Periodic boundary condition

A boundary condition that identifies opposite ends of a domain, requiring a function—and often specified derivatives—to take matching values there.

Boundary condition: A constraint specifying a solution’s values or derivatives at the boundary of a domain. Periodic conditions are one way to constrain solutions at a domain’s boundary.
Periodic boundary conditions in molecular dynamics: A simulation technique that tiles a molecular-dynamics cell with translated copies of itself. It lets a small simulation cell approximate bulk matter without exposed surfaces.
Domain (mathematics): The set of input values on which a mathematical function is defined. Periodic conditions apply at the edges of this set.
Open boundary condition: A boundary treatment intended to let waves or fields leave a finite computational domain without significant reflection. It models an effectively unbounded exterior rather than repeating the domain.
Dirichlet boundary condition: A boundary condition that prescribes a function’s value on the boundary of its domain. Unlike periodic conditions, it fixes boundary values rather than identifying opposite boundaries.
Ewald summation: A method for computing long-range interactions in periodic arrays by splitting sums into rapidly convergent parts. Periodic electrostatic images require specialized methods to sum their long-range interactions.
Boundary value problem: A differential equation problem whose solution must satisfy constraints on the boundary of its domain. Periodic matching is a standard boundary specification for differential equations.
Reflecting boundary condition: A boundary condition that makes waves or particles reflect at a domain edge. Reflection creates an edge response instead of connecting opposite sides.
Neumann boundary condition: A boundary condition that prescribes the normal derivative of a function on a domain’s boundary. It constrains boundary flux or slope instead of matching opposite ends.
Minimum image convention: A simulation rule that evaluates pair interactions using the nearest periodic image of each particle. It is a common way to apply short-range interactions across periodic cell boundaries.

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