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Kernel Methods in the Deep Ritz framework: Theory and practice
Announce Type: replace Abstract: In this contribution, kernel approximations are applied as ansatz functions within the Deep Ritz method. This allows to approximate weak solutions of elliptic partial differential equations with weak enforcement of boundary conditions using Nitsche's method. A priori error estimates are proven in different norms leveraging both standard results for weak solutions of elliptic equations and well-established convergence results for kernel methods.
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Theory for the Rydberg states of helium: quantum defect extensions and comparison with experiment up to $n = 102$ for the singlet and triplet $P$-states
Announce Type: new Abstract: High precision variational calculations for helium in Hylleraas coordinates are used to obtain a combination of quantum defect expansions for the nonrelativistic energy and $1/n$ expansions for the relativistic and quantum electrodynamic (QED) corrections. The extrapolations based on direct calculations for the singlet and triplet $P$-states up to principal quantum number $n = 35$ provide ionization energies of the $1snp\;^1P_1$ and $^3P_c$ (centroid) states up...
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