From: bangerth Date: Sun, 10 Sep 2006 03:59:13 +0000 (+0000) Subject: More on results X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=bd2b21e613688e659514a4d5ed753c2da1008e68;p=dealii-svn.git More on results git-svn-id: https://svn.dealii.org/trunk@13883 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-24/doc/results.dox b/deal.II/examples/step-24/doc/results.dox index c2fdec7dcb..e997942ef4 100644 --- a/deal.II/examples/step-24/doc/results.dox +++ b/deal.II/examples/step-24/doc/results.dox @@ -1,29 +1,51 @@

Results

-The program writes values obtained by the detector to the disk. We then -draw them in plots. Experimental data are also collected for comparision. -Currently our experiments have only been done in two dimenstions by -circually scanning a single detector. We make the sample as a thin slice -in the X-Y plane (Z=0), and assume that signals from other Z directions -won't contribute to image construnction. By such an assumption we -only compare our experimental data with two dimensional simulated data. +The program writes both graphical data for each time step as well as the +values evaluated at each detector location to disk. We then +draw them in plots. Experimental data were also collected for comparison. +Currently our experiments have only been done in two dimensions by +circually scanning a single detector. The tissue sample here is a thin slice +in the X-Y plane (Z=0), and we assume that signals from other Z directions +won't contribute to the data. Consequently, we only have to compare +our experimental data with two dimensional simulated data.

One absorber

-This movie shows the thermoacoustic waves generated by a small absorber +This movie shows the thermoacoustic waves generated by a single small absorber propagating in the medium (in our simulation, we assume the medium is mineral -oil, which has a acoustic speed of 1.437 mm$\mu$s). +oil, which has a acoustic speed of 1.437 $\frac{mm}{\mu s}$): @image html step-24.one_movie.gif -The following two figures show the results obtained by the detector. The left -side figure is obtained through experiments, and the right side figure is the -simulated data. In the experiment, a small strong absorber was embedded in weaker -absorbing tissue, we can still see the signals generated by the weak absoring -tissue, which surrounds the signals generated by the small strong absorber in -the center. In the simulated data, we only simulate the small strong absorber. +For a single absorber, we of course have to change the +InitialValuesP class accordingly. + +Next, let us compare experimental and computational results. The visualization +uses a technique long used in seismology, where the data of each detector is +plotted all in one graph. The way this is done is by offsetting each +detector's signal a bit compared to the previous one. For example, here is a +plot of the first four detectors (from bottom to top, with time in +microseconds running from left to right) using the source setup used in the +program, to make things a bit more interesting compared to the present case of +only a single source: + +@image html step-24.traces.png + +One thing that can be seen, for example, is that the arrival of the second and +fourth signals shifts to earlier times for greater detector numbers (i.e. the +topmost ones), but not the first and the third; this can be interpreted to +mean that the origin of these signals must be closer to the latter detectors +than to the former ones. + +If we stack not only 4, but all 160 detectors in one graph, the individual +lines blur, but where they run together they create a pattern of darker or +lighter grayscales. The following two figures show the results obtained at +the detector locations stacked in that way. The left figure is obtained from +experiments, and the right is the simulated data. +In the experiment, a single small strong absorber was embedded in +weaker absorbing tissue: @@ -36,30 +58,39 @@ the center. In the simulated data, we only simulate the small strong absorber.
-In real situation, the detector has limited bandwidth. The thermoacoustic waves -passing through the detector will be filtered. By using a high-pass filter, -the simulated results look closer to the experimenal data. This is being done -in MATLAB. +It is obvious that the source location is closer to the detectors at angle +$180^\circ$. All the other signals that can be seen in the experimental data +result from the fact that there are weak absorbers also in the rest of the +tissue, which surrounds the signals generated by the small strong absorber in +the center. On the other hand, in the simulated data, we only simulate the +small strong absorber. + +In reality, detectors have limited bandwidth. The thermoacoustic waves passing +through the detector will therefore be filtered. By using a high-pass filter +(implemented in MATLAB and run against the data file produced by this program), +the simulated results can be made to look closer to the experimental +data: @image html step-24.one_sf.png -Because the mesh mismatch in the coarse mesh used in above the simulation, -we observe that waves are reflected before they travel to the boundary. -The problem can be alleviated by using finer mesh. This result is not filtered. +In our simulations, we see spurious signals behind the main wave that +result from numerical artifacts. This problem can be alleviated by using finer +mesh, resulting in the following plot: @image html step-24.one_s2.png +

Multiple absorbers

-We have done the simulation for one small absrober. To further verify the program, -we will shown the simulation results for multiple absorbers. +To further verify the program, we will also show simulation results for +multiple absorbers. This corresponds to the case that is actually implemented +in the program. The following movie shows the propagation of the generated +thermoacoustic waves in the medium by multiple absorbers: -First we will use a movie to show the propagation of the generated thermoacoustic -waves in the medium by multiple absorbers: @image html step-24.multi_movie.gif -Then the experimental data and our simulated data are compared in the following two +Experimental data and our simulated data are compared in the following two figures: @@ -71,18 +102,22 @@ figures:
-The data points in experimental data are about eight times more than that in the -simulated data. In order to get similiar results as in the experiment, we need finer -mesh and smaller time step in the simulation. - -Same as for the one absorber case, by using a high-pass filter, we get the following -results: - -@image html step-24.multi_sf.png -By using finer mesh, we obtain better simulated results. The results shown is not filtered. +As before, the numerical result better matches experimental ones by applying a +bandwidth filter that matches the actual behavior of detectors (left) and by +choosing a finer mesh (right): + + + + + +
+@image html step-24.multi_sf.png + @image html step-24.multi_s2.png +
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