Publications
24 results found
Cotter CJ, Ham DA, Pain CC, et al., 2009, LBB stability of a mixed Galerkin finite element pair for fluid flow simulations, Journal of Computational Physics, Vol: 228, Pages: 336-348
We introduce a new mixed finite element for solving the 2- and 3-dimensional wave equations and equations of incompressible flow. The element, which we refer to as P1D–P2, uses discontinuous piecewise linear functions for velocity and continuous piecewise quadratic functions for pressure. The aim of introducing the mixed formulation is to produce a new flexible element choice for triangular and tetrahedral meshes which satisfies the LBB stability condition and hence has no spurious zero-energy modes. The advantage of this particular element choice is that the mass matrix for velocity is block diagonal so it can be trivially inverted; it also allows the order of the pressure to be increased to quadratic whilst maintaining LBB stability which has benefits in geophysical applications with Coriolis forces. We give a normal mode analysis of the semi-discrete wave equation in one dimension which shows that the element pair is stable, and demonstrate that the element is stable with numerical integrations of the wave equation in two dimensions, an analysis of the resultant discrete Laplace operator in two and three dimensions on various meshes which shows that the element pair does not have any spurious modes. We provide convergence tests for the element pair which confirm that the element is stable since the convergence rate of the numerical solution is quadratic.
Cotter CJ, Frank J, Reich S, 2007, The remapped particle-mesh semi-Lagrangian advection scheme, QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Vol: 133, Pages: 251-260, ISSN: 0035-9009
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- Citations: 21
Cotter CJ, Reich S, 2006, Semigeostrophic particle motion and exponentially accurate normal forms, MULTISCALE MODELING & SIMULATION, Vol: 5, Pages: 476-496, ISSN: 1540-3459
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- Citations: 16
Bridges TJ, Hydon PE, Reich S, 2005, Vorticity and symplecticity in Lagrangian fluid dynamics, JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, Vol: 38, Pages: 1403-1418, ISSN: 0305-4470
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- Citations: 22
Cotter CJ, Reich S, 2004, Adiabatic invariance and applications: From molecular dynamics to numerical weather prediction, BIT NUMERICAL MATHEMATICS, Vol: 44, Pages: 439-455, ISSN: 0006-3835
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- Citations: 15
Moore BE, Reich S, 2004, Multi- symplectic integration methods for Hamiltonian PDEs (vol 19, pg 395, 2003), FUTURE GENERATION COMPUTER SYSTEMS, Vol: 20, Pages: 699-700, ISSN: 0167-739X
Frank J, Reich S, 2004, The Hamiltonian particle-mesh method for the spherical shallow water equations, ATMOSPHERIC SCIENCE LETTERS, Vol: 5, Pages: 89-95, ISSN: 1530-261X
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- Citations: 23
Cotter CJ, Reich S, 2004, Geometric integration of a wave-vortex model, Pages: 293-305
Cotter CJ, Jason F, Reich S, 2004, Hamiltonian particle-mesh method for two-layer shallow-water equations subject to the rigid-lid approximation, SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, Vol: 3, Pages: 69-83, ISSN: 1536-0040
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- Citations: 9
Leimkuhler B, Reich S, 2004, Simulating Hamiltonian dynamics, Cambridge, Publisher: Cambridge University Press, ISBN: 9780521772907
Cotter CJ, Reich S, 2003, An extended dissipative particle dynamics model, EUROPHYSICS LETTERS, Vol: 64, Pages: 723-729, ISSN: 0295-5075
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- Citations: 6
Moore B, Reich S, 2003, Backward error analysis for multi-symplectic integration methods, NUMERISCHE MATHEMATIK, Vol: 95, Pages: 625-652, ISSN: 0029-599X
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- Citations: 101
Moore BE, Reich S, 2003, Multi-symplectic integration methods for Hamiltonian PDEs, FUTURE GENERATION COMPUTER SYSTEMS, Vol: 19, Pages: 395-402, ISSN: 0167-739X
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- Citations: 63
Frank J, Reich S, 2003, Conservation properties of smoothed particle hydrodynamics applied to the shallow water equation, BIT NUMERICAL MATHEMATICS, Vol: 43, Pages: 41-55, ISSN: 0006-3835
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- Citations: 29
Frank J, Reich S, 2002, A particle-mesh method for the shallow water equations near geostrophic balance, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 180, Pages: 407-426, ISSN: 0021-9991
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- Citations: 4
Frank J, Gottwald G, Reich S, 2002, A Hamiltonian Particle-Mesh method for the rotating shallow-water equations, Meshfree methods for partial differential equations, Editors: Schweitzer, Griebel, Berlin, Publisher: Springer-Verlag, Pages: 131-142, ISBN: 9783540438915
Barth E, Leimkuhler B, Reich S, 2002, A test set for molecular dynamics algorithms, New York, Computational methods for macromolecules: challenges and applications, proceedings of the 3rd international workshop on algorithms for macromolecular modeling, New York, 12 - 14 October 2000, Publisher: Springer, Pages: 73-103
Holder T, Leimkuhler B, Reich S, 2001, Explicit variable step-size and time-reversible integration, APPLIED NUMERICAL MATHEMATICS, Vol: 39, Pages: 367-377, ISSN: 0168-9274
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- Citations: 28
Bridges TJ, Reich S, 2001, Computing Lyapunov exponents on a Stiefel manifold, PHYSICA D, Vol: 156, Pages: 219-238, ISSN: 0167-2789
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- Citations: 38
Leimkuhler B, Reich S, 2001, A reversible averaging integrator for multiple time-scale dynamics, JOURNAL OF COMPUTATIONAL PHYSICS, Vol: 171, Pages: 95-114, ISSN: 0021-9991
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- Citations: 22
Bridges TJ, Reich S, 2001, Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity, PHYSICS LETTERS A, Vol: 284, Pages: 184-193, ISSN: 0375-9601
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- Citations: 336
Bridges TJ, Reich S, 2001, Multi-symplectic spectral discretizations for the Zakharov-Kuznetsov and shallow water equations, PHYSICA D, Vol: 152, Pages: 491-504, ISSN: 0167-2789
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- Citations: 89
Reich S, 2000, Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations, Journal of Computational Physics, Vol: 157, Pages: 473-499, ISSN: 0021-9991
Reich S, 1999, Backward error analysis for numerical integrators, SIAM Journal on Numerical Analysis, Vol: 36, Pages: 1549-1570, ISSN: 0036-1429
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