Scalable low nDOF hp-FEM model of IPMC actuation

Document Type

Conference Proceeding

Publication Date


Publication Title

The International Society for Optical Engineering






IPMC actuation is described with a system of partial differential equations – the Poisson’s equation, the Nernst- Planck equation, and the Navier’s equations for the displacement field. In such systems, one physical field can be very smooth while others are not. This can possibly result in very large problem size in terms of number of degrees of freedom (nDOF) when implemented with the finite element method (FEM). Furthermore, finding an optimal mesh is challenging due to the fact that the physical fields are time dependent. In order to overcome these deficiencies, hp-FEM was used to solve the system of equations. The hp-FEM is a modern version of the FEM that is capable of exponential convergence (the approximation error drops exponentially as new degrees of freedom are added during adaptivity). It is shown how the multi-meshing allows reducing the problem size in terms of nDOF; also, how the solution domain that describes IPMC can be scaled without a significant increase in the nDOFs and solution time. The model was implemented in Hermes that is a free hp-FEM solver. © (2013) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.


Actuators; Mathematical models; Metal-filled plastics


Acoustics, Dynamics, and Controls | Materials Science and Engineering | Mechanical Engineering




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