A Perturbation Method for the 3D Finite Element Modeling of Electrostatically Driven MEMS

Area of Science:

• * Computational Mechanics
• * Microelectromechanical Systems (MEMS)

Background:

• * Modeling electrostatic actuation in MEMS is crucial for device design and analysis.
• * Conventional finite element (FE) methods can be computationally intensive for complex MEMS geometries.

Purpose of the Study:

• * To present a novel finite element (FE) perturbation procedure for modeling electrostatically actuated MEMS.
• * To improve computational efficiency in simulating electrostatic field distortions caused by moving conductors.

Main Methods:

• * A two-step FE computation: solving an unperturbed problem in the complete domain, followed by a perturbation problem in a reduced region.
• * Utilizing the solution of the unperturbed problem as a source for the perturbation step.
• * Employing problem-adapted meshes for sub-problems solved in reduced domains.

Main Results:

• * The perturbation method allows for solving sub-problems in reduced domains, decreasing overall problem size.
• * Iterative computation may be required when the perturbing region is close to the original source field.
• * Demonstrates enhanced computational efficiency compared to conventional methods.

Conclusions:

• * The developed FE perturbation procedure offers a computationally efficient approach for modeling electrostatically actuated MEMS.
• * The method's ability to use reduced domains and adapted meshes significantly decreases computational load.