Development of boundary conforming and adaptive high order schemes for beam dynamics simulations

High order numerical methods received considerable attention. This stems from their inherent capability of providing detailed and accurate numerical solutions of partial differential equations(PDE) on computational meshes built from a smaller number of elements.

For curved boundary, straight-edged elements cannot achieve results accurate enough. Elements are better to be conforming to the boundary. Curved elements are employed to described the curved boundary, so that the geometric discretization errors will be reduced. Consequently, more accurate computation, e.g. numerical integration, based on such curved elements can be expected.

From a reference element to a curved element, one can employ mapping deformation technique such as Transfinite Interpolation(TFI)[2], which projects certain element edges onto the curved boundary of geometry.

As a numerical investigation, Discontinuous Galerkin Method(DGM)[1] is carried out to solve electromagnetic pulse propagation within a curved domain .

References

[1] Jan S. Hesthaven, Tim Warburton, Nodal Discontinuous Galerkin Methods Algorithms, Analysis, and Applications, 373-386, Springer 2007

[2] Joe F. Thompson, Bharat K. Soni, Nigel P. Weatherill, Handbook of Grid Generation, Chap.3, CRC press 1999.

[3] Steven J, Owen and Jason F. Shepherd, Embedding Features in a Cartesian Grid, 117-138,International Meshing Roundtable 2009.

High order method, Body-fitting meshes and Electrodynamics

Prof. Dr.-Ing. Thomas Weiland (TEMF, Computational Electromagnetic Laboratory)

M.Sc.

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