Boundaryskipping

Boundaryskipping is a term used to describe a class of techniques in computational methods that deliberately avoid or defer processing near the boundaries of a domain. It is not a single algorithm but a collection of heuristics designed to reduce cost, improve stability, or bypass issues that commonly arise at domain edges. The concept can be applied across numerical analysis, optimization, and simulation domains.

In numerical PDE solvers, boundaryskipping may involve using interior-point stencils that do not require exact boundary values at every iteration, or applying simplified boundary treatments and extrapolated values. In Monte Carlo integration and similar stochastic methods, practitioners may sample primarily from interior regions and estimate boundary contributions indirectly, through interpolation or importance sampling. In optimization with constraints, interior-point approaches and barrier methods act as a form of boundary-skipping by keeping iterates within the interior of the feasible set and avoiding steps that lie on or cross the boundary.

Benefits of boundary-skipping include reduced computational load, smoother numerical behavior, and avoidance of singularities or ill-conditioned boundary conditions. However, these gains often come with trade-offs, such as bias or reduced accuracy near the domain boundary, which can be unacceptable for certain applications. The appropriateness of boundary-skipping depends on the problem’s tolerance for boundary-related errors and the availability of reliable interior approximations.

See also: boundary conditions, interior-point methods, stencil methods, extrapolation and interpolation, numerical analysis.