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.