In some cases, I've included the final journal .pdf of my papers. In other cases, preprints are linked; the final journal version may be more up-to-date.
| [1] | Emma Naden, Thomas März, and Colin B. Macdonald. Anisotropic diffusion on curved surfaces. 2014. Undergoing revision. [ bib | arXiv | .pdf | Abstract ] |
| [2] | Ingrid von Glehn, Thomas März, and Colin B. Macdonald. An embedded method-of-lines approach to solving partial differential equations on surfaces. 2014. Undergoing revision. [ bib | arXiv | .pdf | Abstract ] |
| [3] | Andrew J. Christlieb, Colin B. Macdonald, Benjamin W. Ong, and Raymond J. Spiteri. Revisionist integral deferred correction with adaptive stepsize control. Comm. App. Math. Com. Sc., 2015. To appear. [ bib | arXiv | .pdf | Abstract ] |
| [4] | Yujia Chen and Colin B. Macdonald. The Closest Point Method and multigrid solvers for elliptic equations on surfaces. SIAM J. Sci. Comput., 37(1), 2015. [ bib | DOI | arXiv | .pdf | Abstract ] |
| [5] | Harry Biddle, Ingrid von Glehn, Colin B. Macdonald, and Thomas März. A volume-based method for denoising on curved surfaces. In Proc. ICIP13, 20th IEEE International Conference on Image Processing, pages 529-533, 2013. [ bib | DOI | .pdf | Abstract ] |
| [6] | David I. Ketcheson, Colin B. Macdonald, and Steven J. Ruuth. Spatially partitioned embedded Runge-Kutta methods. SIAM J. Numer. Anal., 51(5):2887-2910, 2013. [ bib | arXiv | .pdf | Abstract ] |
| [7] | Colin B. Macdonald, Barry Merriman, and Steven J. Ruuth. Simple computation of reaction-diffusion processes on point clouds. Proc. Natl. Acad. Sci., 110(23), 2013. [ bib | DOI | Abstract ] |
| [8] | Yiannis Hadjimichael, Colin B. Macdonald, David I. Ketcheson, and James H. Verner. Strong stability preserving explicit Runge-Kutta methods of maximal effective order. SIAM J. Numer. Anal., 51(4):2149-2165, 2013. [ bib | DOI | arXiv | .pdf | Abstract ] |
| [9] | Thomas März and Colin B. Macdonald. Calculus on surfaces with general closest point functions. SIAM J. Numer. Anal., 50(6):3303-3328, 2012. [ bib | DOI | arXiv | .pdf | Abstract ] |
| [10] | S. Auer, C. B. Macdonald, M. Treib, J. Schneider, and R. Westermann. Real-time fluid effects on surfaces using the Closest Point Method. Comput. Graph. Forum, 31(6):1909-1923, 2012. [ bib | DOI | .pdf | Abstract ] |
| [11] | Colin B. Macdonald, Jeremy Brandman, and Steven J. Ruuth. Solving eigenvalue problems on curved surfaces using the Closest Point Method. J. Comput. Phys., 230(22):7944-7956, 2011. [ bib | DOI | arXiv | .pdf | Abstract ] |
| [12] | David I. Ketcheson, Sigal Gottlieb, and Colin B. Macdonald. Strong stability preserving two-step Runge-Kutta methods. SIAM J. Numer. Anal., 49(6):2618-2639, 2012. [ bib | DOI | arXiv | .pdf | Abstract ] |
| [13] | Mohammad Motamed, Colin B. Macdonald, and Steven J. Ruuth. On linear stability of the fifth-order WENO discretization. J. Sci. Comput., 47(2):127-149, 2010. [ bib | DOI | .pdf | Abstract ] |
| [14] | Andrew J. Christlieb, Colin B. Macdonald, and Benjamin W. Ong. Parallel high-order integrators. SIAM J. Sci. Comput., 32(2):818-835, 2010. [ bib | DOI | .pdf | Abstract ] |
| [15] | Li (Luke) Tian, Colin B. Macdonald, and Steven J. Ruuth. Segmentation on surfaces with the Closest Point Method. In Proc. ICIP09, 16th IEEE International Conference on Image Processing, pages 3009-3012, Cairo, Egypt, 2009. [ bib | DOI | .pdf | Abstract ] |
| [16] | Colin B. Macdonald and Steven J. Ruuth. The implicit Closest Point Method for the numerical solution of partial differential equations on surfaces. SIAM J. Sci. Comput., 31(6):4330-4350, 2009. [ bib | DOI | .pdf | Abstract ] |
| [17] | David I. Ketcheson, Colin B. Macdonald, and Sigal Gottlieb. Optimal implicit strong stability preserving Runge-Kutta methods. Appl. Numer. Math., 59(2):373-392, 2009. [ bib | DOI | .pdf | Abstract ] |
| [18] | Colin B. Macdonald and Steven J. Ruuth. Level set equations on surfaces via the Closest Point Method. J. Sci. Comput., 35(2-3):219-240, 2008. [ bib | DOI | .pdf | Abstract ] |
| [19] | Colin B. Macdonald, Sigal Gottlieb, and Steven J. Ruuth. A numerical study of diagonally split Runge-Kutta methods for PDEs with discontinuities. J. Sci. Comput., 36(1):89-112, 2008. [ bib | DOI | .pdf | Abstract ] |
| [20] | Colin B. Macdonald and Raymond J. Spiteri. The predicted sequential regularization method for differential-algebraic equations. In D'Attellis, Kluev, and Mastorakis, editors, Mathematics and Simulation with Biological, Economic, and Musicoacoustical Applications, pages 107-112. WSES Press, 2001. [ bib ] |
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