Computer simulation using particles
Computer simulation using particles
Plasma Physics Via Computer
VORPAL: a versatile plasma simulation code
Journal of Computational Physics
Solving PDEs in C++: Numerical Methods in a Unified Object-Oriented Approach
Solving PDEs in C++: Numerical Methods in a Unified Object-Oriented Approach
Locally conformal finite-difference time-domain techniques for particle-in-cell plasma simulation
Journal of Computational Physics
Journal of Computational Physics
A fast multigrid-based electromagnetic eigensolver for curved metal boundaries on the Yee mesh
Journal of Computational Physics
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The Dey-Mittra conformal boundary conditions have been implemented for the finite-difference time-domain (FDTD) electromagnetic solver of the VORPAL plasma simulation framework and studied in the context of three-dimensional, large-scale computations. The maximum stable time step when using these boundary conditions can be arbitrarily small, due to the presence of small fractional cells inside the vacuum region. Use of the Gershgorin Circle theorem allows the determination of a rigorous criterion for exclusion of small cells in order to have numerical stability for particular values of the ratio f"D"M=@Dt/@Dt"C"F"L of the time step to the Courant-Friedrichs-Lewy value for the infinite system. Application to a spherical cavity shows that these boundary conditions allow computation of frequencies with second-order error for sufficiently small f"D"M. However, for sufficiently fine resolution, dependent on f"D"M, the error becomes first order, just like the error for stair-step boundary conditions. Nevertheless, provided one does use a sufficiently small value of f"D"M, one can obtain third-order accuracy through Richardson extrapolation. Computations for the TESLA superconducting RF cavity design compare favorably with experimental measurements.