Decomposition.md

@@ -20,6 +20,8 @@ The Fixed decomposition just divide the domain as the user specified and assign
 
 The data driven decomposition instead consider the volume of the information the structure store and divide the volume equally them equally regardless of the communication.
 
+### Domain definition
+
 In the following we will consider structures that map over N-dimensional spaces because at the moment is our main interest
 
 ### Model decomposition
@@ -28,7 +30,7 @@ In a distributed-memory setting, where data are scattered across
 processors, two factors are important: equal division of work across
 processors and reduction of the communication overhead.
 A typical approach, is to formulate the problem as a 
-graph-partitioning problem: the physical domain is divided into sub-sub-domains (_Domain decomposition_)
+graph-partitioning problem: the domain is divided into sub-sub-domains (_Domain decomposition_)
  (vertices of the graph), each of them  carrying a weight modelling the computational cost.
  The communication pattern between sub-domains is represented as links
 between the sub-sub-domains (edges of the graph) with weights formalizing