On polynomial hyperreduction for nonlinear structural mechanics

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Abstract
Summary: This paper proposes an approach for hyperreduction of nonlinear structural mechanics equations. For hyperreduction, the nonlinear term is approximated by the third‐degree multivariate polynomials represented in terms of a monomial basis. The chosen basis leads to an ill‐conditioned minimization problem with the multivariate Vandermonde matrix. The condition number of the resulting problem is significantly improved by choosing an appropriate sparse subset of the initial basis. As a byproduct of the sparse basis, the evaluation time for the hyperreduced model is reduced drastically. The performance of the new approach is demonstrated for two typical applications.

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