A Novel and General Approach for Solving the Ion-Flow Field Problem by a Regularization Technique

In order to have a better convergence and accuracy for solving the ion-flow field problem, a novel and general numerical approach is proposed. In the past, the framework of the traditional mesh based method has a dilemma that the Kapzov boundary condition can be imposed properly, and it must have two loops: the well-posed problem is solved in the inner loop and the secant based method is applied to impose the Kapzov assumption in the outer loop. In contrast, the proposed method solves the ion flow field problem from the perspective of the inverse problem. The original boundary value problem is transformed into a regularized optimization problem based on the prior information about the smooth ion distribution on the conductors. The objective function is separated into two parts and minimized by the alternating direction iterative method. In contrast to the traditional methods, the proposed method has removed the redundant iterations and the contentious simplifications. Numerical experiments show that the performance of the proposed method is superior to the traditional method and the results obtained by the proposed method agree better with the physical law than the traditional method. The new method presents a general and rigorous way to analysis the ion-flow field problem.

Automated summary

The proposed method for solving the ion-flow field problem adopts a novel and general numerical approach, focusing on the inverse problem perspective. By transforming the original boundary value problem into a regularized optimization problem and minimizing it in two parts using the alternating direction iterative method, the proposed method eliminates redundant iterations and contentious simplifications. Numerical experiments demonstrate superior performance compared to traditional methods, with results aligning more closely with physical laws. This new approach provides a comprehensive and rigorous analytical tool for studying ion-flow field problems.