Mesh/element

docs/element.md

@@ -1,5 +1,34 @@
 # Finite element
 
-The  finite element is the basic  entity in FinEtools.
+The  finite element set is one of the basic entities in FinEtools.
+
+The finite element set is a collection of  finite elements defined by the connectivity (array of node numbers, listing the nodes connected by the element in  a specific order). The finite element set  provides  specialized methods  to compute values of basis functions and the values of  the gradients of the basis functions  with respect to the parametric coordinates.
+
+The finite element sets are instances of concrete types. Each particular shape and order of element has its own type. There are types for  linear  and quadratic quadrilaterals, for instance, `FESetQ4` and `FESetQ8`. Each element set provides access to the number of nodes  connected by the element (`nodesperelem`),  the connectivity as the two dimensional array    `conn`,  and the  integer label vector `label`. 
+
+The concrete finite element set types are subtypes of the abstract type for elements of different manifold dimension (3, 2, 1, and 0), for instance for the quadrilaterals that would be `FESet2Manifold`. These types are in turn  subtypes of the abstract finite element set type `FESet`.
+
+The concrete finite element set type provides specialized methods to compute the values of the basis functions, `bfun`, and methods to compute  the gradients of the basis functions with respect to the parametric coordinates, `bfundpar`.
+
+## Finite element set functions
+
+- `manifdim`: Return the manifold dimension..
+- `nodesperelem`: Get the number of nodes  connected  by  the finite element.
+- `count`:  Get the number of individual connectivities in the FE set.
+- `getconn!`: Get the connectivity of the jth element in the set.
+- `boundaryconn`: Get boundary connectivity.
+- `boundaryfe`: Return the constructor of the type of the boundary finite element.
+- `setlabel!`: Set the label of the entire finite elements set.
+- `subset`: Extract a subset of the finite elements from the given finite element set.
+- `cat`: Concatenate the connectivities of two FE sets.
+- `updateconn!`: Update the connectivity after the IDs of nodes changed.
+- `bfun`: Compute the values of the basis functions at a given parametric coordinate.
+- `bfundpar`: Compute the values of the basis function gradients at a given parametric coordinate.
+- `Jacobian`: Evaluate the  Jacobian.
+- `gradN!`: Compute the gradient of the basis functions with the respect to the "reduced" spatial coordinates.
+- `inparametric`: Are given parametric coordinates inside the element parametric domain?
+- `map2parametric`: Map a spatial location to parametric coordinates.
+- `centroidparametric`: Return the parametric coordinates  of the centroid of the element.
+
 
 

docs/mesh.md

@@ -14,7 +14,7 @@ As an example,  the following code generates a hexahedral mesh of simple rectang
 fens, fes  = H8block(h, l, 2.0 * pi, nh, nl, nc)
 ```
 
-The finite element node set and the finite element set  are returned. This is typical:  a mesh generation function  would return these data structures. More complicated meshes can be constructed from such mesh parts. There are  functions for  merging  nodes  and even multiple meshes together.
+The finite element node set and the finite element set  are returned. More complicated meshes can be constructed from such mesh parts. There are  functions for  merging  nodes  and even multiple meshes together.
 
 The code snippet below  constructs the mesh of an  L-shaped  domain  from  the meshes of three rectangles.
 ```julia
@@ -49,8 +49,8 @@ candidates = selectnode(fens, box = boundingbox([Rmed - h -Inf 0.0; Rmed + h +In
 fens, fes = mergenodes(fens, fes,  tolerance, candidates);
 ```
 
-
 The final mesh used for a simulation  consists of a single  node set and one or more finite element sets.
+The  finite elements may be  divided into separate sets  to  accommodate different material properties, different orientations of the material  coordinate systems, or different formulations  of the discrete model. The  aassignment  of the finite elements to sets  may be based on geometrical proximity, topological connections, or some other characteristic. See the  "mesh selection"  module for details.
 
 
 

examples/meshing/L_shaped_mesh.jl

@@ -6,11 +6,11 @@ Meshing an L-shaped membrane: merging multiple meshes.
 
 t0 = time()
 
-W = 100. # strip width
-L = 200. # length of the strip
-nL = 15
-nW = 10
-tolerance = W / nW / 1.0e5
+W = 100. # width of the leg
+L = 200. # length of the leg
+nL = 15 # number of elements along the length of the leg
+nW = 10 # number of elements along the width
+tolerance = W / nW / 1.0e5 # tolerance for merging nodes
 Meshes = Array{Tuple{FENodeSet,FESet},1}()
 push!(Meshes, Q4quadrilateral([0.0 0.0; W W], nW, nW))
 push!(Meshes, Q4quadrilateral([-L 0.0; 0.0 W], nL, nW))