Alternating direction adaptive grid generation
An alternating direction method has been developed to adaptively resolve numerical solutions to physical problems by moving the points of a coordinate grid. With the solution or with the salient quantities derived from it, a surface grid is defined over the grid on the physical region. Grid movement is computed on this abstractly defined solution surface with the use of pointwise weights and is then projected back to determine new locations in the physical region. The weights cause clustering relative to the uniform conditions of surface arc length and are formed with magnitudes of quantities that are used for point attraction. When the salient quantities have been used to form the surface, the gradients are implicitly revolved and surface curvature becomes the primary remaining quantity. In each coordinate direction, the magnitude of normal curvature is used; With arbitrary weights, a movement cycle generally consists of a sweep through the coordinate curves in a given direction on a curve-by-curve basis and then in alternating directions to do the same thing until all directions have been covered.