The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM （Finite Difference Method） and FEM （Finite Element Method） mostly to implement fa...The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM （Finite Difference Method） and FEM （Finite Element Method） mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM （Boundary Element Method） based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU （Central Processor Unit） desktop computer. New algorithm is iterative one, but exponential convergence for the Schwatlz＇s algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code ＂POISSON-3＂.展开更多
The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the princi...The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the BEM （boundary element method） for the field evaluation, and 3rd order aberration expansion for the trajectory analysis. The first version of such computer code ＂OPTICS-3＂ and some results of numerical simulations with this code were presented.展开更多
文摘The decomposition method was successfully used in solving of 3D problems with complex geometry shape in electron optics for the FDM （Finite Difference Method） and FEM （Finite Element Method） mostly to implement fast and robust parallel algorithms and computer codes. We suggest a new version of similar approach for the BEM （Boundary Element Method） based on the alternating method by Schwartz. This approach substantially reduce the dimension of dense global matrix of algebraic system produced by BEM algorithm to solve a complex problem on as single CPU （Central Processor Unit） desktop computer. New algorithm is iterative one, but exponential convergence for the Schwatlz＇s algorithm creates the fast numerical procedures. We describe the results of numerical simulation for a multi electrode ion transport system. The algorithms were implemented in the computer code ＂POISSON-3＂.
文摘The comparative analysis of modem mathematical models for 3D problems in electron optics is presented. The new approach to solve the electron optics problems in three dimensions is presented. It is based on the principal ray method suggested by G. Grinberg in 1948. That perspective approach was not realized before for full three-dimensional electron optic systems, probably because of the complexity of its mathematical apparatus. We describe the analytical technique of the BEM （boundary element method） for the field evaluation, and 3rd order aberration expansion for the trajectory analysis. The first version of such computer code ＂OPTICS-3＂ and some results of numerical simulations with this code were presented.
