.
• A survey of discrete Galerkin methods for parabolic equations in one space variable, Math. Colloq. Univ. Cape Town, 7 (1971-1972), 43-77.
• Galerkin methods for vibration problems in two space variables, SIAM J. Numer. Anal., 9(1972), 702-714.
• Three level Galerkin methods for parabolic equations, SIAM. J. Numer. Anal., 11(1974), 392-410, (with T. Dupont and J. P. Johnson).
• Alternating direction Galerkin methods for parabolic and hyperbolic problems on rectangular polygons, SIAM J. Numer. Anal., 12(1975), 144-163, (with J. E. Dendy).
• On the extrapolation of Galerkin methods for parabolic problems, Numer. Math., 23(1975), 269-287, (with J. P. Johnson).
• A note on the efficient implementation of certain Pad\'e methods for linear parabolic problems, BIT, 18(1978), 106-109.
• An investigation of Romberg quadrature, ACM Trans. Math. Software, 4(1978), 316-322, (with P. Keast).
• On the numerical solution of two-dimensional potential problems by an improved boundary integral equation method, J. Comput. Phys., 31(1979), 96-112, (with F. J. Rizzo, D. J. Shippy and Y. S. Wu).
• On the approximate solution of a diffusion problem by Galerkin methods, J. Inst. Math. Appl., 24(1979), 121-137.
• A linear ADI method for the shallow water equations, J. Comput. Phys., 36(1980), 1-18, (with I. M. Navon).
• Annular bed reactor - methanation of carbon dioxide, Can. J. Chem. Eng., 59(1981), 497-500, (with M. Davis and J. Yamanis).
• On the use of spline collocation for boundary value problems arising in chemical engineering, Comput. Methods Appl. Mech. Engrg., 18(1981), 179-189, (with M. Davis).
• Analysis of SO² oxidation in non-isothermal catalyst pellets using the dusty-gas model, Chem. Eng. Sci., 37(1982), 447-452, (with M. Davis and J. Yamanis).
• A computational study of finite element methods for second order two-point boundary value problems, Math. Comp., 40(1983), 499-518, (with P. Keast and J. C. Diaz).
• Solution of boundary value problems using software packages: DD04AD and COLSYS, Chem. Eng. Commun., 22(1983), 1-9, (with K. S. Denison and C. E. Hamrin, Jr.).
• The effect of Prandtl number on heat transfer from a rotating disk with blowing at the wall, Int. Comm. Heat Mass Transfer, 10(1983), 287-297, (with P. H. Muir and M. Vedha-Nayagam).
• Fortran packages for solving certain almost block diagonal systems by modified alternate row and column elimination, ACM Trans. Math. Software, 9(1983), 358-375, (with J. C. Diaz and P. Keast).
• Algorithm 603 COLROW and ARCECO: Packages for solving certain almost block diagonal linear systems by modified alternate row and column elimination, ACM Trans. Math. Software, 9(1983), 376-380, (with J. C. Diaz and P. Keast).
• On the application of extrapolation, deferred correction and defect correction to discrete-time Galerkin methods for parabolic problems, IMA J. Numer. Anal., 3(1983), 173-192, (with A. V. Saylor).
• The non-iterative solution of nonlinear parabolic and mixed-type problems arising in reactor design, Chem. Eng. Commun., 23(1983), 89-99, (with M. E. Davis and J. Yamanis).
• On the H^-1-Galerkin method for second-order linear two-point boundary value problems, SIAM J. Numer. Anal., 21(1984), 314-326, (with P. Keast and J. C. Diaz).
• A note on the condition of a matrix, Int. Comm. Heat Mass Transfer, 11(1984), 191-195.
• The method of fundamental solutions for problems in fluid flow, Appl. Math. Modeling, 8(1984), 265-270, (with R. L. Johnston).
• A survey of higher order methods for the numerical integration of semidiscrete parabolic problems, IMA J. Numer. Anal., 4(1984), 375-425, (with W. L. Seward and R. L. Johnston).
• Letter to the Editor, A.I.Ch.E.J., 31(1985), 351-352, (with C. P. Kelkar and C. E. Hamrin, Jr.).
• Prediction of membrane separation characteristics by pore distribution measurements and surface force-pore flow model, Chem. Eng. Commun., 42(1986), 111-128, (with D. Bhattacharyya, M. Jevtitch and J. T. Schrodt).
• Analyses of spline collocation methods for parabolic and hyperbolic problems in two space variables, SIAM J. Numer. Anal., 23(1986), 282-296, (with C. E. Greenwell-Yanik).
• On the asymptotic expansion of the discretization error of certain discrete-time Galerkin methods for parabolic problems, Numer. Funct. Anal. Optim., 8(1985-86), 447-471, (with A. V. Saylor).
• Reformulation and the numerical solution of the equations for a catalytic, porous wall, gas-liquid reactor, Computers Chem. Eng., 10(1986), 361-365, (with A. Akyurtlu, J. F. Akyurtlu and C. E. Hamrin, Jr.).
• The method of fundamental solutions for the numerical solution of the biharmonic equation, J. Comput. Phys., 69(1987), 434-459, (with A. Karageorghis).
• An assessment of numerical software for solving two-point boundary value problems arising in heat transfer, Numerical Heat Transfer, 11(1987), 281-293, (with M. Vedha-Nayagam).
• The effect of surface mass transfer on buoyancy-induced flow in a variable-porosity medium adjacent to a horizontal heated plate, Int. Comm. Heat Mass Transfer, 14(1987), 495-506, (with M. Vedha-Nayagam and P. Jain).
• Numerical simulation of transport from an infinite line source: error analysis, Atmos. Environ., 22(1988), 75-82, (with P. S. Kasibhatla and L. K. Peters).
• The Almansi method of fundamental solutions for solving biharmonic problems, Internat. J. Numer. Methods Engrg., 26(1988), 1665-1682, (with A. Karageorghis).
• Finite element methods for parabolic and hyperbolic partial integro-differential equations, Nonlinear Anal., 12(1988), 785-809, (with E. G. Yanik).
• The method of fundamental solutions for the solution of non-linear plane potential problems, IMA J. Numer. Anal., 9(1989), 231-242, (with A. Karageorghis).
• A survey of spline collocation methods for the numerical solution of differential equations, Mathematics for Large Scale Computing, J. C. Diaz, ed., Lecture Notes in Pure and Applied Mathematics, Volume 120, Marcel Dekker, New York, 1989, pp. 297-341, (with D. Meade).
• The simple layer potential method of fundamental solutions for certain biharmonic problems, Internat. J. Numer. Methods Fluids, 9(1989), 1221-1234, (with A. Karageorghis).
• On the numerical solution of a model air pollution problem with nonsmooth initial data, Comm. Appl. Numer. Methods, 6(1990), 145-156, (with W. L. Seward and P. Kasibhatla).
• A stabilized Galerkin method for a third order evolutionary problem, Math. Comp., 55(1990), 497-507, (with J. M. Sanz-Serna and I. Christie).
• The reformulation and numerical solution of certain non-classical initial-boundary value problems, SIAM J. Sci. Statist. Comput., 12(1991), 127-144, (with R. D. Saylor).
• An alternating direction Galerkin method for a class of second order hyperbolic equations in two space variables, SIAM J. Numer. Anal., 18(1991), 1265-1281, (with R. I. Fernandes).
• A box method for a nonlinear equation of population dynamics, IMA J. Numer. Anal., 11(1991), 525-538, (with J. C. López-Marcos).
• On the use of the software package SPRINT in the study of atmospheric turbulence in a convective boundary layer, Environmental Software, 6(1991), 120-130, (with P. Pai and T. H. Tsang).
• Fast direct solvers for piecewise Hermite bicubic orthogonal spline collocation equations, SIAM J. Numer. Anal., 29(1992), 156-173, (with B. Bialecki and K. R. Bennett).
• Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions, J. Acoust. Soc. Amer., 91(1992), 1844-1854, (with D. J. Shippy and P. S. Kondapalli).
• The method of fundamental solutions for transmission and scattering of elastic waves, Comput. Methods Appl. Mech. Engrg., 96(1992), 255-269, (with D. J. Shippy and P. S. Kondapalli).
• Orthogonal spline collocation methods for some partial integrodifferential equations, SIAM J. Numer. Anal., 29(1992), 755-768, (with Y. Yan).
• The solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions, ACM Trans. Math. Software, 18(1992), 193-204, (with F. Majaess, P. Keast and K. R. Bennett).
• Algorithm 704: ABDPACK and ABBPACK - Fortran programs for the solution of almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions, ACM Trans. Math. Software, 18(1992), 205-210, (with F. Majaess, P. Keast and K. R. Bennett).
• A parallel boundary-value ODE code for shared-memory machines, Internat. J. High Speed Computing, 4(1992), 71-86, (with K. R. Bennett).
• On the numerical solution of the cubic Schrödinger equation in one space variable, J. Comput. Phys., 103(1993), 277-284, (with M. P. Robinson and B. M. Herbst).
• Analysis of alternating direction collocation methods for parabolic and hyperbolic problems in two space variables, Numerical Methods for Partial Differential Equations, 9(1993), 191-211, (with R. I. Fernandes).
• Matrix decomposition algorithms for separable elliptic boundary value problems in two space dimensions, J. Comput. Appl. Math., 46(1993), 369-386, (with B. Bialecki).
• A fourth-order cubic spline method for linear second-order two-point boundary value problems, IMA J. Numer. Anal., 13(1993), 591-607, (with I. H. Sloan and Dat Tran).
• Orthogonal cubic spline collocation solution of underwater acoustic wave propagation problems, J. Comput. Acoust., 1(1993), 355-370, (with M. P. Robinson).
• An explicit extrapolated box scheme for the Gurtin-MacCamy equation, Comput. Math. Appl., 27(1994), 41-53, (with J. C. López-Marcos).
• Fourier methods for piecewise Hermite bicubic orthogonal spline collocation, East-West J. Numer. Math., 2(1994), 1-20, (with B. Bialecki and K. A. Remington).
• Spline collocation methods for a class of hyperbolic partial integro-differential equations, SIAM J. Numer. Anal., 31(1994), 444-460.
• Orthogonal spline collocation methods for Schrödinger-type equations in one space variable, Numer. Math., 68(1994), 355-376, (with M. P. Robinson).
• The current state and future direction of Eulerian models in simulating the tropospheric chemistry and transport of trace species: a review, Atmospheric Environment, 28(1995), 189-222, (with L. K. Peters, C. M. Berkowitz, G. R. Carmichael, R. C. Easter, S. T. Ghan, J. M. Hales, L. R. Leung, W. R. Pennell, F. A. Potra, R. D. Saylor, and T. T. Tsang).
• Matrix decomposition algorithms in orthogonal spline collocation for separable elliptic boundary value problems, SIAM J. Sci. Comput., 16(1995), 330-347, (with B. Bialecki).
• Diffusion flame over a continuous moving fuel plate in a parallel flow of oxidizer under microgravity, AIAA J. Thermophysics and Heat Transfer, 10(1996), 97-101, (with M. Vedha-Nayagam).
• Spline collocation calculation for the hydrogen molecular ion, J. Physics B: At. Mol. Opt. Phys., 29(1996), 2375-2391, (with J. C. Morrison, C. Baunach, L. Larson and B. Bialecki).
• Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions, Adv. Comput. Math., 6(1996), 243-262, (with J. C. López-Marcos).
• Discrete-time orthogonal spline collocation methods for Schrödinger equations in two space variables, SIAM J. Numer. Anal., 35(1998), 453-477, (with B. Li and B. Bialecki).
• Orthogonal spline collocation methods for biharmonic problems, Numer. Math., 80(1998), 267-303, (with Z. Lou and B. Bialecki).
• The method of fundamental solutions for elliptic boundary value problems, Adv. Comput. Math., 9(1998), 69-95, (with A. Karageorghis).
• The method of fundamental solutions for axisymmetric acoustic scattering and radiation problems, J. Acoust. Soc. Am., 104(1998), 3212-3218, (with A. Karageorghis).
• The method of fundamental solutions for axisymmetric potential problems, Internat. J. Numer. Methods Engrg., 44(1999), 1653-1669, (with A. Karageorghis).
• A Crank-Nicolson orthogonal spline collocation method for vibration problems, Appl. Numer. Math., 33(2000), 299-306, (with B. Li and B. Bialecki).
• The method of fundamental solutions for axisymmetric elasticity problems, Computational Mechanics, 25(2000) 524-532, (with A. Karageorghis).
• Almost block diagonal linear systems: sequential and parallel solution techniques and applications, Numer. Linear Algebra Appl., 7(2000) 275-317, (with P. Amodio, J. R. Cash, G. Roussos, R. W. Wright, I. Gladwell, G. L. Kraut and M. Paprzycki).
• Numerical solutions of the orbital equations for diatomic molecules, Molecular Physics, 98 (2000), 1175--1184, (with J. C. Morrison, T. Wolf, B. Bialecki and L. Larson).
• Orthogonal spline collocation methods for partial differential equations, J. Comput. Appl. Math., 128(2001), 55-82, (with B. Bialecki).
• Numerical methods for Schrodinger-type problems, in "Trends in Industrial and Applied Mathematics", A. H. Siddiqi and M. Kocvara, editors, Kluwer Academic Publishers, Boston, 2002, pp. 219-250, (with M. Khebchareon).
• H¹-Galerkin mixed finite element methods for parabolic partial integro-differential equations, IMA J. Numer.Anal., 22(2002), 231--252, (with A. Pani).
• Discrete-time orthogonal spline collocation methods for vibration problems, SIAM J. Numer. Anal., 39(2002), 2045--2065, (with B. Li and B. Bialecki).
• Matrix decomposition algorithms for modified spline collocation for Helmholtz problems, SIAM J. Sci. Comput., 24(2003), 1733--1753, (with B. Bialecki and A. Karageorghis).
• An H¹-Galerkin mixed finite element method for an evolution equation with a positive type memory term, SIAM J. Numer. Anal., 40 (2003), 1475--1490, (with A. Pani).
• The method of fundamental solutions for scattering and radiation problems, Engineering Analysis with Boundary Elements, 27 (2003), 759--769, (with A. Karageorghis and P. A. Martin).
• Algorithms for almost block diagonal linear systems, SIAM Rev., 46(2004), 49--58, (with I. Gladwell).
• A matrix decomposition MFS algorithm for axisymmetric biharmonic problems, Adv. Comput. Math, 23(2005), 55--71, (with Y.-S. Smyrlis and A. Karageorghis).
• Optimal superconvergent one step cubic spline collocation methods, SIAM J. Sci. Comput., 27(2005), 575--598, (with B. Bialecki and A. Karageorghis).
• Asymptotic expansions and Richardson extrapolation of approximate solutions for second order elliptic problems on rectangular domains by mixed finite element methods, SIAM J. Numer. Anal., 44 (2006), 1122--1149, (with Q. Lin, Y. Lin, J. Wang and S. Zhang).
• Potential field based geometric modeling using the MFS, Internat. J. Numer. Methods Engrg., 68 (2006), 1257--1280, (with Y. -S. Smyrlis, A. Karageorghis and R. Tankelevich).

Papers in Refereed Conference Proceedings

• The method of fundamental solutions for problems in potential theory, Treatment of Integral Equations by Numerical Methods, C. T. H. Baker and G. F. Miller, editors, Academic Press, London, 1982, 349-359, (with R. L. Johnston).
• On the use of numerical software for solving two-point boundary value problems arising in heat transfer, AIChE/ASME 23rd National Heat Transfer Conference, Denver, Colorado, August 1985, (with M. Vedha-Nayagam).
• Packages for solving almost block diagonal linear systems arising in spline collocation at Gaussian points with monomial basis functions, Scientific Software Systems, J. C. Mason and M. G. Cox, editors, Chapman and Hall, London, 1990, 47-58, (with F. Majaess and P. Keast).
• An orthogonal spline collocation method for the numerical solution of underwater acoustic wave propagation problems, Computational Acoustics - Volume 2, D. Lee, A. R. Robinson and R. Vichnevetsky, editors, Elsevier Science Publishers, Amsterdam, 1993, pp. 339-353, (with M. P. Robinson).
• An additive Schwarz algorithm for piecewise Hermite bicubic orthogonal spline collocation, Proceedings of the Sixth International Conference on Domain Decomposition Methods in Science and Engineering, Contemporary Mathematics, Vol. 157, American Mathematical Society, Providence, RI, 1994, pp. 237-244, (with B. Bialecki, X.-C. Cai and M. Dryja).

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Questions/comments to: gfairwea@mines.edu
October 2003