Gisela Pöplau

Multigrid Solvers for Poisson’s Equation in Computational Electromagnetics

Complex real life problems, as they appear with the simulation of electromagnetic fields, demand the construction of efficient and robust solvers for the related equations. In the present paper we investigate multigrid algorithms for the solution of static problems on adaptive discretizations. Two multigrid strategies are compared: algebraic multigrid, which performs the adaption to the discretization automatically and geometric multigrid with semi-coarsening, which has fast convergence if the discretization fits the coarsening strategy.

Fast Calculation of Space Charge in Beam Line Tracking by Multigrid Techniques

Numerical prediction of charged particle dynamics in accelerators is essential for the design and understanding of these machines. The calculation of space charge forces influencing the behaviour of a particle bunch is still a bottleneck of existing tracking codes.

Multigrid Algorithms for the Tracking of Electron Beams

The simulation of the motion of a particle beam in linear colliders requires fast and robust numerical algorithms which solve the relativistic equation of motion for a large number of time steps and unknowns. The physical grid—based model of the tracking of particle beams affords the solution of Poisson’s equation on a rectangular grid with large differences in the mesh size of the coordinates. Since the straightforward geometric multigrid technique turns out to be to slow, a geometric multigrid solver with adaptive coarsening has been implemented. Further, the adaptive algorithm is compared to the algebraic multigrid method.

A Self-Adaptive Multigrid Technique for 3-D Space Charge Calculations

Most physical problems contain variations in scale; this holds true for the area of electromagnetic field computation. For this reason, research is ongoing to construct adaptive discretization techniques. The focus of this paper lies in the investigation of an adaptive refinement strategy based on the multigrid technique. Such adaptive discretizations are required, for instance, for the efficient calculation of 3-D space charge effects of bunches of charged particles. The refinement strategy under investigation here employs the -criterion.

Efficiency optimization of a fast Poisson solver in beam dynamics simulation

Abstract Calculating the solution of Poisson’s equation relating to space charge force is still the major time consumption in beam dynamics simulations and calls for further improvement. In this paper, we summarize a classical fast Poisson solver in beam dynamics simulations: the integrated Green’s function method. We introduce three optimization steps of the classical Poisson solver routine: using the reduced integrated Green’s function instead of the integrated Green’s function; using the discrete cosine transform instead of discrete Fourier transform for the Green’s function; using a novel fast convolution routine instead of an explicitly zero-padded convolution. The new Poisson solver routine preserves the advantages of fast computation and high accuracy. This provides a fast routine for high performance calculation of the space charge effect in accelerators.

Calculation of 3D Space-Charge Fields of Bunches of Charged Particles by Fast Summation

Summary. The fast calculation of space-charge fields of bunches of charged particles in three dimensional space is a demanding problem in accelerator design. Since particles of equal charge repel each other due to space-charge forces, it is difficult to pack a high charge in a small volume. For this reason, the calculation of space-charge forces is an important part of the simulation of the behaviour of charged particles in these machines. As the quality of the charged particle bunches increases, so do the requirements for the numerical space-charge calculations. In this paper we develop a new fast summation algorithm for the determination of the electric field generated by N charged particles. Applying the nonequidistant Fast Fourier Transform (NFFT) the fast summation requires only O N log N operations. The numerical test cases confirm this behaviour.

Using Nudg++ to Solve Poisson’s Equation on Unstructured Grids

In this paper we explore the viability of using nodal discontinuous Galerkin methods as implemented in the software library Nudg++ [1] to compute the space charge field of an electron or positron bunch. We will use a benchmark problem to evaluate this method by comparing results from this scheme with solutions obtained analytically.