Publications – Steve Ruuth

Please check my Google Scholar profile for recent publications.

For convenience, preprints of my papers are available below (September 2026). 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

H. Potgieter, R.C. Fetecau, S.J. Ruuth: Numerical approximation of the first p-Laplace eigenpair, submitted.

D.R. Venn, S.J. Ruuth: High-Order Meshfree Surface Integration, Including Singular Integrands, SIAM J. Sci. Comput., 48(4): A2155-A2181, 2026.

D.R. Venn, S.J. Ruuth: A Meshfree Method for Eigenvalues of Differential Operators on Surfaces, Including Steklov Problems, Adv. Comput. Math., 52: Article 57, 46 pages, 2026.

D.R. Venn, S.J. Ruuth: Underdetermined Fourier Extensions for Partial Differential Equations on Surfaces, IMA J. Numer. Anal., draf109, 27 pages, 2025. https://doi.org/10.1093/imanum/draf109

N. King, S. Ruuth, C. Batty: Spatial Adaptivity for Solving PDEs on Manifolds with the Closest Point Method, SIGGRAPH Posters ’25: Proceedings of the Special Interest Group on Computer Graphics and Interactive Techniques Conference Posters, Article No. 7, pages 1-3, 2025. https://doi.org/10.1145/3721250.3743012

H. Potgieter, R.C. Fetecau, S.J. Ruuth: Geodesic distance approximation using a surface finite element method for the p-Laplacian, Computer Aided Geometric Design, 120: 102458, 2025.

N. King, S. Ruuth, C. Batty: A Simple Heat Method for Computing Geodesic Paths on General Manifold Representations, SA ’24: SIGGRAPH Asia 2024 Posters, Article No. 69, pages 1-2, 2024. https://doi.org/10.1145/3681756.3697920

V. Bayona, A. Petras, C. Piret, S.J. Ruuth: A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces, SIAM J. Sci. Comput., 46(6): A3897-A3921, 2024.

A. Yazdani, R.D. Haynes, S.J. Ruuth: Optimized Schwarz Domain Decomposition Algorithms for the Closest Point Method on Closed Manifolds, Numer. Algorithms, 101(1): 33-64, 2026. https://doi.org/10.1007/s11075-024-01995-6

N. King, H. Su, M. Aanjaneya, S. Ruuth, C. Batty: A Closest Point Method for PDEs on Manifolds with Interior 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: Article 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, 2018. 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 148-160, 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. Comput. 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.

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.

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.

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): Article 95, 29 pages, 2021.

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

D. Ketcheson, C. Macdonald, S.J. Ruuth: Spatially partitioned embedded Runge-Kutta methods, 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(254): 655-672, 2006.

S.J. Ruuth: Global optimization of explicit strong-stability-preserving Runge-Kutta methods, Math. Comp., 75(253): 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, June 24-27, pages 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, J. Sci. Comput., 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, B.T.R. Wetton: Implicit-explicit methods for time-dependent PDEs, 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 39-54, October 7-10, 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, 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. Sci. Comput., special issue dedicated to Stan Osher’s 60th birthday, 19(1): 373-384, 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, J. Comput. Phys., 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, J. Comput. Phys., 163: 1-21, 2000.

S.J. Ruuth, B. Merriman: Convolution generated motion and generalized Huygens’ principles for interface motion, SIAM J. Appl. Math., 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, J. Comput. Phys., 151: 836-861, 1999.

S.J. Ruuth: Efficient algorithms for diffusion-generated motion by mean curvature, J. Comput. Phys., 144: 603-625, 1998.

S.J. Ruuth: A diffusion-generated approach to multiphase motion, J. Comput. Phys., 145: 166-192, 1998.

Simulation of Thermonuclear Fusion from Cavitation

D. Krimans, S.J. Ruuth, S. Putterman: Simulation of the high Mach number motion for bubble collapse in a compressible Euler fluid using Basilisk, Phys. Rev. E, 112(6): 065107, 19 pages, 2025.

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.