Here is a little self-contained example on how to integrate quantities in post-processing. Note that GetDP can only integrate quantities on their domain of definition (specified in the function space). To integrate on arbitrary regions you can use, e.g., Plugin(Integrate) in Gmsh.
post_integral.pro
Group {
// Domain [0,2]x[0,1]
Omega = Region[ {1,2} ];
// Left half of Omega
Omega1 = Region[ {1} ];
// Right half of Omega
Omega2 = Region[ {2} ];
// Left and right boundaries
Gamma1 = Region[ {10} ];
Gamma2 = Region[ {11} ];
}
Jacobian {
{ Name Vol ; Case { { Region All ; Jacobian Vol ; } } }
}
Integration {
{ Name Int ; Case { { Type Gauss ;
Case { { GeoElement Triangle ; NumberOfPoints 3 ; } } } } }
}
Constraint {
{ Name Dirichlet ;
Case {
{ Region Gamma1 ; Value -1. ; }
{ Region Gamma2 ; Value 1. ; }
}
}
}
FunctionSpace {
{ Name H1 ; Type Form0 ;
BasisFunction {
{ Name sn ; NameOfCoef vn ; Function BF_Node ;
Support Omega ; Entity NodesOf[ All ] ; }
}
Constraint {
{ NameOfCoef vn; EntityType NodesOf ; NameOfConstraint Dirichlet; }
}
}
}
Formulation {
{ Name Laplace ; Type FemEquation ;
Quantity {
{ Name v ; Type Local ; NameOfSpace H1 ; }
}
Equation {
Integral { [ Dof{d v} , {d v} ] ; In Omega ; Jacobian Vol ; Integration Int ; }
}
}
}
Resolution {
{ Name Laplace ;
System {
{ Name A ; NameOfFormulation Laplace ; }
}
Operation {
Generate[A] ; Solve[A] ; SaveSolution[A] ;
}
}
}
PostProcessing {
{ Name Laplace ; NameOfFormulation Laplace ;
Quantity {
{ Name v ; Value { Term { [ {v} ] ; In Omega ; Jacobian Vol; } } }
// defines the integral of v in a generic way, over the whole domain Omega
{ Name intv ; Value { Integral { [ {v} ] ; In Omega ; Jacobian Vol; Integration Int; } } }
}
}
}
PostOperation{
{ Name v ; NameOfPostProcessing Laplace;
Operation {
Print[ v , OnElementsOf Omega , File "v.pos" ] ;
// Integral of v over Omega (should be 0)
Print[ intv[Omega] , OnGlobal ] ;
// Integral of v over Omega1 (should be -0.5)
Print[ intv[Omega1] , OnGlobal ] ;
// Integral of v over Omega2 (should be 0.5)
Print[ intv[Omega2] , OnGlobal ] ;
}
}
}post_integral.geo
s=1;
Point(1) = {0,0,0,s/10};
Point(2) = {s,0,0,s/10};
Point(3) = {2*s,0,0,s/10};
Point(4) = {0,s,0,s/10};
Point(5) = {s,s,0,s/10};
Point(6) = {2*s,s,0,s/10};
Line(1) = {1,2};
Line(2) = {2,3};
Line(3) = {3,6};
Line(4) = {6,5};
Line(5) = {5,4};
Line(6) = {4,1};
Line(7) = {2,5};
Line Loop(8) = {1,7,5,6};
Plane Surface(9) = {8};
Line Loop(10) = {2,3,4,-7};
Plane Surface(11) = {10};
Physical Surface(1) = 9;
Physical Surface(2) = 11;
Physical Line(10) = 6; // left
Physical Line(11) = 3; // right