From 1776b4725a4ba8b71492f3ce9b5c148b8197c138 Mon Sep 17 00:00:00 2001 From: Jean-Paul Pelteret Date: Thu, 18 Feb 2016 18:10:44 +0200 Subject: [PATCH] Added 2-d results and updated changelog --- doc/news/changes.h | 6 +++++ examples/step-44/doc/results.dox | 39 ++++++++++++++++++++++++++------ 2 files changed, 38 insertions(+), 7 deletions(-) diff --git a/doc/news/changes.h b/doc/news/changes.h index 65c4fed64e..75e448c8c4 100644 --- a/doc/news/changes.h +++ b/doc/news/changes.h @@ -57,6 +57,12 @@ inconvenience this causes.
    +
  1. Updated: step-44 has been been expressed in a more dimension independent + manner, and can be now run in both 2-d and 3-d. +
    + (Jean-Paul Pelteret, 2016/02/17) +
  2. +
  3. Fixed: FE_Nedelec elements up to polynomial order 12 can now be constructed.
    diff --git a/examples/step-44/doc/results.dox b/examples/step-44/doc/results.dox index 22756ccaa3..af87209594 100644 --- a/examples/step-44/doc/results.dox +++ b/examples/step-44/doc/results.dox @@ -1,6 +1,6 @@

    Results

    -Firstly, we present a comparison of a series of results with those +Firstly, we present a comparison of a series of 3-d results with those in the literature (see Reese et al (2000)) to demonstrate that the program works as expected. We begin with a comparison of the convergence with mesh refinement for the $Q_1-DGPM_0-DGPM_0$ and @@ -18,13 +18,13 @@ as it should.

    - Convergence of the $Q_1-DGPM_0-DGPM_0$ formulation. + Convergence of the $Q_1-DGPM_0-DGPM_0$ formulation in 3-d.

    - Convergence of the $Q_2-DGPM_1-DGPM_1$ formulation. + Convergence of the $Q_2-DGPM_1-DGPM_1$ formulation in 3-d.

    @@ -140,7 +140,7 @@ and is opposite to the physically realistic interpretation of pressure.

    - Z-displacement solution. + Z-displacement solution for the 3-d problem.

    @@ -172,7 +172,7 @@ There is a clear distinction and transition between regions of compression and e and the linear approximation of the pressure field allows a refined visualisation of the pressure at the sub-element scale. It should however be noted that the pressure field remains discontinuous - and could be smoothed on a continuous grid for the post-processing purposes. +and could be smoothed on a continuous grid for the post-processing purposes. @@ -182,7 +182,7 @@ It should however be noted that the pressure field remains discontinuous

    - Z-displacement solution. + Z-displacement solution for the 3-d problem.

    @@ -213,7 +213,7 @@ than the $Q_1-DGPM_0-DGPM_0$ for a similar number of degrees-of-freedom This is shown in the graph below for a batch of tests run consecutively on a single 4-core (8-thread) machine. The increase in computational time for the higher-order method is likely due to the increased band-width required for the higher-order elements. -As previously mentioned, the use of a better solver and precondtioner may mitigate the +As previously mentioned, the use of a better solver and preconditioner may mitigate the expense of using a higher-order formulation. It was observed that for the given problem using the multithreaded Jacobi preconditioner can reduce the computational runtime by up to 72% (for the worst case being a higher-order formulation with a large number @@ -233,6 +233,31 @@ some finite-strain problems involving alternative constitutive models. + +Lastly, results for the displacement solution for the 2-d problem are showcased below for +two different levels of grid refinement. +It is clear that due to the extra constraints imposed by simulating in 2-d that the resulting +displacement field, although qualitatively similar, is different to that of the 3-d case. + + + + + + + + +
    + +

    + Y-displacement solution in 2-d for 2 global grid refinement levels. +

    +
    + +

    + Y-displacement solution in 2-d for 5 global grid refinement levels. +

    +
    +

    Possibilities for extensions

    -- 2.39.5