An Etymological Dictionary of Astronomy and Astrophysics
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A type of → algorithm that dynamically achieves high → resolution in localized regions of multidimensional → numerical simulations. AMR provides a higher → accuracy solution at lower costs, through an automatically → optimal distribution of → grid points for the computation region. It relies on locally refined mesh or mesh patches to increase the resolution of an underlying coarse mesh only where needed. It can alleviate some of the complexities of the generation of high quality grid and reduce the number of → iterations of "trial-and-error" between the grid generation and solution required for tailoring the grid to the specification of a problem. Thus, it can offer orders of magnitude saving in computational and storage costs over an equivalent uniformly refined mesh. AMR was originally developed for → inviscid, → compressible flow (Berger et al., 1984, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations. J. Comp. Phy., 53, 484). It has been extended to solve → Navier-Stokes equations, time dependent problems and more. Several AMR techniques have been developed and applied to compressible flow fields to capture characteristics at the strong gradient or discontinuous regions requiring higher space resolution, such as regions involving → shock waves, vortices (→ vortex), and → wakes (see, e.g., Qingluan Xue, "Development of Adaptive Mesh Refinement Scheme and Conjugate Heat Transfer Model for Engine Simulations" (2009), Iowa State Univ., Graduate Theses and Dissertations, Paper 10678).
See also → Smoothed Particle Hydrodynamics.

→ adaptive; → mesh; → refinement.

1) Fineness or elegance of feeling, taste, manners, language, etc.
2) The act or process of refining. the quality or state of being refined.
3) An improved, higher, or extreme form of something.
Math.: A → set whose elements include the elements of a given set (Dictionary.com).

Verbal noun of → refine.