The phrase "automatically refined" is correct and usable in written English.
It can be used in contexts where something is improved or enhanced without manual intervention, often in relation to processes or systems.
Example: "The software features an algorithm that automatically refines the data for better accuracy."
Alternatives: "self-optimized" or "automatically improved".
As the grid is automatically refined over selected regions of the computational domain, the solution becomes invariant to further reductions in grid spacing and time step size.
In addition, we provide an extension of our method to the case of adaptive meshes in both two and three spatial dimensions: we use non-graded quadtree (2D) and octree (3D) data structures to represent the grid that is automatically refined near the irregular domain's boundary.
The user first selects a rough cylinder-like region, the boundary of which is automatically refined.
The user first selects a rough region, which is automatically refined.
The main picture of editing is as follows: The user selects a rough strip region of interest (ROI), which is automatically refined to a better region smooth.
The program automatically refined the initial bone border to identify more precisely the bone boundaries.
An adaptive meshing method is developed to automatically refine the grid near the wavy gas-liquid interface which is moving continuously.
In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refine the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain.
The jump condition is imposed in a sharp manner, using the Voronoi Interface Method of Guittet et al. [14], while adaptive Quad/Oc-tree grids are employed to automatically refine near the cells boundary for increased accuracy.
In addition, to highlight the advantages of grid adaptation in connection with Cartesian mesh methods, we have introduced a rudimentary procedure which detects the shock position and automatically refines the mesh by locally reducing the grid dimension to one fourth of its original dimension.
Apparently, Twitter automatically refines search queries for trending topics to maximize the number of results you get.
