• Node Insertion
• Refining

ALGORITHM

Step 1. Manually Generate a rectangular, two element, four noded mesh which encloses all of the boundary nodes. This mesh will be the starting mesh of the algorithm, and any nodal insertion later will be a modification of this mesh.

Step 2. Using the nodal insertion algorithm, insert the boundary nodes one by one into the existing mesh. When all the of the boundary nodes are inserted, the mesh is called a Box Mesh.

Step 3. Remove all of the elements that are external to the boundary of the given geometry. The resulting mesh is called a boundary mesh.

At this point we have a valid mesh which describes the geometry. However this mesh is not suitable for the finite element analysis and needs to be refined by the insertion of the interior nodes.

Step 4. The elements with poor aspect ratio are modified by inserting a node at the circum-center of the element.

NODE INSERTION

Step1 . We want to insert a new node into an existing mesh which satisfies the Delaunay Criteria. We find out which element this new node is in.

Step 2. We divide the element into three elements by joining the nodes of the parent element to the new node.

Step 3. We then perform the incircle tests of the newly formed elements with their neighbours and do diagonal swapping wherever applicable.

Step 4. New elements formed as a result of diagonal swapping are then checked in the similar fashion for Delaunayhood with their neighbours. This process is continued till the whole mesh becomes Delaunay.

REFINING

Step 1. Choose a criterion for the aspect ratio of the elements, e.g. ratio of the triangle height to the trianle base.

Step 2. For the first triangle in the list check if the aspect ratio is as desired. This checking has to be done with respect to all the three sides as base.

Step 3. If a particular triangle fails to satisfy the aspect ratio criteron then insert a node at the circumcenter of the triangle; use node insertion algorithm for inserting this node.