From: Mark Date: Thu, 2 Dec 2021 17:08:32 +0000 (+0100) Subject: add figures in readme X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=eb1a11c0820eefc5888043a68fda26338bcb084a;p=code-gallery.git add figures in readme add figures in readme --- diff --git a/Distributed_Moving_Laser_Heating/README.md b/Distributed_Moving_Laser_Heating/README.md index f37dd28..b60c727 100644 --- a/Distributed_Moving_Laser_Heating/README.md +++ b/Distributed_Moving_Laser_Heating/README.md @@ -1,8 +1,14 @@ - # Introduction In this tutorial, the studied problem is to simulate temperature distributions of a sample under a moving laser. Light penetrates the substrate without loss. The top-covered thin-film is, however, a light absorbing material. For simplicity, the thin-film is assumed to be TiO$_2$ mixed with silver nanoparticles, which supports light heating of the material by absorbing light energy. For this tutorial, we only consider the isotropic absorption. Figure \ref{fgr:s1} illustrates the sketch of the problem. The absorption coefficient is assumed to be $10^4 m^{-1}$. The substrate is glass. The thickness of the thin-film is assumed to be 400 nm. The spot size at the top of thin film is $20 \mu m$ at $e^{-2}$. The writing speed is assumed to be 10 mm/s. The laser power is 0.4 W. The time step is set as 10 $\mu s$. The initial position of laser center is $-50 \mu m$ with 50 $\mu m$ distance away from the left boundary to avoid boundary effects. +## Illustration of the problem + +![illustration](./doc/structure-2d.png) + +## numerical results +![animation](./doc/animation.gif) + # Discretization of the non-uniform isotropic heat equation In general, the non-uniform isotropic heat equation is as following @f{align*} @@ -64,17 +70,23 @@ The initial temperature can be interpolated over each vertex as follows, which is robust for general use. In fact, Deal.II provides a function (VectorTools::interpolate) doing the same thing, which is, however, may not necessary work for parallel version. +## Mesh + +![mesh](./doc/mesh-2d.png) + ## Results To simplify the question, the heat equation is solved in two-dimensions (x-y) by assuming that the z-axis is homogeneous. Following is part of the running results in 4-threads: + + Solving problem in 2 space dimensions. - Number of active cells: 6567 - Total number of cells: 6567 - Number of degrees of freedom: 11185 - 9 CG iterations needed to obtain convergence. - initial convergence value = nan - final convergence value = 2.31623e-20 - + Number of active cells: 6567 + Total number of cells: 6567 + Number of degrees of freedom: 11185 + 9 CG iterations needed to obtain convergence. + initial convergence value = nan + final convergence value = 2.31623e-20 + Time step 1 at t=1e-05 time_step = 1e-05 80 CG iterations needed to obtain convergence. initial convergence value = nan @@ -111,12 +123,19 @@ To simplify the question, the heat equation is solved in two-dimensions (x-y) by 80 CG iterations needed to obtain convergence. initial convergence value = nan final convergence value = 1.71207e-13 + -# Numerical results + +## Temperature distribution +![temperatureDis](./doc/temperature-2d.png) + +## 8-threads +![threads](./doc/threads-2d.png) # References + @article{ma2021numerical, title={Numerical study of laser micro-and nano-processing of nanocomposite porous materials}, author={Ma, Hongfeng}, @@ -160,4 +179,4 @@ To simplify the question, the heat equation is solved in two-dimensions (x-y) by organization={Cambridge University Press} } - \ No newline at end of file +