4 citations · 5 across the 8 of their papers we have counts for
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Identifying the source term in the potential equation with weighted sparsity regularization
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We explore the possibility for using boundary measurements to recover a sparse source term f(x) in the potential equation. Employing weighted sparsity regularization and standard r…
Modified Tikhonov regularization for identifying several sources
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study whether a modified version of Tikhonov regularization can be used to identify several local sources from Dirichlet boundary data for a prototypical elliptic PDE. This pape…
A regularization operator for source identification for elliptic PDEs
Ole Løseth Elvetun, Bjørn Fredrik Nielsen
We study a source identification problem for a prototypical elliptic PDE from Dirichlet boundary data. This problem is ill-posed, and the involved forward operator has a significan…
Robust preconditioners for PDE-constrained optimization with limited observations
Kent-André Mardal, Bjørn Fredrik Nielsen, Magne Nordaas
Regularization robust preconditioners for PDE-constrained optimization problems have been successfully developed. These methods, however, typically assume that observation data is…