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arXiv · 1805.00114

Algebraic dual polynomials for the equivalence of curl-curl problems

Marc Gerritsma·Varun Jain·Yi Zhang·Artur Palha
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Abstract

In this paper we will consider two curl-curl equation in two dimensions. One curl-curl problem for a scalar quantity $F$ and one problem for a vector field $\bf{E}$. For Dirichlet boundary conditions $\bf{n} \times \bf{E} =$ $ \hat{E}_{\dashv}$ on $\bf{E}$ and Neumann boundary conditions $\bf{n} \times \mbox{curl}$ $F=\hat{E}_{\dashv}$, we expect the solutions to satisfy $\bf{E}=\mbox{curl}$ $F$. When we use algebraic dual polynomial representations, these identities continue to hold at the discrete level. Equivalence will be proved and illustrated with a computational example.

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Marc Gerritsma, Varun Jain, Yi Zhang, Artur Palha. 2018-04-30. Algebraic dual polynomials for the equivalence of curl-curl problems. https://arxiv.org/abs/1805.00114

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