$\Psi$ec: A Local Spectral Exterior Calculus

@article{Lessig2018PsiecAL,
  title={\$\Psi\$ec: A Local Spectral Exterior Calculus},
  author={C. Lessig},
  journal={arXiv: Numerical Analysis},
  year={2018}
}
  • C. Lessig
  • Published 2018
  • Mathematics, Computer Science
  • arXiv: Numerical Analysis
We introduce $\Psi$ec, a discretization of Cartan's exterior calculus of differential forms using wavelets. Our construction consists of wavelet differential r-forms with flexible directional localization that provide tight frames for the spaces $\Omega^r(\mathbb{R}^n)$ of $r$-forms in $\mathbb{R}^2$ and $\mathbb{R}^3$. By construction, the wavelets satisfy the de Rahm co-chain complex, the Hodge decomposition, and that the integral of an $(r+1)$-form is an $r$-form. They also enforce Stokes… Expand

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