20.4.1999

The tools-directory

Solve a 2-dim. problem

Start by pdetool-solution. Then do the assembly yourself using just linear basis functions. The next step would be to extend to quadratic.

How to create the geometry and mesh

• Example session using GUI and Matlab functions)
  Functions used in this session include:
  • pdecirc,initmesh,pdesurf (Pdetool functions)
  • pdeplotn,onboundary (Functions written by J-v-P)

Assembly using linear basis functions

Quadratic basis functions

• The function tofour(by JvP) splits each triangle into four pieces. See an example session here
• Suggestion for quadratic triangle data structure:
  • Start with "p,e,t" created by Pdetool (either gui or initmesh).
  • New p: Append triangle side midpoints into old p
  • New e: Row 2: midpoint indices
    Rows 3-8: old rows 2-7
  • New t: rows 4-6 : midpoint indices
    row 7: the subdomain number (row 4 from the old t)
  You might end up writing a function:

  function [newp,newe,newt]=qmesh(p,e,t);
  %QMESH Modify a pde triangular mesh to be used with quadratic basis functions
  %
  %	[P,E,T]=qmesh(P,E,T) returns a triangular mesh with side midpoints
  %	appended into the point matrix P. In the new Edge matrix E, the second
  %	row contains midpoint indices and rows 3-8 contain rows 2-7 from the
  %	old edge matrix. In the triangle matrix T, rows 4-6 contain midpoint
  %	indices and row 7 contains the subdomain number (row 4 from the old
  %	triangle matrix).
  %	Input arguments P, E and T can be created with pdetool