Changeset 367

Timestamp:

04/27/08 20:05:08 (7 months ago)

Author:

powell

Message:

Skeleton of the new refinement algorithm.

Files:

• trunk/matml/src/ternary/qhull.c (modified) (1 diff)

trunk/matml/src/ternary/qhull.c

@@ -72 +72 @@
   qh_printsummary (stdout);
 #endif
+
+  return 0;
+}
+
+
+/*++++++++++++++++++++++++++++++++++++++
+  This uses Newton iteration to refine a single 
+
+  double *point Composition coordinates of the starting point for refining; the
+  result will be returned here.
+
+  double *corners Coordinates (including energies) of the corners of this
+  facet, used for the facet normal.
+
+  energy_params *eparams Collection of energy parameter structures.
+
+  int nparams Number of energy parameter structures in eparams.
+
+  int globaldims Dimensionality of the global space.
+
+  int localdims Dimensionality over which to do the refinement.
+
+  int side Side of the phase diagram on which to refine, if
+  localdims<globaldims.
+
+  double newton_tolerance Stop Newton iterations when the vertex motion falls
+  below this value.
+++++++++++++++++++++++++++++++++++++++*/
+
+static inline void NewtonRefine
+(coordT *point, coordT *corners, energy_params *eparams, int nparams,
+ int globaldims, int localdims, int side, double newton_tolerance)
+{
+  double distance = 0.;
+
+  /*+ Determine which is the lowest energy function at this point +*/
+
+  while (distance >= newton_tolerance)
+    {
+      /*+ Calculate the energy derivatives +*/
+
+      /*+ Subtract the facet slopes from the energy derivatives +*/
+
+      /*+ Solve the linear system to estimate the distance to the minimum +*/
+
+      /*+ Add that distance to the point +*/
+    }
+}
+
+
+/*++++++++++++++++++++++++++++++++++++++
+  This refines each of the facets in the hull, adding a new vertex at its
+  centroid if in a one-phase region, and using Newton-Raphson iteration to
+  refine down the vertices of multi-phase facets.
+
+  int hullRefine It returns zero or an error code.
+
+  energy_params *eparams Collection of energy parameter structures.
+
+  int nparams Number of energy parameter structures in eparams.
+
+  double newton_tolerance Stop Newton iterations when the vertex motion falls
+  below this value.
+
+  double vertex_tolerance Minimum distance between two vertices.  When refining
+  a two-phase facet, two of the vertices should go to the same local minimum;
+  choose this parameter to indicate how close to consider them the "same"
+  point.
+  ++++++++++++++++++++++++++++++++++++++*/
+
+int hullRefine (energy_params *eparams, int nparams, double newton_tolerance,
+                double vertex_tolerance)
+{
+  facetT *facet;
+
+  /*+ Steps in the algorithm:
+    +latex+\begin{enumerate}
+    +latex+\item
+    +html+ <ol><li>
+    Loop over the facets
+    +html+ </li>
+    +*/
+
+  FORALLfacets
+    {
+      coordT corners [6], centroid [2];
+      vertexT *vertex, **vertexp;
+
+      /*+
+        +latex+\item
+        +html+ <li>
+        If the lowest free energy function at the centroid has lower energy
+        than the average energy of the vertices, add it as a new vertex.
+        +html+ </li>
+        +*/
+      if (centroid[0] < corners[0])
+        ;
+
+      /*+
+        +latex+\item
+        +html+ <li>
+        Otherwise, use Newton-Raphson iteration to refine each vertex.
+        +html+ </li>
+        +*/
+      else
+        {
+
+          /*+
+            +latex+\item
+            +html+ <li>
+            Find the lowest free energy function at this vertex.
+            +html+ </li>
+            +*/
+
+          /*+
+            +latex+\item
+            +html+ <li>
+            If the vertex is on a side of the phase diagram (one or more
+            composition variables is zero or they sum to one), refine along
+            each side that it's on, to avoid the "infinite slope at the edge"
+            problem.  If it's on more than one side, add a new candidate vertex
+            for each side it's on.
+            +html+ </li>
+            +*/
+
+          /*+
+            +latex+\item
+            +html+ <li>
+            Otherwise refine starting at this vertex.
+            +html+ </li>
+            +*/
+        }
+
+      /*+
+        +latex+\item
+        +html+ <li>
+        If any two new candidate vertices are in the same place (closer than
+        vertex_tolerance), eliminate one.
+        +html+ </li>
+        +*/
+    }
+  /*+
+    +latex+\end{enumerate}
+    +html+ </ol>
+    +*/
 
   return 0;