Application of modified Arnoldi algorithm to passive macromodeling of MEMS

Area of Science:

• Computational Mechanics
• Microelectromechanical Systems (MEMS)
• Nanoelectromechanical Systems (NEMS)

Background:

• Accurate simulation of dynamical responses in complex MEMS and NEMS is computationally intensive.
• Reduced-order modeling (ROM) is crucial for efficient analysis of these systems.
• Existing ROM methods require significant computational resources.

Purpose of the Study:

• To apply a modified Block Arnoldi algorithm for enhanced reduced-order modeling.
• To reduce computational run time and resource usage in MEMS/NEMS simulations.
• To maintain the essential dynamic properties of the systems during model reduction.

Main Methods:

• Implementation of a modified Block Arnoldi algorithm.
• Reduction of the computational matrix size from 2n x 2n to n x n.
• Analysis of floating-point operation (FLOP) count reduction.

Main Results:

• Significant reduction in FLOP count from (56n^3 - 216n^2 + 22n) / 3 to (7n^3 - 54n^2 + 11n) / 3.
• CPU run time reduction for a resonator example (n=39) from 0.091s to 0.080s.
• Achieved a 65% improvement in CPU time for a butterfly gyroscope example (n=17361), reducing it from 4343s to 1528s.

Conclusions:

• The modified Block Arnoldi algorithm offers substantial computational savings for MEMS/NEMS simulations.
• This approach effectively reduces run time and resource demands while preserving system accuracy.
• The method demonstrates significant performance improvements, especially for large-scale systems.