- Magnet fringe fields, nonlinear effects, and compensation in large acceptance rings
- Free Symplectic Approximation Of Hamiltonian Flows And Accurate Simulation Of Fringe Field Effects
- Symplectic Approximation Of Hamiltonian Flows And Accurate Simulation Of Fringe Field Effects
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Matioc Well-posedness, instabilities, and bifurcation results for the flow in a rotating Hele-Shaw cell Journal of Mathematical Fluid Mechanics. Tisdell and E. Escher and E. Markus Grasmair Well-posedness classes for sparse regularization Communications in Mathematical Sciences. Markus Grasmair Linear convergence rates for Tikhonov regularization with positively homogeneous functionals Inverse Problems. Yuri Bazilevs, M. Hsu, Y.

Zhang, W. Series B.

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Markus Grasmair and Frank Lenzen Anisotropic total variation filtering Applied mathematics and optimization. Markus Grasmair Generalized Bregman distances and convergence rates for non-convex regularization methods Inverse Problems. Lax's contributions to mathematics The Abel Prize The First Five Years. Multiscale Modeling and Simulation in Science. Elena Celledoni and Trond Kvamsdal Parallelization in time for thermo-viscoplastic problems in extrusion of aluminium International Journal for Numerical Methods in Engineering. Helge Holden, Kenneth Hvistendahl Karlsen and D Mitrovic Zero diffusion-dispersion-smoothing limits for scalar conservation law with discontinuous flux function International Journal of Differential Equations.

Helge Holden, Kenneth Hvistendahl Karlsen and Darko Mitrovic Zero diffusion-dispersion-smoothing limits for a scalar conservation law with discontinuous flux function International Journal of Differential Equations. Helge Holden, Nils H. Karlsen Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions Numerische Mathematik. Karlsen Error estimates for a class of finite difference-quadrature schemes for fully nonlinear degenerate parabolic integro-PDEs Journal of Hyperbolic Differential Equations.

Part 2. Aarnes and Knut-Andreas Lie A comparison of multiscale methods for elliptic problems in porous media flow Computational Geosciences.

## Magnet fringe fields, nonlinear effects, and compensation in large acceptance rings

Jostein Roald Natvig and Knut-Andreas Lie Fast computation of multiphase flow in porous media by implicit discontinuous Galerkin schemes with optimal ordering of elements Journal of Computational Physics. Imran Habib Biswas, Espen Robstad Jakobsen and Kenneth Hvistendahl Karlsen Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion Contemporary Mathematics. Karlsen Error estimates for finite difference-quadrature schemes for a class of nonlocal Bellman equations with variable diffusion Contemporary Mathematics.

Trond Runar Hagen, Martin O. Henriksen, Jon M. Helge Holden and Giuseppe M.

Helge Holden and Xavier Raynaud Global conservative solutions of the generalized hyperelastic-rod wave equation Journal of Differential Equations. Dahle, G.

## Free Symplectic Approximation Of Hamiltonian Flows And Accurate Simulation Of Fringe Field Effects

Part 1. Analytical Riemann solver Transport in Porous Media.

Peter Lindqvist and Juan J. Manfredi Viscosity supersolutions of the evolutionary p-Laplace equation Differential and Integral Equations. Jostein R. Espen Robstad Jakobsen On error bounds for monotone approximation schemes for multi-dimensional Isaacs equations Asymptotic Analysis. Espen R. Jakobsen and Kenneth Hvistendahl Karlsen A "maximum principle for semicontinuous functions" applicable to integro-partial differential equations NoDEA.

Juha Kinnunen and Peter Lindqvist Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation Annali di Matematica Pura ed Applicata.

Natvig Fast computation of arrival times in heterogeneous media Computational Geosciences. Trond R Hagen, Jon M. Henriksen Visual simulation of shallow-water waves Simulation modelling practice and theory. Espen Robstad Jakobsen and Kenneth h. Karlsen Convergence rates for semi-discrete splitting approximations fordegenerate parabolic equations with source terms BIT Numerical Mathematics.

Petri Juutinen and Peter Lindqvist Removability of a level set for solutions of quasilinear equations Communications in Partial Differential Equations. Knut-Andreas Lie and Ruben Juanes A front-tracking method for the simulation of three-phase flow in porous media Computational Geosciences.

Iserles Efficient quadrature of highly oscillatory integrals using derivatives Proceedings of the Royal Society. Espen Robstad Jakobsen W-2,W-infinity regularizing effect in a nonlinear, degenerate parabolic equation in one space dimension Proceedings of the American Mathematical Society. Serie VII. Helge Holden, Kenneth Hvistendahl Karlsen and Nils Henrik Risebro On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations Electronic Journal of Differential Equations.

Espen Robstad Jakobsen On the rate of convergence of approximation schemes for Bellman equations associated with optimal stopping time problems Mathematical Models and Methods in Applied Sciences. Knut-Andreas Lie An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions Journal of Scientific Computing.

Developments in Water Science. Helge Holden and Fritz Gesztesy Dubrovin equations and integrable systems on hyperelliptic curves Mathematica Scandinavica. Espen Robstad Jakobsen and Kenneth Hvistendahl Karlsen Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations Electronic Journal of Differential Equations.

Espen Robstad Jakobsen and Kenneth Hvistendahl Karlsen Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate parabolic equations Journal of Differential Equations. Brynjulf Owren and Arne Marthinsen Integration methods based on canonical coordinates of the second kind Numerische Mathematik. Helge Holden, Kenneth Hvistendahl Karlsen and Knut-Andreas Lie Operator splitting methods for degenerate convection-diffusion equations II: numerical examples with emphasis on reservoir simulation and sedimentation Computational Geosciences.

Knut-Andreas Lie Front tracking for one-dimensional quasilinear hyperbolic equations with variable coefficients Numerical Algorithms.

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## Symplectic Approximation Of Hamiltonian Flows And Accurate Simulation Of Fringe Field Effects

Zanna Lie-group methods Acta Numerica. Journel Mathematical Geology. Welfert Pseudospectra of waveform relaxation operators Computers and Mathematics with Applications. Elena Celledoni Metodi di Krylov per sistemi lineari di equazioni differenziali ordinarie Doctoral Dissertation. Helge Holden and N. Risebro Conservation laws with a random source Applied mathematics and optimization. Burrage, Z. Jackiewicz and R. It performs trial integrations in parallel.

Also the trial integrations are further accelerated by balancing computational load among PUs by the technique of folding. The method is all-purpose and achieves an acceleration factor of around 3. Finally, we give a perspective on the parallelization of some implicit integrators which require multiple corrections in solving implicit formulas like the implicit Hermitian integrators Makino and Aarseth, , Hut et al.

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On the symplectic structure of harmonic superspace. In this paper, the symplectic properties of harmonic superspace are studied. Other features are discussed. Infinitesimal Deformations of a Formal Symplectic Groupoid. Characterization and solvability of quasipolynomial symplectic mappings. Quasipolynomial or QP mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, physics, chemistry or economy. In addition, QP mappings are a natural discrete-time analogue of the continuous QP systems, which have been extensively used in different pure and applied domains.

After presenting the basic definitions and properties of QP mappings in a previous paper [1], the purpose of this work is to focus on their characterization by considering the existence of symplectic QP mappings. In what follows such QP symplectic maps are completely characterized. Moreover, use of the QP formalism can be made in order to demonstrate that all QP symplectic mappings have an analytical solution that is explicitly and generally constructed. Examples are given. Geometric integration in Born-Oppenheimer molecular dynamics.

Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear and electronic degrees of freedom. This provides highly efficient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field SCF convergence. We investigate three different geometric integration schemes: 1 regular time reversible Verlet, 2 second order optimal symplectic , and 3 third order optimal symplectic.