Provides a generic interface to boundary conditions, and provides a set of standard boundary conditions for one, two, and three dimensional grid variables.

Boundary Conditions

Techniques are developed for projecting the solutions of symmetric-hyperbolic evolution systems onto the constraint submanifold (the constraint-satisfying subset of the dynamical field space). These optimal projections map a field configuration to the nearest configuration in the constraint submanifold, where distances between configurations are measured with the natural metric on the space of dynamical fields. The construction and use of these projections are illustrated for a new representation of the scalar field equation that exhibits both bulk and boundary generated constraint violations. Numerical simulations on a black hole background show that bulk constraint violations cannot be controlled by constraint-preserving boundary conditions alone, but are effectively controlled by constraint projection. Simulations also show that constraint violations entering through boundaries cannot be controlled by constraint projection alone, but are controlled by constraint-preserving boundary conditions. Numerical solutions to the pathological scalar field system are shown to converge to solutions of a standard representation of the scalar field equation when constraint projection and constraint-preserving boundary conditions are used together.

http://www.ccom.ucsd.edu/~lindblom/Publications/77_PhysRevD.70.084017.pdf

Optimal constraint projection for hyperbolic evolution systems

/pdf/constraint-preserving-boundary-conditions-for-the-linearized-4igf5i1uqm.pdf

Constraint preserving boundary conditions for the linearized Einstein equations

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Boundary Conditions

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References

Optimal constraint projection for hyperbolic evolution systems

Constraint preserving boundary conditions for the linearized Einstein equations