On a vector potential formulation for 3D electromechanical finite element analysis

A vector potential for the electric induction is applied to static three-dimensional fully coupled electromechanical problems. A Coulomb gauge condition imposed on the electric vector potential improves the convergence behaviour of nonlinear problems, and in combination with a discrete set of Dirichlet boundary conditions, it can enforce unique vector potential solutions. Based on a spectral analysis of the stiffness matrix, the Coulomb gauge is compared with other gauge conditions. A penalized version of the weak vector potential formulation with Coulomb gauge is proposed and tested on some numerical examples in electrostatics, piezoelectricity and ferroelectricity. Copyright (c) 2005 John Wiley & Sons, Ltd.