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This paper presents a case study of solving very large sparse linear systems in end-to-end accelerator structure simulations. Both direct solvers and iterative solvers are investigated. A parallel multilevel preconditioner based on hierarchical finite element basis functions is considered and has been implemented to accelerate the convergence of iterative(More)
Thrombus formation in intracranial aneurysms, while sometimes stabilizing lesion growth, can present additional risk of thrombo-embolism. The role of hemodynamics in the progression of aneurysmal disease can be elucidated by patient-specific computational modeling. In our previous work, patient-specific computational fluid dynamics (CFD) models were(More)
A fourth order compact nite diierence scheme and a multigrid method are employed to solve the two dimensional convection diiusion equations with boundary layers. The computational domain is rst discretized on a nonuniform (stretched) grid to resolve the boundary layers. A grid transformation technique is used to map the nonuniform grid to a uniform one. The(More)
Nine point fourth order compact nite diierence scheme, central diierence scheme, and upwind diierence scheme are compared for solving the two dimensional convection diiusion equations with boundary layers. The domain is discretized with a stretched nonuniform grid. A grid transformation technique maps the nonuniform grid to a uniform one, on which the(More)
Higher-order finite element method requires valid curved meshes in three-dimensional domains to achieve the solution accuracy. When applying adaptive higher-order finite elements in large-scale simulations, complexities that arise include moving the curved mesh adaptation along with the critical domains to achieve computational efficiency. This paper(More)
We present a symbolic computation procedure for deriving various high order compact diierence approximation schemes for certain three dimensional linear elliptic partial diierential equations with variable coeecients. Based on the Maple software package, we approximate the leading terms in the truncation error of the Taylor series expansion of the governing(More)
  • Lie-Quan Lee, Volkan Akcelik, Sheng Chen, Lixin Ge, Ernesto Prudencio, Greg Schussman +32 others
  • 2007
The SciDAC2 accelerator project at SLAC aims to simulate an entire three-cryomodule radio frequency (RF) unit of the International Linear Collider (ILC) main Linac. Petascale computing resources supported by advances in Applied Mathematics (AM) and Computer Science (CS) and INCITE Program are essential to enable such very large-scale electromagnetic(More)
  • Jun Zhang, Lixin Ge, Jules Kouatchou
  • 2000
A new fourth order compact diierence scheme for the three dimensional convection diiu-sion equation with variable coeecients is presented. The novelty of this new diierence scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel(More)
  • Zenghai Li, Nathan T Folwell, Lixin Ge, Adam Guetz, Valentin Ivanov, Marc Kowalski +7 others
  • 2004
This paper describes a major computational effort that addresses key design issues in the high gradient accelerating structures for the proposed X-band linear collider, GLC/NLC. Supported by the US DOE's Accelerator Simulation Project, SLAC is developing a suite of parallel electromagnetic codes based on unstructured grids for modeling RF structures with(More)
  • Xiaojuan Luo, Mark Shephard, Lie-Quan Lee, Cho Ng, Lixin Ge
  • 2008
SLAC performs large-scale simulations for the next-generation accelerator design using higher-order finite elements. This method requires using valid curved meshes and adaptive mesh refinement in complex 3D curved domains to achieve its fast rate of convergence. ITAPS has developed a procedure to address those mesh requirements to enable petascale(More)