20 problems

Let $\mathcal M$ be the parameter set, let $H$ be the coarse-mesh size, let $ell$ be the oversampling parameter, and let … be the localization error indicator for $mu\in\mathcal M$…

The Robin-Robin schemes for the Stokes-Biot fluid-poroelastic structure interaction model use a common parameter $\gamma=\gamma_f=\gamma_p$, and numerical experiments with…

Actual decay-rate conjecture. The actual decay rate is

Let $A$ be the discretization of the first-kind Fredholm equation for Laplace's equation in three dimensions, and let $T^{-1}$ be the preconditioner defined from the domain decompo…

Let $A$ be the discretized integral operator in the referenced two- or three-dimensional models, and let $T^{-1}_{\text{Schwarz}}$ be the Schwarz preconditioner associated with the…

Let $t\mapsto\bm{\pi}_t$ be the limit trajectory of couplings, and let $\pi_\infty$ be a stationary coupling. For a cost $c(x,y)=h(x-y)$ with strictly convex…

Let $(\bm{\pi},\bm{\omega})$ be the limiting trajectory and momentum, and let $\eta=\lim_{n\to\infty}n\,\veps^n$. Zero-regularization conjecture. If $\eta=0$, then the problem desc…

Let $X=[0,1]^d$ be the source domain, let $Y\subset\mathbb{R}^d$ be compact, and consider the domain decomposition optimal-transport results established in the paper. Compact-domai…

Let $\bm{\pi}^n_t$ and $\bm{\pi}_t$ denote the discrete and limiting trajectories, and let the required regularity assumption be the bounded-variation-type oscillation bound on the…

Let a sequence in the expansion of the four-subdomain product define a corresponding term in that product, and suppose the term is associated with a sequence of subdomains. Repeate…

Let $\Lambda_1$ and $\Lambda_2$ be the trace spaces associated with the two subdomains $\Omega_1$ and $\Omega_2$, and let $\Lambda$ be the common interface trace space defined in t…

Reduced-oversampling conjecture. Less oversampling should already be sufficient to extract the significant modes.

Domain-independent local-space conjecture. In general, it should be possible to construct suitable local reduced spaces without knowledge of the global computational domain…

The Deep Domain Decomposition Method (DeepDDM) is applied to an elliptic interface problem, and the numerical convergence factor measures the error reduction between successive out…

Discrete Helmholtz decomposition conjecture. A discrete Helmholtz decomposition may become relevant to the theoretical analysis of convergence on geometric problems.

Consider the overlapping FEM–BEM method for the stated wave-propagation problem, with overlapped region $\Omega_{12}$ bounded by the selected BEM boundary $\Gamma$. In the reported…

Localization conjecture. The number of Newton iterations required for the system to converge to a desired tolerance is dominated by a narrow region in space and time where the nonl…

In adaptive-multilevel BDDC, let $\tau$ be the a-priori chosen threshold controlling the number of coarse degrees of freedom and the resulting coarse basis functions across decompo…

Let the meshes on the sub-domains be globally non-conforming, with the trace meshes from different sides of an interface edge approaching each other in a certain sense as the meshe…

The primal variant of FETI-DP, denoted P-FETI-DP, and the Balancing Domain Decomposition by Constraints method, denoted BDDC, are the two preconditioners under consideration. Cros'…