Browsing by Author "Hwang, Feng-Nan"

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Development of a parallel implicit solver of fluid modeling equations for gas discharges
(2011-01-01)
Hung, Chieh-Tsan
;
Chiu, Yuan-Ming
;
Hwang, Feng-Nan
;
Wu, Jong-Shinn
;
機械工程學系
A parallel fully implicit PETSc-based fluid modeling equations solver for simulating gas discharges is developed Fluid modeling equations include the neutral species continuity equation the charged species continuity equation with drift-diffusion approximation for mass fluxes the electron energy density equation and Poisson s equation for electrostatic potential Except for Poisson s equation all model equations are discretized by the fully implicit backward Euler method as a time integrator and finite differences with the Scharfetter-Gummel scheme for mass fluxes on the spatial domain At each time step the resulting large sparse algebraic nonlinear system is solved by the Newton-Krylov-Schwarz algorithm A 2D-GEC RF discharge is used as a benchmark to validate our solver by comparing the numerical results with both the published experimental data and the theoretical prediction The parallel performance of the solver is investigated (C) 2010 Elsevier B V All rights reserved
Parallel 2D Axisymmetric Fluid Modeling of CF4 Discharge in an Inductively Coupled Plasma Source During SiO2 Etching
(2014-04-01)
Chiu, Yuan-Ming
;
Chiang, Chung-Hua
;
Hung, Chieh-Tsan
;
Hu, Meng-Hua
;
Wu, Jong-Shinn
A parallel 2D axisymmetric plasma fluid modeling for an inductively coupled plasma source with tetrafluoromethane precursor is reported. In total, 32 species with 96 gas-phase and 27 surface reactions with site-balance equations are considered. The predicted results of major species densities are in reasonable agreement with reported experiments. The etching products, e.g. SiFx and O-2, are found to be appreciable (approximate to 10%) compared to the precursor near the substrate. The predicted density trends, such as CFx+ and CFx (x=1-3), are also consistent with reported experiments. Finally, the predicted etching rate on the SiO2 substrate is presented and discussed in detail.
Parallel Newton-Krylov-Schwarz algorithms for the three-dimensional Poisson-Boltzmann equation in numerical simulation of colloidal particle interactions
(2010-09-01)
Hwang, Feng-Nan
;
Cai, Shang-Rong
;
Shao, Yun-Long
;
Wu, Jong-Shinn
;
機械工程學系
We investigate fully parallel Newton-Krylov-Schwarz (NKS) algorithms for solving the large sparse nonlinear systems of equations arising from the finite element discretization of the three-dimensional Poisson-Boltzmann equation (PBE), which is often used to describe the colloidal phenomena of an electric double layer around charged objects in colloidal and interfacial science. The NKS algorithm employs an inexact Newton method with backtracking (INB) as the nonlinear solver in conjunction with a Krylov subspace method as the linear solver for the corresponding Jacobian system. An overlapping Schwarz method as a preconditioner to accelerate the convergence of the linear solver. Two test cases including two isolated charged particles and two colloidal particles in a cylindrical pore are used as benchmark problems to validate the correctness of our parallel NKS-based PBE solver. In addition, a truly three-dimensional case, which models the interaction between two charged spherical particles within a rough charged micro-capillary, is simulated to demonstrate the applicability of our PBE solver to handle a problem with complex geometry. Finally, based on the result obtained from a PC cluster of parallel machines, we show numerically that NKS is quite suitable for the numerical simulation of interaction between colloidal particles, since NKS is robust in the sense that INB is able to converge within a small number of iterations regardless of the geometry, the mesh size, the number of processors. With help of an additive preconditioned Krylov subspace method NKS achieves parallel efficiency of 71% or better on up to a hundred processors for a 3D problem with 5 million unknowns. (C) 2010 Elsevier B.V. All rights reserved.