From 1abd9036bb3ed3b9a91ade8083c786a731a5c8ab Mon Sep 17 00:00:00 2001
From: Oliver Sander <sander@igpm.rwth-aachen.de>
Date: Mon, 12 Nov 2012 17:11:09 +0000
Subject: [PATCH] add a set of Dirichlet boundary conditions that seems to
allow optimal convergence order for third-order finite elements
[[Imported from SVN: r8989]]
---
harmonicmaps-eoc.cc | 36 ++++++++++++++++++++++++++++++------
1 file changed, 30 insertions(+), 6 deletions(-)
diff --git a/harmonicmaps-eoc.cc b/harmonicmaps-eoc.cc
index ccbaad30..a111d56b 100644
--- a/harmonicmaps-eoc.cc
+++ b/harmonicmaps-eoc.cc
@@ -62,12 +62,36 @@ struct DirichletFunction
rotation.matrix(rMat);
out = rMat[2];
#endif
- double angle = 0.5 * M_PI * x[0];
- angle *= -4*x[1]*(x[1]-1);
- out = 0;
-// out[0] = std::cos(angle);
-// out[1] = std::sin(angle);
- out[2] = 1;
+#if 1 // This data seems to have the necessary smoothness to have optimal
+ // convergence order even for 3rd-order elements
+ double localX = (x[0] + 2)/4;
+ double localY = (x[1] + 1)/2;
+ double angleX = 0.5 * M_PI * sin(M_PI*localX);
+ double angleY = 0.5 * M_PI * sin(M_PI*localY);
+
+ // Rotation matrix around the x axis
+ FieldMatrix<double,TargetSpace::CoordinateType::dimension,TargetSpace::CoordinateType::dimension> rotationX(0);
+ rotationX[0][0] = 1;
+ rotationX[1][1] = cos(angleY);
+ rotationX[1][2] = -sin(angleY);
+ rotationX[2][1] = sin(angleY);
+ rotationX[2][2] = cos(angleY);
+
+ // Rotation matrix around the y axis
+ FieldMatrix<double,TargetSpace::CoordinateType::dimension,TargetSpace::CoordinateType::dimension> rotationY(0);
+ rotationY[0][0] = cos(angleX);
+ rotationY[0][2] = -sin(angleX);
+ rotationY[1][1] = 1;
+ rotationY[2][0] = sin(angleX);
+ rotationY[2][2] = cos(angleX);
+
+ //angle *= -4*x[1]*(x[1]-1);
+ TargetSpace::CoordinateType unitVector(0); unitVector[2] = 1;
+
+ TargetSpace::CoordinateType tmp;
+ rotationX.mv(unitVector,tmp);
+ rotationY.mv(tmp,out);
+#endif
}
};
--
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