Papers

Accepted In Refereed Journals

1. Cao W., Haynes, R.D., and Trummer, M.R. Preconditioning for a Class of Spectral Differentiation Matrices. J. Sci. Comput. Vol. 24, No.3, pp. 343-371, September 2005. PDF

2. Turner, C., Haynes, R.D. A Numerical and Theoretical Study of Blow-up for a System of Ordinary Differential Equations using the Sundman Transformation, Atlantic Electronic Journal of Mathematics, Issue 2, 2007. PDF

3. Haynes, R.D., Kennedy, S.C. and Trummer, M.R., Persistently Positive Inverses of Perturbed M--Matrices, Linear Algebra and Applications, Volume 422, Issue 2-3, Pages 742-754, 2007. PDF

4. Haynes, R.D., and Russell, R.D. A Schwarz Waveform Moving Mesh Method, SIAM J. Sci. Comput. Vol. 29, No. 2, pp. 656-673, 2007. PDF

5. Haynes, R.D., Huang, W., and Russell, R.D. A Moving Mesh Method for Time--dependent Problems based on Schwarz Waveform Relaxation, Proceedings of the 17th International Domain Decomposition Methods Meeting, Lecture Notes in Computational Science and Engineering (LNCSE), Springer--Verlag, Vol. 60, pages 229--236, 2008. PDF

6. Dulong, B., Haynes, R.D., and Robertson, M. A study in the computation time required for the inclusion of strain field effects in Bloch-wave simulations of TEM diffraction contrast images, Ultramicroscopy, Vol. 108, Iss. 5, pp. 415--425, 2008. PDF

7. R. Karsten, J. McMillan, M. Lickley, and R.D. Haynes. Assessment of Tidal Current Energy for Minas Passage, Bay of Fundy. Proc. IMechE Part A: J. Power and Energy, Vol. 222, pp. 493--507, 2008 PDF

8. McMillan, J., Lickley, M., Karsten, R. and Haynes, R.D. Potential of Tidal Power and its Effects on the Bay of Fundy. SIAM Undergraduate Research Online, Volume 1, Issue 1, pp. 20--37, 2008. PDF

9. Kennedy, S. and Haynes, R.D. Inverse Positivity of Perturbed Tridiagonal M-Matrices, Linear Algebra and its Applications, Volume 430, Issues 8-9, pp. 2312-2323, 2009. PDF

10. Haynes, R.D., Recent Advances in Schwarz Waveform Moving Mesh Methods -- A New Moving Subdomain Method, Lecture Notes in Computational Science and Engineering (LNCSE), Springer--Verlag, Volume 78, 2011. PDF

11. Ranjan, P., Haynes, R.D., Karsten, R., A Computationally Stable Approach to Gaussian Process Interpolation of Deterministic Computer Simulation Data Pritam Ranjan, Ronald D. Haynes and Richard Karsten, Technometrics. Nov 2011, Vol. 53, No. 4: 366-378 PDF

Under Revision

12. Gander, M.J., Haynes, R.D. and Howse, A.M., Alternating and Linearized Alternating Schwarz Methods for Equidistributing Grids (LNCSE).

13. Haynes, R.D., Huang, J., and Haung, T--Z., Monotonicity of Perturbed Tridiagonal $M$--matrices (SIMAX)

14. Christlieb, A., Haynes, R.D. and Ong, B., A Parallel Space--Time Algorithm (SISC)

Submitted

15. Haynes, R.D., Huang, W., Zegeling, P.A., A Numerical Study of Blowup in the Harmonic Map Heat Flow using the MMPDE moving mesh method.

16. Gander, M.J., Haynes, R.D. Domain Decomposition approaches for mesh generation via the Equidistribution Principle.

Preprints

Papers in Preparation

17. Haynes, R.D., Howse, A. Two-Dimensional Equidistributing Grids obtained by Domain Decomposition.

18. Haynes, R.D. and Howse, A. Schwarz iterations for Fredholm Integral Equations of the Second Kind.

19. Haynes, R.D. and Huang, W. Persistance of Monotonicty and the Discrete Maximum Principle.

20. Colbry, D., Haynes, R.D., and Ong,B., An MPI/OpenMP implementation of the RIDC-DD method for time dependent partial differential equations.

21. Haynes, R. D. and Ong, B., A RIDC--Optimized Schwarz Space--Time Method for Time Dependent PDEs.

22. Haynes, R.D. and Kwok, F., A Theoretical and Computational Comparison of Domain Decomposition Approaches for the 2D Heat Equation.

23. Haynes, R.D. and Kwok, F., Discrete analysis of Domain Decomposition Algorithms for Grid Generation via the Equidistribution Principle.

Published Teaching Resources

24. Brown, M. and Haynes, R.D. Student Solution's Manual for Numerical Analysis and Scientific Computation: Jeffrey Leader, Addison--Wesley,ISBN-10: 0321257332 ISBN-13: 9780321257338

Simulations

Some Schwarz Moving Mesh Movies

Current Projects

• Optimization problems whose function evaluations depend on the numerical solution of partial differential equations - Thomas Humphries (MUN), Richard Karsten (Acadia)
• Domain Decomposition and Moving Mesh Methods for time dependent PDEs - Bob Russell (SFU), Weizhang Huang (Kansas), Martin Gander (Geneve)