From 3fb9764847e9791d8d931e8c526ffe6d0f12c942 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Maximilian=20H=C3=B6rl?=
<maximilian.hoerl@mathematik.uni-stuttgart.de>
Date: Sun, 19 Apr 2020 13:50:58 +0200
Subject: [PATCH] add exact 3d solution to problem dg3
---
README.md | 1 -
dune/mmdg/problems/dgproblem3.hh | 39 ++++++++++++++++++++++++++------
src/dg.cc | 2 +-
3 files changed, 33 insertions(+), 9 deletions(-)
diff --git a/README.md b/README.md
index 0f305c8..2519df9 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,6 @@ Dependencies
------------
`dune-mmdg` requires the DUNE core modules, version 2.7 or later, and a current version of the `dune-mmesh` module.
-
Additionally, for the `dune-mmesh` module, you will need a current version of `CGAL` installed on your system.
diff --git a/dune/mmdg/problems/dgproblem3.hh b/dune/mmdg/problems/dgproblem3.hh
index 2942138..21659d8 100644
--- a/dune/mmdg/problems/dgproblem3.hh
+++ b/dune/mmdg/problems/dgproblem3.hh
@@ -13,7 +13,9 @@ class DGProblem3 : public DGProblem<Coordinate, Scalar>
public:
static constexpr int dim = Coordinate::dimension;
- //the exact solution at position pos
+ //the exact solution at position pos,
+ //in 2D and 3D the exact solution is obtained by a Fourier series expansion
+ //of the rectangular function
Scalar exactSolution (const Coordinate& pos) const
{
if constexpr (dim == 1)
@@ -21,19 +23,42 @@ class DGProblem3 : public DGProblem<Coordinate, Scalar>
return 0.5 * pos[0] * (pos[0] - 1);
}
- if constexpr (dim == 2) //approximate series
+ if constexpr (dim == 2) //Fourier series with cut-off
{
- const int cutoff = 21;
+ constexpr int cutoff = 31;
double solution = 0.0;
+
for (int m = 1; m <= cutoff; m = m + 2)
{
for (int n = 1; n <= cutoff; n = n + 2)
{
solution += sin(M_PI * m * pos[0]) * sin(M_PI * n * pos[1])
- / (m * n * (m*m + n*n));
+ / (m * n * (m * m + n * n));
}
}
- solution *= -16 / pow(M_PI, 4);
+
+ solution *= -16.0 / pow(M_PI, 4);
+ return solution;
+ }
+
+ if constexpr (dim == 3) //Fourier series with cut-off
+ {
+ constexpr int cutoff = 21;
+ double solution = 0.0;
+
+ for (int k = 1; k <= cutoff; k = k + 2)
+ {
+ for (int l = 1; l <= cutoff; l = l + 2)
+ {
+ for (int m = 1; m <= cutoff; m = m + 2)
+ {
+ solution += sin(M_PI * k * pos[0]) * sin(M_PI * l * pos[1])
+ * sin(M_PI * m* pos[2]) / (k * l * m * (k * k + l * l + m * m));
+ }
+ }
+ }
+
+ solution *= -64.0 / pow(M_PI, 5);
return solution;
}
@@ -42,10 +67,10 @@ class DGProblem3 : public DGProblem<Coordinate, Scalar>
std::to_string(dim) + "!");
}
- //exact solution is implemented for dim = 1, 2
+ //exact solution is implemented
bool hasExactSolution() const
{
- return (dim == 1 || dim == 2);
+ return true;
};
//source term
diff --git a/src/dg.cc b/src/dg.cc
index 1b21492..21363da 100644
--- a/src/dg.cc
+++ b/src/dg.cc
@@ -77,7 +77,7 @@ int main(int argc, char** argv)
{
problem = new DGProblem3<Coordinate>();
- if constexpr (dim == 2)
+ if constexpr (dim >= 2)
{
std::cout << "NOTE: The exact solution of your problem is given by "
"an infinite series; increase the cut-off if necessary!\n\n";
--
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