From a279a84395eccdef351c70abc8ab7331c1724308 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Maximilian=20H=C3=B6rl?=
<maximilian.hoerl@mathematik.uni-stuttgart.de>
Date: Thu, 19 Mar 2020 14:39:58 +0100
Subject: [PATCH] add mmdg problems
---
dune/mmdg/problems/coupleddgproblem.hh | 31 +-
dune/mmdg/problems/dgproblem.hh | 2 +-
.../mmdg/problems/inhomogeneousbulkproblem.hh | 6 -
dune/mmdg/problems/mmdgproblem1.hh | 61 +
dune/mmdg/problems/mmdgproblem2.hh | 89 +
dune/mmdg/problems/poisson.hh | 8 +-
dune/mmdg/problems/zeropoisson.hh | 8 +-
src/grids/mmdg2.geo | 33 +
src/grids/mmdg2.msh | 1633 +++++++++++++++++
src/mmdg.cc | 42 +-
src/parameterMMDG.ini | 2 +-
11 files changed, 1873 insertions(+), 42 deletions(-)
create mode 100644 dune/mmdg/problems/mmdgproblem1.hh
create mode 100644 dune/mmdg/problems/mmdgproblem2.hh
create mode 100644 src/grids/mmdg2.geo
create mode 100644 src/grids/mmdg2.msh
diff --git a/dune/mmdg/problems/coupleddgproblem.hh b/dune/mmdg/problems/coupleddgproblem.hh
index e6fe7a4..72b1f03 100644
--- a/dune/mmdg/problems/coupleddgproblem.hh
+++ b/dune/mmdg/problems/coupleddgproblem.hh
@@ -6,34 +6,39 @@
//abstract class providing an interface for a coupled flow problem in a
//fractured porous medium that is to be solved with a coupled discontinuous
//Galerkin scheme
-template<class Vector, class Scalar = double>
-class CoupledDGProblem : public DGProblem<Vector, Scalar>
+template<class Coordinate, class Scalar = double>
+class CoupledDGProblem : public DGProblem<Coordinate, Scalar>
{
public:
- static constexpr int dim = Vector::dimension;
- using Base = DGProblem<Vector, Scalar>;
+ static constexpr int dim = Coordinate::dimension;
+ using Base = DGProblem<Coordinate, Scalar>;
using Matrix = typename Base::Matrix;
//the exact solution on the interface at position pos
- virtual Scalar exactInterfaceSolution (const Vector& pos) const
+ virtual Scalar exactInterfaceSolution (const Coordinate& pos) const
{
return Scalar(0.0);
}
//interface source term at position pos
- virtual Scalar qInterface (const Vector& pos) const
+ virtual Scalar qInterface (const Coordinate& pos) const
{
return Scalar(0.0);
}
//aperture d of the fracture at position pos
- virtual Scalar aperture (const Vector& pos) const
+ virtual Scalar aperture (const Coordinate& pos) const
{
return Scalar(1.0);
}
+ virtual Scalar interfaceBoundary(const Coordinate& pos) const
+ {
+ return exactInterfaceSolution(pos);
+ }
+
//tangential permeability tensor of the interface at position pos
- virtual Matrix Kparallel (const Vector& pos) const
+ virtual Matrix Kparallel (const Coordinate& pos) const
{
Matrix permeability(0.0);
@@ -47,12 +52,11 @@ class CoupledDGProblem : public DGProblem<Vector, Scalar>
}
//permeability of the fracture in normal direction at position pos
- virtual Scalar Kperp (const Vector& pos) const
+ virtual Scalar Kperp (const Coordinate& pos) const
{
return Scalar(1.0);
}
-
//returns the recommended quadrature order to compute an integral
//over x * qInterface(x)
virtual int quadratureOrder_qInterface () const
@@ -60,6 +64,13 @@ class CoupledDGProblem : public DGProblem<Vector, Scalar>
return 1;
}
+ //returns the recommended quadrature order to compute an integral
+ //over x * interfaceBoundary(x)
+ virtual int quadratureOrderInterfaceBoundary () const
+ { //NOTE: only relevant for 3d, not implemented!
+ return 1;
+ }
+
//returns the recommended quadrature order to compute an integral
//over Kparallel(x)
virtual int quadratureOrder_Kparallel () const
diff --git a/dune/mmdg/problems/dgproblem.hh b/dune/mmdg/problems/dgproblem.hh
index 13d0bc4..b59b0a6 100644
--- a/dune/mmdg/problems/dgproblem.hh
+++ b/dune/mmdg/problems/dgproblem.hh
@@ -31,7 +31,7 @@ class DGProblem
//boundary condition at position pos
virtual Scalar boundary (const Coordinate& pos) const
{
- return Scalar(0.0);
+ return exactSolution(pos);
}
//permeability tensor at position pos
diff --git a/dune/mmdg/problems/inhomogeneousbulkproblem.hh b/dune/mmdg/problems/inhomogeneousbulkproblem.hh
index 8cf6424..4dcc907 100644
--- a/dune/mmdg/problems/inhomogeneousbulkproblem.hh
+++ b/dune/mmdg/problems/inhomogeneousbulkproblem.hh
@@ -32,12 +32,6 @@ class InhomogeneousBulkProblem : public DGProblem<Coordinate, Scalar>
return pos * Coordinate(2.0);
}
- //boundary condition
- virtual Scalar boundary (const Coordinate& pos) const
- {
- return exactSolution(pos);
- }
-
//permeability tensor at position pos
virtual Matrix K (const Coordinate& pos) const
{
diff --git a/dune/mmdg/problems/mmdgproblem1.hh b/dune/mmdg/problems/mmdgproblem1.hh
new file mode 100644
index 0000000..c2008c8
--- /dev/null
+++ b/dune/mmdg/problems/mmdgproblem1.hh
@@ -0,0 +1,61 @@
+#ifndef __DUNE_MMDG_MMDGPROBLEM1_HH__
+#define __DUNE_MMDG_MMDGPROBLEM1_HH__
+
+#include <cmath>
+#include <dune/mmdg/problems/coupleddgproblem.hh>
+
+//a coupled dg problem for dim = 2,
+//taken from [Antonietti et al. (2019): Example 6.3]
+template<class Coordinate, class Scalar = double>
+class MMDGProblem1 : public CoupledDGProblem<Coordinate, Scalar>
+{
+ public:
+ static constexpr int dim = Coordinate::dimension;
+
+ //the exact bulk solution at position pos
+ Scalar exactSolution (const Coordinate& pos) const
+ {
+ Scalar solution = pos * Coordinate(1.0);
+
+ if (pos[0] > 0.5)
+ {
+ solution += 1.0;
+ }
+
+ return solution;
+ }
+
+ //the exact solution on the interface at position pos
+ Scalar exactInterfaceSolution (const Coordinate& pos) const
+ {
+ return pos * Coordinate(1.0) + 0.5;
+ }
+
+ //indicates whether an exact solution is implemented for the problem
+ bool hasExactSolution () const
+ {
+ return true;
+ };
+
+ //aperture d of the fracture at position pos
+ Scalar aperture (const Coordinate& pos) const
+ {
+ return Scalar(1.0);
+ }
+
+ //returns the recommended quadrature order to compute an integral
+ //over x * boundary(x)
+ int quadratureOrderBoundary () const
+ {
+ return 2;
+ }
+
+ //returns the recommended quadrature order to compute an integral
+ //over x * interfaceBoundary(x)
+ int quadratureOrderInterfaceBoundary () const
+ { //NOTE: only relevant for 3d, not implemented!
+ return 2;
+ }
+};
+
+#endif
diff --git a/dune/mmdg/problems/mmdgproblem2.hh b/dune/mmdg/problems/mmdgproblem2.hh
new file mode 100644
index 0000000..79e0595
--- /dev/null
+++ b/dune/mmdg/problems/mmdgproblem2.hh
@@ -0,0 +1,89 @@
+#ifndef __DUNE_MMDG_MMDGPROBLEM2_HH__
+#define __DUNE_MMDG_MMDGPROBLEM2_HH__
+
+#include <cmath>
+#include <dune/mmdg/problems/coupleddgproblem.hh>
+
+//a coupled dg problem for dim = 2,
+//taken from [Antonietti et al. (2019): Example 6.3]
+template<class Coordinate, class Scalar = double>
+class MMDGProblem2 : public CoupledDGProblem<Coordinate, Scalar>
+{
+ public:
+ static constexpr int dim = Coordinate::dimension;
+
+ //the exact bulk solution at position pos
+ Scalar exactSolution (const Coordinate& pos) const
+ {
+ Scalar solution =
+ (pos[0] < 0.5) ? std::sin(4 * pos[0]) : std::cos(4 * pos[0]);
+ return solution * std::cos(M_PI * pos[1]);
+ }
+
+ //the exact solution on the interface at position pos
+ Scalar exactInterfaceSolution (const Coordinate& pos) const
+ {
+ constexpr Scalar cos2 = std::cos(2.0);
+ constexpr Scalar sin2 = std::sin(2.0);
+ return 0.75 * (cos2 - sin2) * std::cos(M_PI * pos[1]);
+ }
+
+ //indicates whether an exact solution is implemented for the problem
+ bool hasExactSolution () const
+ {
+ return true;
+ };
+
+ //bulk source term at position pos
+ Scalar q (const Coordinate& pos) const
+ {
+ constexpr Scalar sourcefactor = 16.0 + M_PI * M_PI;
+ Scalar source =
+ (pos[0] < 0.5) ? std::sin(4 * pos[0]) : std::cos(4 * pos[0]);
+ return sourcefactor * source * std::cos(M_PI * pos[1]);
+ }
+
+ //interface source term at position pos
+ Scalar qInterface (const Coordinate& pos) const
+ {
+ constexpr Scalar sourcefactor =
+ (std::cos(2.0) + std::sin(2.0)) * (4.0 + 0.1875 * M_PI * M_PI);
+ return sourcefactor * aperture(pos) * std::cos(M_PI * pos[1]);
+ }
+
+ //aperture d of the fracture at position pos
+ Scalar aperture (const Coordinate& pos) const
+ {
+ return Scalar(0.25);
+ }
+
+ //returns the recommended quadrature order to compute an integral
+ //over x * q(x)
+ int quadratureOrder_q () const
+ {
+ return 10;
+ }
+
+ //returns the recommended quadrature order to compute an integral
+ //over x * boundary(x)
+ int quadratureOrderBoundary () const
+ {
+ return 10;
+ }
+
+ //returns the recommended quadrature order to compute an integral
+ //over x * interfaceBoundary(x)
+ int quadratureOrderInterfaceBoundary () const
+ { //NOTE: only relevant for 3d, not implemented!
+ return 10;
+ }
+
+ //returns the recommended quadrature order to compute an integral
+ //over x * qInterface(x)
+ int quadratureOrder_qInterface () const
+ {
+ return 10;
+ }
+};
+
+#endif
diff --git a/dune/mmdg/problems/poisson.hh b/dune/mmdg/problems/poisson.hh
index e6f3757..571d176 100644
--- a/dune/mmdg/problems/poisson.hh
+++ b/dune/mmdg/problems/poisson.hh
@@ -12,7 +12,7 @@ class Poisson : public DGProblem<Coordinate, Scalar>
//1d: f(x) = x,
//2d: f(x,y) = x*y,
//3d: f(x,y,z) = x*y*z
- virtual Scalar exactSolution (const Coordinate& pos) const
+ Scalar exactSolution (const Coordinate& pos) const
{
Scalar solution(1.0);
@@ -29,12 +29,6 @@ class Poisson : public DGProblem<Coordinate, Scalar>
{
return true;
};
-
- //boundary condition
- virtual Scalar boundary (const Coordinate& pos) const
- {
- return exactSolution(pos);
- }
};
#endif
diff --git a/dune/mmdg/problems/zeropoisson.hh b/dune/mmdg/problems/zeropoisson.hh
index dce45f3..56525ab 100644
--- a/dune/mmdg/problems/zeropoisson.hh
+++ b/dune/mmdg/problems/zeropoisson.hh
@@ -15,7 +15,7 @@ class ZeroPoisson : public DGProblem<Coordinate, Scalar>
static constexpr int dim = Coordinate::dimension;
//the exact solution at position pos
- virtual Scalar exactSolution (const Coordinate& pos) const
+ Scalar exactSolution (const Coordinate& pos) const
{
if constexpr (dim == 1)
{
@@ -54,6 +54,12 @@ class ZeroPoisson : public DGProblem<Coordinate, Scalar>
{
return Scalar(-1.0);
}
+
+ //boundary condition at position pos
+ virtual Scalar boundary (const Coordinate& pos) const
+ {
+ return Scalar(0.0);
+ }
};
#endif
diff --git a/src/grids/mmdg2.geo b/src/grids/mmdg2.geo
new file mode 100644
index 0000000..b5958f8
--- /dev/null
+++ b/src/grids/mmdg2.geo
@@ -0,0 +1,33 @@
+//characteristic length
+lc = 5e-2;
+
+//domain corners, domain = [0,1] x [0,1]
+Point(1) = {0, 0, 0, lc};
+Point(2) = {1, 0, 0, lc};
+Point(3) = {1, 1, 0, lc};
+Point(4) = {0, 1, 0, lc};
+
+//points for interface x = 0.5
+Point(5) = {0.5, 0, 0, lc};
+Point(6) = {0.5, 1, 0, lc};
+Point(7) = {0.5, 0.5, 0, lc};
+
+//domain outline
+Line(1) = {1, 2};
+Line(2) = {2, 3};
+Line(3) = {3, 4};
+Line(4) = {4, 1};
+
+//interface outline
+Line(6) = {5, 7};
+Line(7) = {7, 6};
+
+//curve loops
+Curve Loop(1) = {1:4}; //domain boundary
+
+//surfaces
+Plane Surface(1) = {1};
+Physical Surface(1) = {1};
+
+Curve{6:7} In Surface{1};
+Physical Curve(2) = {6:7};
diff --git a/src/grids/mmdg2.msh b/src/grids/mmdg2.msh
new file mode 100644
index 0000000..b339829
--- /dev/null
+++ b/src/grids/mmdg2.msh
@@ -0,0 +1,1633 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$Nodes
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+$EndElements
diff --git a/src/mmdg.cc b/src/mmdg.cc
index e2d4348..4c96269 100644
--- a/src/mmdg.cc
+++ b/src/mmdg.cc
@@ -5,6 +5,7 @@
#include <sys/stat.h>
#include <sys/types.h>
#include <type_traits>
+#include <string>
#include <dune/common/exceptions.hh>
#include <dune/common/parametertree.hh>
@@ -19,7 +20,8 @@
#include <dune/mmdg/mmdg.hh>
#include <dune/mmdg/clockhelper.hh>
#include <dune/mmdg/problems/coupleddgproblem.hh>
-
+#include <dune/mmdg/problems/mmdgproblem1.hh>
+#include <dune/mmdg/problems/mmdgproblem2.hh>
int main(int argc, char** argv)
{
@@ -52,31 +54,39 @@ int main(int argc, char** argv)
const double mu = std::stod(pt["mu"]);
const double xi = std::stod(pt["xi"]); //coupling parameter
- //create a grid from .dgf file
- GridFactory gridFactory( "grids/sphere" + std::to_string(dim) + "d.msh" );
- const Grid& grid = *gridFactory.grid();
- const GridView& gridView = grid.leafGridView();
- const IGrid& iGrid = grid.interfaceGrid();
- const IGridView& iGridView = iGrid.leafGridView();
-
- //element mapper for the leaf grid views
- const Mapper mapper(gridView, Dune::mcmgElementLayout());
- const IMapper iMapper(iGridView, Dune::mcmgElementLayout());
-
Problem* problem; //problem to be solved
+ std::string gridType;
+
//determine problem type
- if (pt["problem"] == "poisson")
- { //TODO
- problem = new CoupledDGProblem<Coordinate>();
+ if (pt["problem"] == "mmdg1")
+ {
+ problem = new MMDGProblem1<Coordinate>();
+ gridType = "mmdg2";
+ }
+ else if (pt["problem"] == "mmdg2")
+ {
+ problem = new MMDGProblem2<Coordinate>();
+ gridType = "mmdg2";
}
else
{
DUNE_THROW(Dune::Exception,
"Invalid problem type or parameter 'problem' not specified in file "
- "parameterDG.ini (use 'poisson' or TODO)");
+ "parameterDG.ini (use 'mmdg2' or TODO)");
}
+ //create a grid from .dgf file
+ GridFactory gridFactory( "grids/" + gridType + ".msh" );
+ const Grid& grid = *gridFactory.grid();
+ const GridView& gridView = grid.leafGridView();
+ const IGrid& iGrid = grid.interfaceGrid();
+ const IGridView& iGridView = iGrid.leafGridView();
+
+ //element mapper for the leaf grid views
+ const Mapper mapper(gridView, Dune::mcmgElementLayout());
+ const IMapper iMapper(iGridView, Dune::mcmgElementLayout());
+
MMDG mmdg(grid, gridView, mapper, iGridView, iMapper, *problem);
mmdg(mu, xi);
diff --git a/src/parameterMMDG.ini b/src/parameterMMDG.ini
index c787684..4abb5ef 100644
--- a/src/parameterMMDG.ini
+++ b/src/parameterMMDG.ini
@@ -1,3 +1,3 @@
mu = 1000
xi = 0.75
-problem = poisson
+problem = mmdg1
--
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