1. L Ge, L Lee, A. Candel, C Ng, K Ko, SLAC
A Moving Window Algorithm with h and p Refinements on Unstructured Grids for Accelerator Wakefield Computations
L Ge, L Lee, A. Candel, C Ng, K Ko, SLAC
X Luo, M Shepard, RPI
The moving window technique is commonly used in simulating short-range wakefields in particle accelerators to reduce computational requirements and its implementation on the finite-difference grid is straightforward. We present the first parallel algorithm for using moving window on the unstructured finite-element grid to resolve small beam bunches with higher resolution and increased speed. This capability has been developed to allow h or/and p refinement with curvilinear tetrahedral meshes and incorporated into the SLAC 3D parallel time domain field solver T3P. Application to an accelerator cavity coupler shows a tenfold reduction in execution time and memory usage without loss in accuracy .
Moving Window using p-refinement
Motivation
Short-range wakefield simulation
High resolution is required in the beam region
Only beam region needs to be simulated
Moving window techniques commonly used in finite difference grids to reduce computational requirements
Inside window: p > 0
Outside window: p = 0
Significantly reduces execution time and memory usage
Snapshots of electric fields in wakefield calculation
ILC coupler short-range wakefield simulation
800 micron beam size
400 micron edge length
13 million elements
5 windows in the run
1/10th of execution time
1/10th of memory usage
Beam size ~ 300 micron
Beam pipe radius: 39 mm
Estimated > 100 million tetrahedral elements 4 1
Parallel Finite-Element Time-Domain Solver – T3P
Moving Window using h-refinement
Inhomogeneous vector wave equation:
Refine mesh only around moving beam 2
Spatial discretization: Hierarchical edge based finite-elements
Transfer solution vectors using a new projection method; significantly reduce computational resources
Temporal discretization: implicit Newmark-beta scheme
Each time step, solve the following linear system:
are previous and current step’s unknown and driven force
Electric fields with three refined meshes 5 2
Moving Window technique in T3P
Summary and Future Work
First moving window algorithm for short-range wakefield computations with unstructured grids
h/p refinement with curvilinear tetrahedral meshes
to be transferred from current window configuration to the next window configuration when particle beam moves out of the window
Both moving window techniques in h- and p- refinements are validated by simulations
New projection method is an effective and accurate way for parameter transfers between two meshes.
Both h- and p- refinements can drastically reduce execution time and memory usage
Future work:
Make mesh refinement on-line
Combine p- and h- refinements in a single moving window
Beam transit through three refined meshes
Solution transfer
Solution transfer 3 6
This work is supported by U.S. DOE ASCR, BES & HEP Divisions under contract DE-AC02-76SF00515.