7 problems

Let $C_R$, $C_{A2}$, and $b1$ be the constants appearing in the multigrid assumptions $(G3)+(R)+(A2)_\alpha$, and let $m$ denote the cycle parameter. V-cycle threshold conjecture.…

Let the fine and coarse discretizations in the two-grid finite-element method for Helmholtz problems have finite-element spaces, with the coarse finite-element space not contained…

The multilevel method uses linear transfer operators $P$ and $R$ between fine and coarse levels; in the square-grid setting, these may be based on bilinear interpolation and restri…

The DNN-MG method uses a neural network trained on oscillatory flow data to predict corrections for individual patches in a multigrid solver. Patchwise network design conjecture. T…

Powell–Sabin robustness conjecture. Similar robustness properties should carry over to the case of Powell–Sabin splits.

Let $\deg>0$, $j>0$, and $z>0$. Let $\hat{f}_{z,j}$ be the symbol appearing in the paper, and let $\lambda”_{\rm min}(\hat{f}_{z,j})|_{0}$ denote the second derivative at $0$ of it…

For the Helmholtz equation, let $G_{\rm c}$ denote the number of grid points per wavelength at the coarse level, and let the coarse and fine scale operators be the corresponding mu…