Refinement - Morpho Manual

We have now solved our first shape optimization problem, and the complete problem script is provided in the examples/tutorial folder inside the git repository as tutorial.morpho. The result we have obtained in Fig. 4.5 is, however, a very coarse, low resolution solution comprising only a relatively small number of elements. To gain an improved solution, we need to refine our mesh. Because modifying the mesh also requires us to update other data structures like fields and selections, a special MeshRefiner object is used to perform the refinement.

To perform refinement we:

Create a MeshRefiner object, providing it a list of all the Mesh, Field and Selection objects (i.e. the mesh and objects that directly depend on it) that need to be updated:
```
var mr = MeshRefiner([m, nn, bnd]); // Set the refiner up
```
Call the refine method on the MeshRefiner object to actually perform the refinement. This method returns a Dictionary object that maps the old objects to potentially newly created ones.
```
var refmap = mr.refine(); // Perform the refinement
```
Tell any other objects that refer to the mesh, fields or selections to update their references using refmap. For example, OptimizationProblem and Optimizer objects are typically updated at this step.
```
for (el in [problem, sopt, fopt]) el.update(refmap); // Update the problem
```

Update our own references

m = refmap[m];
nn = refmap[nn];
bnd = refmap[bnd]; // Update variables

We insert this code after our optimization section, which causes morpho to successively optimize and refine.

The complete code including refinement is in examples/tutorial folder inside the git repository as tutorial2.morpho

The resulting optimized shapes are displayed in Fig. 4.6.

// Optimization loop
var refmax = 3
for (refiter in 1..refmax) {
  print "===Refinement level ${refiter}==="
  for (i in 1..100) {
    fopt.linesearch(20)
    sopt.linesearch(20)
  }

  if (refiter==refmax) break

  // Refinement
  var mr=MeshRefiner([m, nn, bnd]) // Set the refiner up
  var refmap=mr.refine() // Perform the refinement
  for (el in [problem, sopt, fopt]) el.update(refmap) // Update the problem
  m=refmap[m]; nn=refmap[nn]; bnd=refmap[bnd] // Update variables
}