# Key publications of Geometric Integration

Publications of subtheme: Geometric Integration

Publications of subtheme: Geometric Integration

- J. Frank, G. Gottwald and S. Reich, "A Hamiltonian Particle-Mesh Method for the Rotating Shallow Water Equations", in M. Griebel and M.A. Schweitzer, eds.,
*Meshfree Methods for Partial Differential Equations*, Lecture Notes in Computational Science and Engineering, Vol. 26, pp. 131--142, Springer, 2002. - J. Frank and S. Reich, "Conservation properties of smoothed particle hydrodynamics applied to the shallow water equations",
*BIT*43 (2003) 40--54. - J. Frank, "Geometric space-time integration of ferromagnetic materials",
*Applied Numerical Mathematics*, 48 (2004) 307--322. - C. Cotter, J. Frank and S. Reich, "Hamiltonian Particle-Mesh Method for Two-Layer Shallow-Water Equations Subject to the Rigid-Lid Approximation",
*SIAM J. Appl. Dyn. Syst.*, 3 (2004) 69--83. - J. Frank and S. Reich, "The Hamiltonian Particle-Mesh Method for the Spherical Shallow Water Equations",
*Atmospheric Science Letters*, 5 (2004) 89--95. - J. Frank and S. Reich, "On spurious reflections, nonuniform grids and finite difference discretizations of wave equations", submitted.
- J. Frank, S. Reich, A. Staniforth, A. White and N. Wood, "Analysis of a regularized, time-staggered discretization method and its link to the semi-implicit method",
*Atmospheric Science Letters*6 (2005) 97-104. - J.G. Verwer, B.P. Sommeijer and W. Hundsdorfer RKC time-stepping for Advection-Diffusion-Reaction Problems,
*J. Comp. Phys.*201, pp. 61-79 (2004) - J.G. Verwer and B.P. Sommeijer, An Implicit-Explicit Runge-Kutta-Chebyshev Scheme for Diffusion-Reaction Equations,
*SIAM J. Scientific Computing*25, pp. 1824-1835 (2004) - L.F. Shampine, B.P. Sommeijer and J.G. Verwer, IRKC: An IMEX solver for stiff diffusion-reaction PDEs,
*J. Comp. Appl. Math.*(2005), to appear. - J. Frank, B. E. Moore, and S. Reich, Linear PDEs and numerical methods that preserve a multi-symplectic conservation law,
*SIAM J. Sci. Comput.*(2006), to appear.