TrueGrid^{®} Quality Mesh
A quality mesh guarantees the best analysis results for a problem. Factors that can affect the quality of a mesh include: orthogonality, aspect ratio, warpage, shearing, and torsion. When building a mesh you can greatly improve the quality by choose the propoer topology for the design and using smoothing algorithms to evenly distribute elements. TrueGrid^{®} was developed with both of these issues in mind.
Choosing the Right Topology
Proper topology affects the quality of a mesh because it dictates the distortion of the elements in a block. Topology will also determine how parts fit together, how key features will be captured, and how this will affect other regions of the mesh. The key to designing the best topology is to use multiblock structured parts. Structured blocks are preferred because it is possible to decompose the problem into manageable pieces.
To demonstrate the importance of a multiblock structure to the design of a mesh, consider the problem of meshing the inside of a circle with quadrilateral elements.
Four Corners ApproachOne approach is to take a single block and form a circle. This produces 4 elements at the boundary, corresponding to the four corners of the block, that are extremely distorted. This is not an ideal approach because each corner element is almost 180 degrees and the more elements used, the closer the angles will get to 180 degrees. 

Center Triangles ApproachAnother approach places triangular elements at the center of the mesh. This is not ideal because of the poorly shaped triangular elements. The more refined the mesh becomes, the smaller the triangles and the worse the aspect ratio. 

Best Quality ApproachThis approach places the irregularities between the boundary and the center by using a 5 block part. There are 4 irregularities in the mesh, located where only three elements meet. These irregularities are not as severe, since the average angle at these nodes is 120, only 33% away from the ideal of 90 degrees. No matter how many elements are used in this structure, the irregularities do not get worse. 


Best Quality for 3DThe 3D analogue of the circle is the sphere. The best topology is a single cube at the center of the sphere, with 6 more blocks, each extruding from one of the 6 faces of the center cube. This sphere is formed using 7 block grids in one part. TrueGrid^{®} created this mesh using only 6 commands:sd 1 sp 0 0 0 3 block 1 11 21 31;1 11 21 31;1 11 21 31; 1 1 1 1 1 1 1 1 1 1 1 1 dei 1 2 0 3 4; 1 2 0 3 4;; dei 1 2 0 3 4;; 1 2 0 3 4; dei ; 1 2 0 3 4; 1 2 0 3 4; sfi 1 4; 1 4; 1 4;sd 1 
Smoothing with Elliptic Solvers
Smoothing helps acheive a better quality mesh because it redistributes elements for better aspect ratio and near orthogonality. TrueGrid^{®} supports equipotential relaxation, uniform smoothing, and ThomasMiddlecoff elliptic methods.
Smoothing AppliedA smoothing algorithm is applied to a disc similar to the example above. Notice how the smoothing creates a more uniform mesh and angles are more even. 