Finite element analysis of linear boundary value problems with geometrical parameters

The purpose of this paper is to enable fast finite element (FE) analysis of electromagnetic structures with multiple geometric design variables.

The proposed methodology combines multi‐variable model‐order reduction with mesh perturbation techniques and polynomial interpolation of parameter‐dependent FE matrices.

The resulting reduced‐order models are of comparable accuracy as but much smaller size than the original FE systems and preserve important system properties such as reciprocity.

The method is limited to mesh variations that are obtained from a nominal discretization by continuous deformation. Topological changes in the mesh are not permissible.

In contrast to the underlying FE models, the resulting reduced‐order systems are very cheap to analyze. Possible applications include parametric libraries, design optimization, and real‐time control.

The paper extends the scope of moment‐matching order‐reduction techniques to a class of non‐polynomial systems arising from FE models with geometric parameters.