A Three-Dimensional Finite Element Poisson Solver for Monte Carlo Particle Simulators
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A finite element Poisson solver for the calculation of the three-dimensional electricfield in self-consistent particle simulations has been implemented in Fortran and integrated intoan existing Monte Carlo simulator for particle transport. Robust and efficient algorithms for pointlocation 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 thefinite element approximation of the Poisson equation is solved using conjugate gradient methodpreconditioned with an incomplete \(LU\)-factorization, which outperforms two other tested solvers. Special storage schemes are implementedto construct and store the matrices of the linear system and are seamlessly combined with thelinear system solvers.The work has resulted in a new programstructure called Monte Carlo software with finite element Poisson solver (MCFEM), which hasbeen tested by performing short bias simulations of avalanche photodiodes ondifferent grid refinements with the use of both linear and quadratic polynomial basis functions.