Publications

Please check my Google Scholar profile for recent publications.

For convenience, preprints of my papers are available below (June 2023). If you find something interesting, I recommend using the final journal version rather than the somewhat earlier versions supplied here.

Numerical Methods for PDEs on Surfaces

D. Venn, S. Ruuth:  Underdetermined Fourier Extensions for Partial Differential Equations on Surfaces, submitted.

N. King, H. Su, M. Aanjaneya, S. Ruuth, C. Batty:  A Closest Point Method for PDEs on Manifolds with Boundary Conditions for Geometry Processing, ACM Trans. Graph. 43 (5), Article 159, 26 pages (2024).

S. Li, L. Ling, S.J. Ruuth, X. Wang:  Realistic Pattern Formations on Surfaces by Adding Arbitrary Roughness, SIAM J. Appl. Math. 84 (3), 1163-1185 (2024).

I.C.T. May, R.D Haynes, S.J. Ruuth:  A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners, Numer. Algorithms. 93, 615-637 (2023).

A. Yazdani, R.D. Haynes, S.J. Ruuth: A Convergence Analysis of the Parallel Schwarz Solution of the Continuous Closest Point Method, Domain Decomposition Methods in Science and Engineering XXVI, 679-687, 2023.

A. Petras, L. Ling, S.J. Ruuth:  Meshfree Semi-Lagrangian Methods for Solving Surface Advection PDEs, J. Sci. Comput. 93, 11 (2022).

I. May, R.D. Haynes, S.J. Ruuth: Schwarz solvers and preconditioners for the closest point method, SIAM J. Sci. Comput., 42(6): A3584-A3609, 2020.

A. Petras, L. Ling, C. Piret, S.J. Ruuth: A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces, J. Comput. Phys., 381: 146-161, 2019.

I. May, R.D. Haynes, S.J. Ruuth: Domain Decomposition for the Closest Point Method, In: Haynes R. et al. (eds) Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-030-56750-7_53.

A. Petras, L. Ling, S.J. Ruuth: An RBF-FD closest point method for solving PDEs on surfaces, J. Comput. Phys., 370: 43-57, 2018.

N.D. King, S.J. Ruuth: Solving variational problems and partial differential equations that map between manifolds via the closest point method, J. Comput. Phys., 336: 330-346, 2017.

A. Petras, S.J. Ruuth: PDEs on moving surfaces via the closest point method and a modified grid based particle method, J. Comput. Phys., 312: 139-156, 2016.

T. März, P. Rockstroh, S.J. Ruuth: An Embedding Technique for the Solution of Reaction-Diffusion Equations on Algebraic Surfaces with Isolated Singularities, J. Math. Anal. , 436: 911-943, 2016

B. Crestel, B. Russell, S. Ruuth: Moving mesh methods on parametric surfaces, Proceedings of the International Meshing Roundtable, Austin, pages 148 to 160, October 11-14, 2015.

C. Cheung, L. Ling, S.J. Ruuth: A localized meshless method for diffusion on folded surfaces, J. Comput. Phys., 297: 194-206, 2015.

R. Arteaga, S.J. Ruuth: Laplace-Beltrami spectra for shape comparison of surfaces in 3D using the closest point method, Proc. ICIP15, International Conference on Image Processing, Quebec, Canada, September 27-30, 2015.

I. Rozada, S.J. Ruuth, M.J. Ward: The Stability of Localized Spot Patterns for the Brusselator on the Sphere, SIAM J. Appl. Dyn. Syst., 13(1): 564-627, 2014.

C.B. Macdonald, B. Merriman, S.J. Ruuth: Simple computation of reaction-diffusion processes on point clouds, Proc. Natl. Acad. Sci. USA, 110(23): 9209-9214, 2013.

C.B. Macdonald, J. Brandman, S.J. Ruuth: Solving eigenvalue problems on curved surfaces using the closest point method, J. Comp. Phys., 230(22): 7944-7956, 2011.

C.B. Macdonald, S.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.

L. Tian, C.B. Macdonald, S.J. Ruuth: Segmentation on surfaces with the Closest Point Method, Proc. ICIP09, International Conference on Image Processing, Cairo, Egypt, November 7-11, 2009.

C.B. Macdonald, S.J. Ruuth: Level set equations on surfaces via the Closest Point Method, J. Sci. Comput., 35(2-3): 219-240, 2008.

S.J. Ruuth, B. Merriman: A Simple Embedding Method for Solving Partial Differential Equations on Surfaces, J. Comput. Phys., 227(3): 1943-1961, 2008.

B. Merriman, S.J. Ruuth: Diffusion Generated Motion of Curves on Surfaces, J. Comput. Phys., 225(2): 2267–2282, 2007. NumericH. Su

Parallel Computing of PDEs via Domain Decomposition

I.C.T. May, R.D Haynes, S.J. Ruuth:  A closest point method library for PDEs on surfaces with parallel domain decomposition solvers and preconditioners, Numer. Algorithms. 93, 615-637 (2023).

A. Yazdani, R.D. Haynes, S.J. Ruuth: A Convergence Analysis of the Parallel Schwarz Solution of the Continuous Closest Point Method, Domain Decomposition Methods in Science and Engineering XXVI, 679-687, 2023.

I. May, R.D. Haynes, S.J. Ruuth: Schwarz solvers and preconditioners for the closest point method, SIAM J. Sci. Comput., 42(6): A3584-A3609, 2020.

I. May, R.D. Haynes, S.J. Ruuth: Domain Decomposition for the Closest Point Method, In: Haynes R. et al. (eds) Domain Decomposition Methods in Science and Engineering XXV. DD 2018. Lecture Notes in Computational Science and Engineering, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-030-56750-7_53.

Numerical Methods for Time-Dependent PDEs

K. Chow, S.J. Ruuth: Linearly stabilized schemes for the time integration of stiff nonlinear PDEs, J. Sci. Comput., 87(3): 1-29, 2021.

W. Zhao, J. Huang, S.J. Ruuth: Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws, J. Comput. Phys., Volume 421, 2020, 109697.

D. Ketcheson, C. Macdonald, S.J. Ruuth: Spatially partitioned embedded Runge–Kutta mthods, SIAM J. Numer. Anal., 51(5), 2887-2910, 2013.

M. Motamed, C.B. Macdonald, S.J. Ruuth: On the linear stability of the fifth-order WENO discretization. J. Sci. Comput., 47(2): 127-149, 2011.

D. Wang, S.J. Ruuth: Variable step-size implicit-explicit linear multistep methods for time-dependent partial differential equations. J. Comput. Math., 26(6): 838-855, 2008.

C.B.Macdonald, S. Gottlieb, S.J. Ruuth: A numerical study of diagonally split Runge–Kutta methods for PDEs with discontinuities. J. Sci. Comput., 36(1): 89-112, 2008.

W. Hundsdorfer, S.J. Ruuth: IMEX Extensions of Linear Multistep Methods with General Monotonicity and Boundedness Properties. J. Comput. Phys., 225(2): 2016–2042, 2007.

S. Gottlieb, J.S. Mullen, S.J. Ruuth: A Fifth Order Flux Implicit WENO Method. J. Sci. Comput., 27(1-3): 271–287, 2006

S. Gottlieb, S.J. Ruuth: Optimal Strong-Stability-Preserving Time-Stepping Schemes with Fast Downwind Spatial Discretizations. J. Sci. Comput., 27(1-3): 289–303, 2006

W. Hundsdorfer, S.J. Ruuth: On Monotonicity and Boundedness Properties of Linear Multistep Methods. Math. Comp., 75: 655-672, 2006.

S.J. Ruuth: Global optimization of explicit strong-stability-preserving Runge-Kutta methods. Math. Comp., 75: 183-207, 2006.

S.J. Ruuth, W. Hundsdorfer: High-order linear multistep methods with general monotonicity and boundedness properties. J. Comput. Phys., 209(1): 226-248, 2005.

S.J. Ruuth, R.J. Spiteri: High-order strong-stability-preserving Runge-Kutta Methods with downwind-biased spatial discretizations. SIAM J. Numer. Anal., 42(3): 974-996, 2004.

W. Hundsdorfer, S.J. Ruuth: Monotonicity for Time Discretizations. Proceedings 20th Biennial Conference on Numerical Analysis University of Dundee 24-27 June: pp. 85-94, 2003.

W. Hundsdorfer, S.J. Ruuth, R.J. Spiteri: Monotonicity-preserving linear multistep methods. SIAM J. Numer. Anal., 41(2): 605-623, 2003.

R.J. Spiteri, S.J. Ruuth: Nonlinear evolution using optimal fourth order strong-stability preserving Runge-Kutta methods. Mathematics and Computers in Simulation, special issue on “Nonlinear Waves: Computation and Theory II”, 62(1-2): 125-135, 2003.

R.J. Spiteri, S.J. Ruuth: A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J. Numer. Anal., 40(2): 469-491, 2002.

S.J. Ruuth, R.J. Spiteri: Two barriers on strong-stability-preserving time discretization methods. Journal of Scientific Computation, 17(1-4): 211-220, 2002.

U.M. Ascher, S.J. Ruuth, R.J. Spiteri: Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Applied Numerical Mathematics, 25: 151-167, 1997.

S.J. Ruuth: Implicit-explicit methods for reaction-diffusion problems in pattern-formation. J. Math. Biol., 34(2): 148-176, 1995.

U.M. Ascher, S.J. Ruuth and B.T.R. Wetton: Implicit-explicit methods for time-dependent PDE’s. SIAM J. Numer. Anal., 32: 797-823, 1995

Numerical Methods for Interfacial Dynamics

B. Ong, B. Russell, S. Ruuth: An h-r moving mesh method for one-dimensional time-dependent PDEs, Proceedings of the International Meshing Roundtable, San Jose, pages 39 to 54, October 07-10, 2012.

S. Esedoglu, S.J. Ruuth, R. Tsai: Diffusion generated motion using signed distance functions, J. Comput. Phys., 229(4): 1017-1042, 2010.

L. Tian, C.B. Macdonald, S.J. Ruuth: Segmentation on surfaces with the Closest Point Method, Proc. ICIP09, International Conference on Image Processing, Cairo, Egypt, November 7-11, 2009.

S. Esedoglu, S.J. Ruuth, R. Tsai: Threshold Dynamics for High Order Geometric Motions, Interfaces and Free Boundaries, 10(3): 263-282, 2008.

C.B. Macdonald, S.J. Ruuth: Level set equations on surfaces via the Closest Point Method, J. Sci. Comput., 35(2-3): 219-240, 2008.

B. Merriman, S.J. Ruuth: Diffusion Generated Motion of Curves on Surfaces, J. Comput. Phys., 225(2): 2267–2282, 2007.

S. Esedoglu, S.J. Ruuth and R. Tsai: Threshold Dynamics for Shape Reconstruction and Disocclusion, Proc. ICIP05, International Conference on Image Processing, Genova, pages II-502 to II-505, September 11-14, 2005 .

S.J. Ruuth, B.T.R. Wetton: A simple scheme for volume-preserving motion by mean curvature. J. Scientific Computing, special issue dedicated to Stan Osher’s 60th birthday, 19(1): 373-384; Dec 2003.

S.J. Ruuth, B. Merriman, J. Xin, S. Osher: Diffusion-generated motion by mean curvature for filaments, J. Nonlinear Science, 11(6): 473-493, 2001.

S.J. Ruuth, B. Merriman: Convolution-thresholding methods for interface motion, Journal of Computational Physics, 169:678-707, 2001.

S.J. Ruuth, B. Merriman, S. Osher: A fixed grid method for capturing the motion of self-intersecting interfaces and related PDEs. Journal of Computational Physics, 163:1-21, 2000.

S.J. Ruuth, B. Merriman: Convolution generated motion and generalized Huygens’ principles for interface motion, SIAM Journal on Applied Mathematics, 60(3): 868-890, 2000.

S.J. Ruuth, B. Merriman, S. Osher: Convolution generated motion as a link between cellular automata and continuum pattern dynamics, Journal of Computational Physics, 151:836-861, 1999.

S.J. Ruuth: Efficient algorithms for diffusion-generated motion by mean curvature, Journal of Computational Physics, 144:603-625, 1998.

S.J. Ruuth: A diffusion-generated approach to multiphase motion, Journal of Computational Physics, 145:166-192, 1998.

Simulation of Thermonuclear Fusion from Cavitation

D. Krimans, S.J. Ruuth, S. Putterman: Simulation of the high Mach number asymptote for bubble collapse in a compressible Euler fluid. Submitted.

A. Bass, S.J. Ruuth, C. Camara, B. Merriman, S. Putterman: Molecular dynamics of extreme mass segregation in a rapidly collapsing bubble. Phys. Rev. Lett., 101, 234301 (2008).

A. Bass, S. Putterman, B. Merriman, S.J. Ruuth: Symmetry reduction for molecular dynamics simulation of an imploding gas bubble. J. Comput. Phys., 227(3): 2118–2129, 2008.

S.J. Ruuth, S. Putterman, B. Merriman: Molecular dynamics simulation of the response of a gas to a spherical piston: Implications for sonoluminescence. Phys. Rev. E., 66, 036310 (2002)