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We use coarse basis functions construction that combines local spectral problems and a Reduced Basis (RB) approach.
With a careful choice of the coarse basis functions for multiscale finite element methods, we can significantly reduce errors.
In Problem (9), the unknowns are the coefficients c of the coarse basis.
Complexity reduction is achieved by expressing the reconstruction error in a coarse basis.
Additionally, as the slice is reduced on a coarse basis, there are (left( frac{N_2}{s} right) ^2 times N_p) non-zero values to store in this case.
We implement a method handling a reduced number of unknowns by expressing the image in a coarse basis in order to correct the cupping effect.
Similar(50)
Adopting a coarse grained model, the first main task is the calculation of the electric field [4] (on the basis of given dipole arrangements).
We introduce a data-driven approach for the estimation of these coarse scale basis functions.
Several multiscale methods account for sub-grid scale features using coarse scale basis functions.
For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells.
In work [9], the knowledge available as known zone values in the slice is translated in the coarse representation basis: a subset of Gaussian coefficients is fitted to values in the known zone (Omega); these coefficients are then used as a constraint for the reconstruction.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com