An iterative method for solving a large dense matrix in the method of moments solution of an electrostatic problem

Abstract. Computation electromagnetic is an important research field of electromagnetic fields and microwave technology subjects. In this paper, the scaled boundary finite element method (SBFEM) is extended to solve one type of electromagnetic field problems-electrostatic field problems. Based on Laplace equation of electrostatic field, the derivations and solutions of SBFEM equations for both bounded and unbounded domain problems are expressed in details, and the solution for the inclusion of prescribed potential along the side-faces of bounded domain is also presented in details, then the total charges on the side-faces can be semianalytically solved. The accuracy and efficiency of the method are illustrated by numerical examples of electromagnetic field problems with complicated field domains, potential singularities, inhomogeneous media and open boundaries. In comparison with analytic solution method and other numerical methods, the results show that the present method has strong ability to resolve potential field singularities analytically by choosing the scaling centre at the singular point, has the inherent advantage of solving the open boundary problems without truncation boundary condition, has efficient application to the problems with inhomogeneous media by placing the scaling centre in the bi-material interfaces, and produces more accurate solution than conventional numerical methods with far less number of degrees of freedom. The method in electromagnetic field calculation can have broad application prospects. IntroductionWith the rapid development of computer performance over half a century, computational electromagnetics has become a robust tool for many analyses of electromagnetic field problems. It can allow for a faster and cheaper design process, where the use of expensive and time-consuming prototypes is minimized and can also provide crucial information and understanding of a device's electromagnetic operation, which may be difficult or even impossible to achieve by means of experiments or analytical calculations.

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Fast finite element electrostatic analysis with domain decomposition method

Yang

Yin

et al. 2023

IEICE Electron. Express

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Accurate simulation of electrostatic field in electronic devices is very important to improve their performance. When the traditional finite element method is used to analyze the electrostatic field of large and complex structures, the calculation speed is slow and the computing resources are greatly consumed. Therefore, in this paper, we investigate electrostatic analysis with a non-overlapping domain decomposition method based on the scalar finite element method under a novel transmission condition. In order to improve the efficiency of matrix solving and reduce the memory consumption, the block Jacobi preconditioner is introduced. In addition, the multifrontal block incomplete Cholesky preconditioner is utilized to further improve the computational performance based on the block Jacobi preconditioner.Several numerical examples are simulated and compared with the analytical solutions and the commercial software Maxwell 3D. The results demonstrate the accuracy and efficiency of the proposed domain decomposition method.

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An iterative method for solving a large dense matrix in the method of moments solution of an electrostatic problem

Cited by 3 publications

References 8 publications

A scaled boundary finite element method applied to electrostatic problems

A scaled boundary finite element method applied to electrostatic problems

The scaled boundary finite element method applied to electromagnetic field problems

Fast finite element electrostatic analysis with domain decomposition method

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