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A Three-Dimensional Finite Element Poisson Solver for Monte Carlo Particle Simulators

Fatnes, Siri Narvestad
Master thesis
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18766_FULLTEXT.pdf (55.07Mb)
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http://hdl.handle.net/11250/2567223
Utgivelsesdato
2018
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  • Institutt for matematiske fag [1396]
Sammendrag
A finite element Poisson solver for the calculation of the three-dimensional electric

field in self-consistent particle simulations has been implemented in Fortran and integrated into

an existing Monte Carlo simulator for particle transport. Robust and efficient algorithms for point

location in unstructured two and three-dimensional grids is implemented, used in a new injection routine adapted to unstructured meshes and for assembling the load vector of the finite element system. The linear system arising from the

finite element approximation of the Poisson equation is solved using conjugate gradient method

preconditioned with an incomplete \(LU\)-factorization, which outperforms two other tested solvers. Special storage schemes are implemented

to construct and store the matrices of the linear system and are seamlessly combined with the

linear system solvers.

The work has resulted in a new program

structure called Monte Carlo software with finite element Poisson solver (MCFEM), which has

been tested by performing short bias simulations of avalanche photodiodes on

different grid refinements with the use of both linear and quadratic polynomial basis functions.
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