1.   ``Blocktran for the ILLIAC IV,'' Final report for ASEE-NASA Summer Fellowship, 1976.

2.   ``Solving the three-dimensional Navier-Stokes Equations on the ILLIAC IV,'' Final report for ASEE-NASA Summer Fellowship, 1977.

3.   ``Stability of Numerical Schemes that Contain a Mesh Refinement,'' Final report for a NASA-Ames Consortium Grant.

4.   ``Vectorization of the Beam-Warming Scheme on the CRAY-1 Computer,'' Final report, AFOSR Report No. F49620-79-0121.

5.   ``Analysis of the Computer Program Breakup for Modeling the Mist Lift Process,'' Final report for DOE/ASEE Summer Fellowship, 1981.

6.   ``The Development of a Multi-level Scheme for the Cauchy-Riemann Equations,'' Final report for NASA-Ames Consortium Grant.

7.   ``Multigrid Methods and Adaptive Techniques for Oil Reservoir Simulation:   A Progress Report,'' Institute for Computational Studies, Colorado State University, 1983 (with S. McCormick, J. Ruge and S. Schaffer).

8.   ``Numerical Analysis on Massively Parallel Processing Computers,'' Final Technical Report, AFOSR Contract # F33615-91-C-3001, 1991 (with Michael Andrews and Michael Brewer).
 
 

BOOKS REVIEWED

1.   Group Theoretic Methods in Bifurcation Theory, Bulletin of AMS, Vol. 7, #2, (1982).

2.   Numerical Methods for Scientific and Engineering Computation, SIAM Review, 29, #1, (1987).
 

BOOKS

1.  Finite Mathematics, Allyn & Bacon, Inc. (Boston), 1973, with Ann M. Thomas.

2.  Numerical Partial Differential Equations: Finite Difference Methods, Springer-Verlag (New York), 1995.

3.  Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations , Springer-Verlag (New York), 1999.
 

INVITED TALKS

1.   ``A Numerical Solution of the Exact Irrotational Gravity-Wave Problem,'' First International Conference on Numerical Ship Hydrodynamics, Bethesda, Maryland, 1975.

2.   ``Numerical Simulation of Water Waves,'' Fluid Mechanics and Wind Engineering Program, College of Engineering, Colorado State University, 1980.

3.   ``Multigrid Methods Applied to a Water Wave Problem,'' Third International Conference on Numerical Ship Hydrodynamics, Paris, France, 1981 (with S. McCormick).

4.   ``Bifurcation in the Benard Problem with a Free and Deformable Surface,'' Second IUTAM Symposium on Stability

in the Mechanics of Continua, Numbrecht, Fed. Rep. of Germany, 1981 (with S. Tento).

5.   ``An Implicit Scheme for Water Wave Problems,'' Symposium on the Numerical Generation of Curvilinear Coordinate Systems and Use in the Numerical Solution of Partial Differential Equations, Nashville, Tenn., 1982 (with M. Aston).

6.   ``The Fast Adaptive Composite Grid Method for Solving Differential Boundary Value Problems,'' Fifth ASCE Specialty Conference, Laramie, Wyoming, 1984 (with D. Ewing and S. McCormick).

7.   ``The Fast Adaptive Composite Grid Method for Elliptic Equations'' Special Session on Adaptive Local Grid Refinement, SIAM Meeting, Houston, Texas, 1985 (with S. McCormick).

8.   ``Fast Adaptive Composite Grid Methods,'' Second Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO, 1985.

9.   ``Analysis of a Free Boundary Ferro-Fluid Problems,'' Conference on Nonlinear Partial Differential Equations, Salt Lake City, UT, February, 1986.

10.   ``An Introduction to Vector Algorithms,'' Department of Mathematics, Montana State University, March, 1986.

11.   ``The Fast Adaptive Composite Grid Method,'' Department of Mathematics, Montana State University, March,

1986.

12.   ``Application of the fast adaptive composite multigrid method to computational fluid dynamics,'' Workshop on Numerical Solution of Nonlinear Differential Equations, Univ. of Arizona, Tucson,1987.

13.   ``Adaptive FAC algorithms and applications,'' Third Copper Mountain Conference on Multigrid Methods, Copper Mountain, Co(1987).

14.   ``Applicationns of the fast adaptive composite grid method to computational fluid dynamics,'' Fifth International Conference on Numerical Methods in Laminar and Turbulent Flow, Montreal, Canada, 1987.

15.   ``A mesh refinement scheme for the numerical solution of partial differential equations,''Angewandte Mathematik, Universität Hamburg, Hamburg, West Germany, December, 1987.

16.   ``The free surface of a magnetic fluid,''   Mathematisches Institut A,  Universität Stuttgart, Stuttgart, West Germany, December, 1987.

17.   ``Mesh Refinement Schemes for Computational Fluid Dynamics: the Fast Adaptive Composite Grid Method,'' Fluid Mechanics and Wind Engineering Program, College of Engineering, Colorado State University, October, 1988.

18.   ``Generation of FAC patched grids,'' Second Conference on Grid Generation in Computational Fluid Dynamics, Miami, Fla., December, 1988.

19.   ``Application of the fast adaptive composite grid method to nonlinear partial differential equations,'' AMS- SIAM Summer Seminar on Computational Solutions of Nonlinear Systems of Equations, Colorado State University, July, 1988.

20.   ``Application of the self adaptive time dependent fast adaptive composite grid method,'' Fourth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO.,1989 (with S. McKay).

21   ``TDFAC: A composite grid method for time dependent problems,'' Fourth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO., 1989 (with M. Heroux).

22.   ``A comparison of FAC and PCG methods for solving composite grid problems,'' Fifth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO., 1991 (with M. Heroux).

23.   ``Resolution of moving fronts using the self adaptive time dependent composite grid method,'' Fifth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO., 1991, (with S. McKay).

24.   ``The fast adaptive composite grid method for hyperbolic problems,'' Fifth Copper Mountain Conference on Multigrid Methods, Copper Mountain, CO., (with John Arvidson).
 
 
 

PAPERS

[1]   ``Irrotational gravity waves of finite height. A numerical study,'' Mathematika 15 (1968), 139-148.

[2]   ``A note on the fixed point theorem due to Furi and Vignoli,'' Bull. UMI, Vol. 4, #1 (1971), 45-46.

[3]  -coherent multifunctions, Bull. UMI, Vol. 4, #4 (1971).

[4]   ``A fixed point theorem for semigroups of mappings with a contractive iterate,'' Proc. Am. Math. Soc. Vol. 29 #3 (1971), 565-568 (with V. M. Sehgal).

[5]   ``On the equivalence of multiplicity and the generalized topological degree,'' Trans. of the Amer. Math.

Soc. Vol. 167 (May 1972), 333-345 (with T. O'Neil).

[6]   ``A bifurcation theorem for k-set contractions,'' Pacific J. Vol. 44 #3 (1973), 749-756.

[7]   ``On a lower bound to the number of solutions to a nonlinear operator equation,'' Scripta Mathematica.

[8]   ``On the Liapunov type fixed point theorem,'' Fundamenta Mathematicae 78 (1973), 141-143.

[9]   ``Upper and lower bounds for the number of solutions of functional equations involving k-set contractions,'' Rocky Mtn. J. of Math. Vol. 4 #1 (1974), 89-93.

[10]   ``The multiplicity of an operator in a special case of the topological degree for k-set contractions,'' Duke Math. J. Vol. 40 #2 (June 1973), 233-240.

[11]   ``Free streamline problems and the Milne-Thompson integral equation,'' J. of Math. and Phys. Sciences Vol. VIII # 1 (February 1974), 67-92 (with W. Conway).

[12]   ``A numerical study of the relationship between the dimensionless parameters in the problem of periodic waves of permanent type in a liquid of finite depth,'' Qtly. for Applied Math., January 1975.

[13]   ``On the numerical calculation of topological degree,'' SIAM Num. Anal. 12 (1975), 673-680.

[14]   ``A nonlinear three-point boundary value problem,'' J. of Math. Anal. and Applications, Vol. 58 #3 (May 1977) (with D. W. Zachmann).

[15]   ``A numerical solution of the exact irrotational gravity-wave problem,'' Proc. of the First Int'l. Conf. on Numerical Ship Hydrodynamics, Bethesda, Maryland, 1975.

[16]   ``Mathematical methods in in situ oil shale retorting,'' in the Proc. of the Symposium on the Impact of Oil Shale Development, Colorado State Univ., Ft. Collins, CO, 1979.

[17]   ``Mathematical modelling of in situ oil shale retorting processes,'' Energy Conversion and Fluid Mechanics, SIMS Conf., 1979, Alta, Utah.

[18]   ``Mathematical theory of nonlinear waves on the surface of a magnetic fluid,'' IEEE Trans. on Magnetics, Vol. 16 #2 (March, 1980) (with E. Twombly).

[19]   ``Multigrid methods applied to a water wave problem,'' in Proc. of the Third Int'l. Conf. on Numerical Ship Hydrodynamics, Paris, France, 1981 (with S. McCormick).

[20]   ``Bifurcation in the Benard problem with a free and deformable surface,'' in Proc. of the Second IUTAM Symp. on Stability in the Mechanics of Continua, Numbrecht, Fed. Rep. of Germany, 1981 (with S. Tento).

[21]   ``An implicit scheme for water wave problems,'' Proc. of the Symp. on the Numerical Generation of Curvilinear Coordinate Systems and Use in the Numerical Solution of Partial Differential Equations, Nashville, TN, April 1982 (with M. Aston).

[22]   ``Bifurcating instability of the free surface of a ferro fluid,'' SIAM J. Math. Anal. Vol. 14 #4 (July 1983) (with E. Twombly).

[23]   ``Bifurcation in double-diffusive convection: I. Equilibrium solution,'' SIAM J. Math. Anal. 17 (1986), pp. 91-113 (with W. Nagata).

[24]   ``Bifurcations in double-diffusive convection: II. Time periodic solutions,'' SIAM J. Math. Anal. 17 (1986), pp. 114-127 (with W. Nagata).

[25]   ``Efficient modeling of time-dependent, maldistributed flow in packed beds,'' AIChE Journal31 871 (1985) (with K. Bowers).

[26]   ``The fast adaptive composite grid method for solving differential boundary value problems,'' Proc. of Fifth ASCE Specialty Conf., Laramie, WY, 1984 (with D. Ewing and S. McCormick).

[27]   ``The fast adaptive composite grid method (FAC) for elliptic boundary value problems,'' Math. of Comp. Vol. 49 No. 174 (April, 1986) (with S. McCormick).

[28]   ``Bifurcations in double-diffusive systems: III. Interaction of equilibrium and time periodic solutions,'' SIAM J. Math. Anal. 17 (1986), pp. 289-311 (with W. Nagata).

[29]   ``The fast adaptive composite grid method (FAC): Algorithms for advanced computers,'' Applied Math & Comp. 19 (1986), 103-126, (with L. Hart, S. McCormick and A. O'Gallagher).

[30]   ``Thermal behavior of an oil shale retort,'' submitted (with K. Bowers).

[31]   ``The Benard problem with a free and deformable surface,'' submitted (with S. Tento).

[32]   ``Application of the fast adaptive composite grid method (FAC) to computational fluid dynamics,'' Proceedings of the 10th International Conference on Computational Fluid Dynamics, Lecture Notes in Physics, Springer-Verlag(1986), pp. 606-611 (with R. Schweitzer, M. Heroux, S. McCormick and A.M. Thomas).

[33]   ``Applications of the fast adaptive composite grid method,'' Lecture Notes in Pure and Applied Mathematics 110, Marcel-Decker, (1988) (with M. Heroux, S. McKay and S. McCormick).

[34]   ``Applications of the fast adaptive composite grid method to computational fluid dynamics,'' Numerical Methods in Laminar and Turbulent Flow, (C. Taylor, W. G. Habashi and M. M. Hafez, eds.), Pineridge Press, Swansea, UK, (1987), (with M. Heroux, S. McKay, S. McCormick and A.M. Thomas).

[35]   ``Application of the fast adaptive composite grid method to nonlinear partial differential equations,'' Computational Solution of Nonlinear Systems of Equations, Lecture Notes in Applied Mathematics 26 E.L. Allgower & K. Georg, eds., American Mathematical Society, 1990, (with S. McKay).

[36]   ``Generation of FAC patched grids,'' Numerical Grid Generation in Computational Fluid Mechanics '88, (S. Sengupta, J. Häuser, P. R Eiseman, and J. F. Thompson, eds.), Pineridge Press, Swansea, UK, (1988), (with S. McKay).

[37]   ``Computational complexity of the fast adaptive composite grid (FAC) method,'' Applied Numerical Mathematics, Vol. 6, 1989/90, (with Steve  F. McCormick and Steven  M. McKay).

[38]   ``Application of the self adaptive time dependent fast adaptive composite grid method,'' Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods,, Jan Mandel, etal eds., SIAM, 1989 (with S. McKay).

[39]   ``TDFAC: A composite grid method for time dependent problems,'' Proceedings of the Fourth Copper Mountain Conference on Multigrid Methods, Jan Mandel, etal, eds. SIAM, 1989 (with M. Heroux).

[40]   ``The time dependent fast adaptive composite grid method: theory and applications,'' preprint (with M. Heroux).

[41]   ``Resolution of moving fronts using the self adaptive time dependent composite grid method,'' Communications in Applied Numerical Methods, Vol. 8, No. 9,(1992), pp. 651-660(with S. McKay).

[42]   ``A comparison of FAC and PCG methods for solving composite grid problems,'' Communications in Applied Numerical Methods, Vol. 8, No. 9,(1992), pp. 573-584(with Michael A. Heroux).

[43]   ``Numerical Simulation of Taylor-Couette Experiments for Short Cylinders,'' preprint, (with Ron Adair).