Moving Mesh simulation of contact sets in two dimensional models of elastic-electrostatic deflection problems
For researchers in MEMS and nonlinear PDEs, this provides a combined numerical-analytical framework to predict contact sets, though the approach is incremental and domain-specific.
The paper develops numerical and analytical methods to study contact sets in electrostatic-elastic deflection models for MEMS, using a moving mesh PDE for adaptive simulation and singular perturbation analysis for geometric prediction. The methods are validated on test cases, showing accurate tracking of singularities.
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial differential equation and the contact events occur in this system as finite time singularities. Primary research interest is in the dependence of the contact set on model parameters and the geometry of the domain. An adaptive numerical strategy is developed based on a moving mesh partial differential equation to dynamically relocate a fixed number of mesh points to increase density where the solution has fine scale detail, particularly in the vicinity of forming singularities. To complement this computational tool, a singular perturbation analysis is used to develop a geometric theory for predicting the possible contact sets. The validity of these two approaches are demonstrated with a variety of test cases.