TU Darmstadt, Darmstadt
TEMF, TU Darmstadt, Darmstadt
The problem of self-consistent simulations of short relativistic particle bunches in long accelerator structures exhibits a pronounced multi-scale character. The adequate resolution of the THz space charge fields excited by short ultra-relativistic bunches requires mesh spacings in the micrometer range. On the other hand, the discretization of complete accelerator sections using such fine meshes results in a vast number of degrees of freedom. Due to the spatial concentration of the particles and the excited space charge fields, the application of time-adaptive mesh refinement is an emerging idea. We reported on the implementation of time-adaptive mesh refinement for the Finite Integration Technique (FIT)*. Based on this work, we implemented an hp-adaptive discontinuous Galerkin (DG) code. The twofold refinement mechanisms of the hp-adaptive DG method offer maximum modeling freedom. We present details of the h- and p-adaptations for the DG method on Cartesian grids. Special emphasis is put on the stability and efficiency of the adaptation techniques.
Muroran Institute of Technology, Department of Electrical and Electronic Engineering, Muroran
In addition to standard high performance computing technologies such as supercomputers and grid computers, a method of dedicated computers have been attempted to construct portable high performance computing environments in the vicinity of office PC. The method of dedicated computers have also been adopted into electromagnetic field simulations, which are mainly in a linear algebra equation solver for general electromagnetic field analysis and the FDTD solver for microwave simulations. In this paper, attempts of FDTD/FIT dedicated computer (FDTD/FIT machine) are introduced*. The basic scheme of the FDTD/FIT method itself is very simple and suitable for implementation as hardware circuits. In addition, it is also essential to realize many other functions such as imposing of boundary conditions, treatment of non-uniform materials, power input, etc. Moreover, to fully bring out the advantage of the method of dedicated computer, the computer architecture should be designed to achieve efficient computing of all of FDTD/FIT scheme including the boundary condition setting, etc. Especially various efforts of minimization of memory access overhead are discussed in this paper.
ANL, Argonne
MSU, East Lansing, Michigan
Many processes in Physics can be described by Partial Differential equations (PDE’s). For various practical problems, very precise and verified solutions of PDE are required; but with conventional finite element or finite difference codes this is difficult to achieve because of the need for an exceedingly fine mesh which leads to often prohibitive CPU time. We present an alternative approach based on high-order quadrature and a high-order finite element method. Both of the ingredients become possible through the use of Differential Algebra techniques. Further the method can be extended to provide rigorous error verification by using the Taylor model techniques. Application of these techniques and the precision that can be achieved will be presented for the case of 3D Laplace’s equation. Using only around 100 finite elements of order 7, verified accuracies in the range of 10-7 can be obtained.