Grid Generation Methods

Many numerical approximation techniques, such as finite element analysis, involve dividing the surface into a number of grid elements so that calculations can be performed in a systematic, and in many cases simplified, manner. Grids can be divided into three basic types: structured, unstructured and mixed grids. Each of these types of grids can be subdivided. Grid generation is sometimes also referred to as mesh generation.
  1. Structured

    • Structured grids are the simplest type, using regular shapes throughout to map out a surface. It is important for elements on the edge of a structured grid to line up with the boundary of the surface in question. Also, grid lines need to intersect the boundaries orthogonally so that the derivatives at the boundary are easier to analyze. This also will increase the accuracy of the approximation.

    Single or Composite

    • Structured grids can be subclassified as single or composite grids, and composite grids can be further subdivided as completely discontinuous, partially discontinuous, completely continuous or partially discontinuous. These divisions have to do with the way the vertices of the grid are joined together.

    Unstructured

    • Unstructured grid generation is much more computationally complex. Instead of simply choosing a shape for the grid and then overlaying it on a surface, unstructured grid generation methods use an algorithm that creates the grid based on certain desired characteristics.

    Triangulation

    • Many unstructured grid generation techniques use triangles for the underlying shape because this is computationally inexpensive and the grid that is ultimately created is not too irregular. Common triangulation algorithms include Delauney triangulation, the Bowyer-Watson algorithm and the Green-Sibson algorithm.

    Quadtree Method

    • The Quadtree method divides the surface into quarters, and then divide each quarter into quarters, and so forth. This creates a large number of grid elements in a simple way, and then grid elements are removed along the edge to conform to the boundary of the surface. The Octree method works the same way, except that sections are divided into eighths.

    Advancing Front

    • The Advancing Front method starts by dividing up the boundaries of the surface and then creates the grid, element by element, spreading out across the surface--thus the name. Although this method is known to create quality grids, it is also considered relatively inefficient.

    Adaptive Methods

    • A number of Adaptive grid generation techniques also exist. For example, a grid can be formed by first overlaying a regular, structured grid onto the surface and then adjusting the grid lines to meet a set of desired conditions; this is known as the Deformation method.

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