non-zero to preserve properties of hosted equations (one to one mapping) where Jacobian matrix is: • Smooth, orthogonal grids (or grids without small angles) usually result in the smallest error.

or three dimensions for transformation • Interpolation between pair of boundaries • If boundaries are given as data points, approximation must be used to fit function to data points first.

system of PDEs whose solutions are boundary conforming grid coordinate lines with specified line spacing • Solving the system gives grid • For large grids the computing time is considerable

= G(x,y) are unknowns in Poisson eq with condition so x,y boundaries are mapped to boundaries of computational domain where P and Q defines grid point spacing • Then instead solving ξ and η we change independent and dependent variables

to generate on complex domains • Easy local refinement • Complex data structure (link matrix or else) • Can be generated more automatically even on complex domains, compared to structured grids

• Connect boundary points to create edges (called “front”) • Select any edge in front and create its perpendicular bisector. On a bisector pick a point at the distance d inside the domain • In that point, create a circle of radius r, order any points inside circle by distance from center and for each create triangles with edge vertices • Pick up the first triangle that is not intersecting edges, and update front (connect, remove edges)

unnecessary computational costs • Regions of rapid variations of solution needs better resolution • Using AGR we can discretize huge domains (astrophysics) and/or domains with non-uniform variations across regions of interest • Save both memory and CPU time • Trivial to implement for unstructured grids

regions of “rapid variations” moves in time (like Burgers' flow equation) • Let grid points move with “whatever fronts are present” keeping number of grid points constant

points changing position with equidistribution principle of error in computed PDE solution • Having an error-monitor function we want it to be equal over average on all grid sections • They also must prevent rapid grid movement

• In structured domains, algebraic methods are preferred for speed and simplicity • Usually implemented in multi disciplinary software packages that goes with CAD interface, surface editing and visualization tools • Multi-block