From: David Wells Date: Sat, 11 May 2019 18:05:29 +0000 (-0400) Subject: step-34: update output. X-Git-Tag: v9.1.0-rc1~57^2~4 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=5cb09fec15b5fc0dbc11d0a1aa09fe7568a0f351;p=dealii.git step-34: update output. --- diff --git a/examples/step-34/doc/results.dox b/examples/step-34/doc/results.dox index 7507e6bfff..830fc51802 100644 --- a/examples/step-34/doc/results.dox +++ b/examples/step-34/doc/results.dox @@ -14,7 +14,7 @@ set Run 3d simulation = true subsection Exact solution 2d # Any constant used inside the function which is not a variable name. - set Function constants = + set Function constants = # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. @@ -28,7 +28,7 @@ end subsection Exact solution 3d # Any constant used inside the function which is not a variable name. - set Function constants = + set Function constants = # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. @@ -58,7 +58,7 @@ end subsection Wind function 2d # Any constant used inside the function which is not a variable name. - set Function constants = + set Function constants = # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. @@ -72,7 +72,7 @@ end subsection Wind function 3d # Any constant used inside the function which is not a variable name. - set Function constants = + set Function constants = # Separate vector valued expressions by ';' as ',' is used internally by the # function parser. @@ -88,7 +88,7 @@ When we run the program, the following is printed on screen: @verbatim DEAL:: DEAL::Parsing parameter file parameters.prm -DEAL::for a 2 dimensional simulation. +DEAL::for a 2 dimensional simulation. DEAL:GMRES::Starting value 2.21576 DEAL:GMRES::Convergence step 1 value 2.37635e-13 DEAL::Cycle 0: @@ -110,14 +110,14 @@ DEAL::Cycle 3: DEAL:: Number of active cells: 160 DEAL:: Number of degrees of freedom: 160 DEAL:: -cycle cells dofs L2(phi) Linfty(alpha) - 0 20 20 4.465e-02 - 5.000e-02 - - 1 40 40 1.081e-02 2.05 2.500e-02 1.00 - 2 80 80 2.644e-03 2.03 1.250e-02 1.00 - 3 160 160 6.529e-04 2.02 6.250e-03 1.00 +cycle cells dofs L2(phi) Linfty(alpha) + 0 20 20 4.465e-02 - 5.000e-02 - + 1 40 40 1.081e-02 2.05 2.500e-02 1.00 + 2 80 80 2.644e-03 2.03 1.250e-02 1.00 + 3 160 160 6.529e-04 2.02 6.250e-03 1.00 DEAL:: DEAL::Parsing parameter file parameters.prm -DEAL::for a 3 dimensional simulation. +DEAL::for a 3 dimensional simulation. DEAL:GMRES::Starting value 2.84666 DEAL:GMRES::Convergence step 3 value 8.68638e-18 DEAL::Cycle 0: @@ -139,11 +139,11 @@ DEAL::Cycle 3: DEAL:: Number of active cells: 1536 DEAL:: Number of degrees of freedom: 1538 DEAL:: -cycle cells dofs L2(phi) Linfty(alpha) - 0 24 26 6.873e-01 - 2.327e-01 - - 1 96 98 1.960e-01 1.81 1.239e-01 0.91 - 2 384 386 4.837e-02 2.02 6.319e-02 0.97 - 3 1536 1538 1.176e-02 2.04 3.176e-02 0.99 +cycle cells dofs L2(phi) Linfty(alpha) + 0 24 26 3.437e-01 - 2.327e-01 - + 1 96 98 9.794e-02 1.81 1.239e-01 0.91 + 2 384 386 2.417e-02 2.02 6.319e-02 0.97 + 3 1536 1538 5.876e-03 2.04 3.176e-02 0.99 @endverbatim As we can see from the convergence table in 2d, if we choose @@ -154,11 +154,11 @@ equal size generates a regular polygon with N faces, whose angles are exactly $\pi-\frac {2\pi}{N}$, therefore the error we commit should be exactly $\frac 12 - (\frac 12 -\frac 1N) = \frac 1N$. In fact this is a very good indicator that we are performing the singular integrals in -an appropriate manner. +an appropriate manner. The error in the approximation of the potential $\phi$ is largely due to approximation of the domain. A much better approximation could be -obtained by using higher order mappings. +obtained by using higher order mappings. If we modify the main() function, setting fe_degree and mapping_degree to two, and raise the order of the quadrature formulas in @@ -166,21 +166,21 @@ the parameter file, we obtain the following convergence table for the two dimensional simulation @verbatim -cycle cells dofs L2(phi) Linfty(alpha) - 0 20 40 5.404e-05 - 2.306e-04 - - 1 40 80 3.578e-06 3.92 1.738e-05 3.73 - 2 80 160 2.479e-07 3.85 1.253e-05 0.47 - 3 160 320 1.856e-08 3.74 7.670e-06 0.71 +cycle cells dofs L2(phi) Linfty(alpha) + 0 20 40 5.414e-05 - 2.306e-04 - + 1 40 80 3.623e-06 3.90 1.737e-05 3.73 + 2 80 160 2.690e-07 3.75 1.253e-05 0.47 + 3 160 320 2.916e-08 3.21 7.670e-06 0.71 @endverbatim and @verbatim -cycle cells dofs L2(phi) Linfty(alpha) - 0 24 98 9.187e-03 - 8.956e-03 - - 1 96 386 3.991e-04 4.52 1.182e-03 2.92 - 2 384 1538 2.113e-05 4.24 1.499e-04 2.98 - 3 1536 6146 1.247e-06 4.08 1.896e-05 2.98 +cycle cells dofs L2(phi) Linfty(alpha) + 0 24 98 3.770e-03 - 8.956e-03 - + 1 96 386 1.804e-04 4.39 1.182e-03 2.92 + 2 384 1538 9.557e-06 4.24 1.499e-04 2.98 + 3 1536 6146 6.617e-07 3.85 1.892e-05 2.99 @endverbatim for the three dimensional case. As we can see, convergence results are @@ -191,7 +191,7 @@ of Q2 case in the three dimensional simulation, the error is roughly three orders of magnitude lower. The result of running these computations is a bunch of output files that we -can pass to our visualization program of choice. +can pass to our visualization program of choice. The output files are of two kind: the potential on the boundary element surface, and the potential extended to the outer and inner domain. The combination of the two for the two dimensional case looks