Output of FE solution in 2D hp-adaptive space

Filename

waveprop/showSol2D.cc

• Output of a finite element solution in 2D or its gradient to a file format readable by Matlab.

Call	showSol2D.cc -f <FILE> -v <VFILE> [-c -d]

Usage

The files for the mesh are expected to have the following specified relation to the input file <FILE> e.g. for the input file example.cig it is searched for:

example_Coord.dat	File with coordinates of the mesh vertices.
example_Elms.dat	File with information of the mesh cells.
example_Attr.dat	File with cell, edge and vertex attributes.
example_EdgRadia.dat	File with radia of circular edges.
example_EdgCorr.dat	File with information about periodic edges.

Furthermore, semi-infinite rectangles can be defined via the file for the input parameter.

Type	Name (default value)	Stands for		Compulsory
string array	InfiniteQuad (empty)	Array of semi-infinite rectangles, e.g. string array InfiniteQuad { 1 "2 1 4", 2 "104 103 4" }		No

The mesh, the refinement information and the boundary condition, given with the input parameters, have to coincide with those which have been used to generate the finite element solution, i.e. the same finite element space will be generated.

In <VFILE> the coefficient vector of the finite element solution is stored and one of the flags -c and -d has been used to define the data type (complex double or double).

Input Parameter

Type	Name (default value)	Stands for		Compulsory
string	dirichl_bdAttrib ( "")	List of attributes of edges with Dirichlet boundary condition, the attributes are separated by spaces, e.g. "1 3 8 7"		No
int	p (1)	Starting polynomial degree, will be set at least to 1.		No
string	refinement ( "")	Further refinement, e.g. ="p2 in 1, h2 in 2, p2|0 in 3".		No
		h -refinement	"h" - once
			"h2" - twice
			"h2|1" - twice in local x1-direction and once in x2-direction.
		p -refinement	"p" - increase polynomial degrees by 1
			"p2" - increase polynomial degrees by 2
			"p2|0" - increase in local x1-direction by 2
		only in some cells	"p2|0 in 3" - refinement as above, but only in cells with attribute 3
		h - or hp -refinement towards vertices or edges	"hp -> v101" - one step of hp -refinement towards the vertex/vertices with attribute 101
			h2 in 3 -> e20" - twofold h -refinement towards the edge(s) with attribute 20, only in cells with attribute 3
bool	trunk ( true)	Use of linear trunk space.		No
string	quadrature_type ( "trapeze")	Points on which the solution will be evaluated are quadrature point of some rule. Trapezoidal rule corresponds to uniform points. As also the weights of the quadrature are written it make sense to define other quadrature types.		No
		""trapeze"	Trapezoidal rule.
		""gauss_lobatto"	Gauß-Lobatto rule.
		""gauss_jacobi"	Gauß-Jacobi rule.
int	graphicpoints (12)	Number of points in each direction of each cell.		No
string	graphicfun	Function of the solution, by default solution itself.		No
		""	The solution itself.
		"grad"	The function of the gradient.

string	outputdirectory (".")	Directory of the output files, by default the current working directory (where the executable is called from), and related to current the working directory.		No
string	outputprefix (<FILEPRE>)	Prefix of the output files, for input file example.cig the prefix is by default example.		No
bool	verbose (false)	Let print more information out.		No

Output

Filename	sol.m in the same directory as <VFILE>
Type	Matlab
Variables	Attr	Atributes of the cells.
	edgeAttr	Edge attributes for each cell, i.e. four attributes for each quadrilateral, cell after cell.
	edgemsh	Indices of the points on the edges of the mesh, cell after cell.
	msh	Indices of the points in the cells of the mesh, cell after cell.
	p	Polynomial degrees in each cell (two rows with polynomial degrees).
	u	FE solution or a function of it on the (quadrature) points. Each component is in one row, e.g. the gradient has two rows.
	vtxmsh	Indices of the points on the vertices of the mesh, five for each quadrilateral to form a cycle, cell after cell.
	w	Quadrature weights on the quadrature points.
	x	Physical x-coordinate of the (quadrature) points.
	y	Physical x-coordinate of the (quadrature) points.
	U	Cell arrays where each entrance is row of u.

The FE-mesh of triangles or quadrilaterials is given by edgemsh, while vtxmsh consists of the vertices. For a FE-mesh with cells with only straight edges its more efficient to use vtxmsh instead of edgemesh. In each column there are the numbers of the vertices of one cell given, and can be plotted by

      plot(x(edgemsh),y(edgemsh),'k');
      

The solution itself can be shown as flat plot with

      patch(x(msh), y(msh), u(msh), 'edgecolor', 'none')
      

or as surface plot

      patch(x(msh), y(msh), u(msh), u(msh), 'edgecolor', 'none')
      

You can plot the gradient of the solution with

      quiver(x(msh), y(msh), U{1}(msh), U{2}(msh))