Figure 1. Task control group in the TC program launcher.

Figure 1 shows the new Task control group in the TC program launcher. The CREATE TASK button calls up the dialog of Figure 2. The user supplies a file prefix FPREFIX that indicates the function of the Task. The Task information will be stored in a DOS batch file FPREFIX.BAT created in the current TC data directory. Commands in the file are compatible with all recent Windows versions including Windows 7.

Figure 2. Create task dialog

Each row represents an operation (batch file command). The first column defines the action. Clicking on a cell brings up a menu that includes all TriComp programs capable of background operation that are installed on the user’s computer. In addition, several relatively safe DOS commands are included (ERASE, COPY, MOVE, RENAME and REM). All commands operate on a file (FILEIN). The DOS commands COPY, MOVE and RENAME require a second file name (FILEOUT). You can type file names in the cells. By default, the files are in the TC working directory, but you can include path information if the files are in other directories. Alternatively, you can click in a cell and pick the SELECT FILE command to raise the standard Windows dialog for choosing files anywhere on the computer. There is a nice feature for the TriComp programs — only files with appropriate suffixes are displayed (e.g., *.EIN or *.SCR for EStat).

Click the OK button when the sequence is complete to create the batch file. Here is an example:

REM TriComp batch file, Field Precision
START /B /WAIT C:\fieldp\tricomp\mesh64.exe C:\Temp\convergegun
START /B /WAIT C:\fieldp\tricomp\estat64.exe C:\Temp\convergegun
START /B /WAIT C:\fieldp\tricomp\trak64.exe C:\Temp\convergegun
ERASE *.?ls
START /B /WAIT C:\fieldp\tricomp\notify.exe
IF EXIST Electrode01.ACTIVE ERASE Electrode01.ACTIVE

The operations listed perform a complete Trak calculation in the background and then erase all listing files. Here are some notable features:

• The operations are performed sequentially because data from one operation may be used in the next. To run calculations in parallel, define and run multiple Tasks.
• You can modify the file with an editor if you are familiar with DOS commands.
• The DOS commands recognize the standard wildcard conventions (* for any character grouping, ? for any character).
• The programs adds the command notify.exe to the task sequence if AUDIO ALARM is checked. In this case, the computer beeps when a task is completed.
• The final command to erase a file FPREFIX.ACTIVE is added to all batch files. The presence of an activate file indicates that the task is running.

Figure 3. Run task dialog

Click the RUN TASK button when you have created Tasks or moved predefined task files to the data directory. The dialog (Figure 3) organizes tasks into two groups: ones that are available to run and ones that are currently running (i.e., FPREFIX.ACTIVE has been detected). To launch a task, choose one from the top list and click OK. The program creates a file FPREFIX.ACTIVE and runs the batch file. The program sequence runs silently in the background and the results appear almost magically. In the meantime, you can prepare other inputs or run other tasks.

This year, we’re concentrating on program features to improve the user experience. We have two goals: 1) increase the computation speed and efficiency and 2) reduce the setup times. Clearly, users should worry less about program details so they can concentrate on physic issues. Our next job is to add macro capabilities to the 2D and 3D postprocessors. With this feature, the programs will remember the steps in a session to create an analysis script.

For the design of other diagnostics, the researchers wanted the spatial distribution of the X-ray flux emitted from the target. Such plots could be created using the GenDist utility program from information in the GamBet escape file. The escape file is a record of parameters for all particles leaving the solution volume. GenDist is a general-purpose program to create and to analyze large distributions of particles (e.g., electrons, ions, photons, positrons). For the application, the procedure was to load the escape file into GenDist and then to add filters that admit only photons at the exit face (i.e., z coordinate great than or equal to the exit face position). Of the GenDist plot types, the 2D histogram was appropriate for the application. Here, particles are assigned to a 2D matrix of bins according to their position in the x-y plane. The probability function N(x,y) may be weighted by the model particle current, energy or combined current/energy. In this way, the program can generate spatial distributions of the following quantities:

• Model particle density.
• Particle flux (weighted by model-particle current or flux).
• Power flux (weighted by model-particle current and kinetic energy).

The previous version of GenDist had only one available style for 2D histograms —  a projected 3D view showing N(x,y) as height above the x-y plane. Although the style gave attractive plots for presentations, it was not useful for quantitative work. We added the three new styles shown in the figure for better display of spatial particle distributions:

• The existing 3D bin height plot improved with color coding.
• A 3D plot with bin height displayed as an interpolated shape.
• A 2D contour line plot, showing surfaces of equal probability density.
• A 2D filled contour plot.

b) 3D plot with bin height display as an interpolated shape.
3) 2D contour line plot, showing surfaces of equal probability density.
4) 2D filled contour plot.

Figure 1. Outline generation utility in Geometer

I’ll start with a review of the old procedure for extrusions. The basic principle in MetaMesh is to define basic parts (i.e., set model types and dimensions) in a reference workbench space and then to move them to the model space by SHIFT and ROTATE operations. In the old convention, an extrusion extended along z in the workbench space with its cross-section outline defined in the x-y plane. The outline consists of a set of line and arc vectors that form a closed shape. The outline editor of Geometer (a full-featured 2D CAD utility shown in Fig. 1) is a convenient way to create vector sets. Once created, an outline may be used to define multiple extrusions at different positions or orientation by adding SHIFT or ROTATE parameters. An extrusion using the outline of Fig. 1 has the following TYPE form in the MetaMesh script:

Type Extrusion
  L    5.2912 -1.000 7.500 -1.000 S
  L    7.5000 -1.000 7.500  1.000 S
  L    7.5000  1.000 5.291  1.000 S
  A    5.2912  1.000 3.000  2.500  3.000  0.000 S
  A    3.0000  2.500 0.500  0.000  3.000  0.000 S
  A    0.5000  0.000 3.000 -2.500  3.000  0.000 S
  A    3.0000 -2.500 5.291 -1.000  3.000  0.000 S
End

The data lines contain the x-y coordinates of the start and end points of lines and the start-end-center points of arcs.

Because the outline may specified at absolute positions in the x-y plane, it is easy to create desired extrusions that point along z. In most cases, SHIFT and ROTATE operations are unnecessary The problem arises if you want extrusions that extend along x or y. It is not immediately obvious to most people (myself included) how the x-y coordinates of Fig. 1 map to y-z or z-x coordinates when 90° rotations are applied about different axes. Positioning x or y extrusions often requires considerable experimentation in Geometer.

Figure 2. Add/Edit part dialog in Geometer

We have modified both Geometer and MetaMesh so that you can directly define extrusions along x and y. For extrusions along x, the outline coordinates are interpreted as absolute values in the y-z plane. For an extrusion along y, the outline data gives z-x values. It is easy to apply the feature. Figure 2 shows the modified Add/Edit part dialog in Geometer. The red arrow shows new radio buttons that are active only when the part type is set to EXTRUSION. The choice of extrusion axis determines how the path coordinates are interpreted. In the MetaMesh script, the TYPE command has a modified form:

Type Extrusion [X,Y,Z]

Some usage notes:

• If no direction option appears in the TYPE EXTRUSION command, the default is Z. Therefore, existing scripts are interpreted correctly.
• The new capabilities affect the extrusion shape and direction in the workbench frame. SHIFT and ROTATION operations may still be applied in the transfer to the assembly frame.
• The same outline may be used in Geometer for multiple extrusion parts with different extrusion directions. Figure 3 shows an example.

Figure 3. Multiple extrusions with different directions from the same outline

In reviewing the application, it occurred to me that there was a much easier approach to model such a structure, based on technology that we had already incorporated in the two-dimensional Mesh program. The idea is to assign elements in a plane to regions according to values in a photographic image. The advantages are easy setup and high reliability. In this article, I will describe new MetaMesh capabilities for analyzing photographs and illustrate them with an example of a layer in a printed circuit.

Figure 1. Sample printed circuit, PNG format.

Figure 1 is a photograph of the test geometry. The image has only two colors — white represents thin conductors. In the benchmark example, conductors (Region 2) are mapped to a 1.0 mm layer in a uniform solution volume (air, Region 1). The first step is to set the interpretation of photographs. The following entries appear in the GLOBAL section of the MetaMesh script:

INTERVALS  Lightness
  50.0  100.0  2
END

The construct states that photographs will be interpreted in terms of lightness values (0.0 to 100.0 percent). Lighter areas will be assigned to Region 2. An INTERVAL section may contain up to 250 data lines — in this case, only one interval is needed. Alternatively, assignment may be via hue values (0.0 to 360.0 degrees) in the image.

Parts are basic building blocks in MetaMesh. The concept is flexible — parts range from simple geometric solids to complex STL shapes. We have added a new PHOTO part type. The following section defines a photo part in the example:

PART
  Type Photo PC01.PNG 0.00  0.00  50.00  50.00
  Name PC
  Fab 1.00
END

In the workbench frame, the photograph image is mapped into an x-y plane centered at z = 0.0 with thickness Δz set by the fabrication parameter. The resulting solid can be moved to any position or orientation with optional SHIFT and ROTATE commands. In the example, the photographic image is contain in the file PC01.PNG. (MetaMesh also handles BMP and PCX formats.) The information is mapped to an area with spatial dimensions xmin = 0.0, ymin = 0.0, xmax = 50.0 and ymax = 50.0, independent of the image pixel dimensions. Figure 2 shows the resulting mesh in the slice plane z = 0.0, while Figure 3 shows a three view with perspective. The entire structure was created with the two simple statements listed above.

Figure 2. MetaMesh screen shot, slice in the plane z = 0.0.

Figure 3. Three dimensional view, printed-circuit example.

Photographic analysis is a powerful new feature of MetaMesh. It greatly simplifies the representation of multi-layer printed circuits and striplines for electromagnetic analysis. Complex printed-circuit assemblies can be built in two steps:

1. Set up a foundation mesh with element layers of the appropriate thicknesses.
2. Use photographic layouts to set conductors or dielectrics in each layer. If there are different components in a single layer, they can be represented with different colors in the photograph.

The photographic method has unlimited applications. Information from up to 250 photographs may be included in a MetaMesh script. The technique applies to any three-dimensional structure with photographic slice data, such as MRI scans.

Program: TriComp
PlotStyle: Spatial
Outline: ON
Grid: ON
Scientific: OFF
FixedPoint: OFF
Vectors: OFF
XGMin:  3.500000E+00
XGMax:  9.000001E+00
...

The file contains all necessary parameters to reconstruct spatial plots (in the z-r or x-y planes). The file includes the following information for spatial plots:

• Style information, like whether to display a reference grid, element outlines or field vectors.
• Boundaries of zoomed views
• The plot type (e.g., mesh, filled contour, contour lines,…)
• The plotted quantity.

You can also save information to reconstruct scan plots:

• Style information (number of scan points, symbol display,…)
• Coordinates of the scan start and end Limits of the scan.
• Plotted quantity.

Spatial versus scan plots in TriComp programs

The simplest application of saved views is to restore a complex plot when you reload the solution at a later time. We have included several features in our implementation to enable a higher level of data analysis:

• A saved view works even if a completely different solution than one use to create the view in loaded. In fact, views can be reloaded even if the user is running a different TriComp program. The current program analyzes the parameters and uses only ones that are relevant. For example, if a view-boundary or scan point is outside the current solution volume, the point is moved to the boundary. If a plot quantity is undefined, the first valid quantity  is used.
• A free-form parser is employed when a view is loaded. Therefore, a file need not contain a complete set of parameters. Changes are made only to the quantities listed in the file.
• Users can modify entries in the view file, either directly with an editor or via a Perl or Python script. You can include comments, change parameter values or remove parameter lines.

Another important feature is related to the fact that analysis functions of all TriComp postprocessors may be controlled by a text script. We have added the following  script command:

PLOT FSaveView FOutput Nx Ny
PLOT (DiodeRegion VIEW001 800 600)

The string FSaveView is the prefix of a saved view file. The string FOutput is the prefix of a plot file in BMP format. The integer parameters give the image resolution in pixels. In response to the command, the program loads the saved view file, applies the parameters to create a plot for the currently-loaded solution and saves it as a graphics file.

Here are some possible scenarios:

• You have a set of electric field solutions with different applied voltage and possibly different boundaries and you want to check electric field levels in a critical region (e.g., an electron source). Use the Zoom command to create the desired plot and save a view file. Remove all information lines except the view boundaries and load the view when you load a different solution.
• You have a set of magnetic field solutions and want precision plots of field lines passing through specific points. Add a field line interactively in PerMag and save a template view file. Then edit the view file to remove unnecessary information, change the number of field lines and add coordinates for the desired points.
• You want to create a large set of radial temperature scans moving along the axis of a probe assembly. In TDiff, create a template view file for one scan. Write a Python or Perl script with a loop of axial positions that modifies the axial scan coordinates in the view file and then runs TDiff in the analysis mode. The set of BMP files could then be stitched into an AVI movie with our Cecil_B utility.
• A sequence of annotated view files could be employed in a training session or educational demonstration.
• You want to show how the levels of magnetic flux induction change with changing coil currents, preserving magnitude scaling in the plots. After creating a set of solutions, load one of them adjust the view, plot style and plot quantity. Turn off autoscaling, specify values for BMin and BMax and then save a view file. Load the view for the other solutions.

To review, interaction forcing is used in GamBet to improve statistics for low-probability events like photon-production via bremsstrahlung or pair production. In the Penelope routines, the probability of an event is increased by Fb, but the weight of secondary particles (and their descendants) is decreased by 1/Fb. If you use Fb = 100 to find a bremsstrahlung spectrum, the variance between bins is decreased by about a factor of 10. At the same time, the run time should be significantly less than Fb times the run time with no forcing.

The user’s example involved a 16 MeV electron beam striking a 6 mm thick sheet of tantalum. To understand the effect of forcing factor on the validity of results, I made a series of runs with different values of Fb. The first plot shows the global energy balance as a function of Fb. Here, GamBet sums energy lost from primary and secondary particles to the escape file and to absorption in the solution volume. The code compares this value to the input energy of primaries. The plot shows that conservation of energy holds to within a few percent up to Fb = 100. An abrupt change occurs near Fb = 150 — energy conservation is lost at higher values. The second plot shows the run time versus Fb. It increases linearly (as expected) up to around Fb = 150 and then saturates.

Energy error as a function of forcing factor

I identified the cause of the problem as overflow of the Penelope secondary-particle stack. In a shower calculation, Penelope tracks a primary particle and stores the parameters of secondaries on the stack. Then it pops each secondary from the stack and tracks it. In the process, additional secondaries may be pushed on the stack. Tracking continues until the stack is empty, and then the code proceeds to the next primary. The Penelope routines do not halt program operation when an overflow occurs because there may be rare showers with a large number of secondaries. Rather, Penelope ignores extra secondaries leading to unaccounted energy. Application of a forcing factor increases the number of entries per shower to store on the stack by about a factor of Fb. Therefore, a value Fb = 1000 could clearly lead to trouble. I confirmed the hypothesis by increasing the stack size from 2000 to 5000 entries. In this case, energy was conserved to Fb = 200.

Run time as a function of forcing factor

To reduce the chance of errors in future user calculations, I made some changes in GamBet:

1. I increased the secondary stack size to 5000. The larger static array increases the code RAM utilization by only about 10 MB.
2. I added cautionary material to the section on the FORCE command in the GamBet reference manual.
3. I modified GamBet to count the number of instances of stack overflow. If the value exceeds zero, the code writes a warning in the listing file (GLS).

Finally, we can gauge the utility of interaction forcing from low-Fb entries in the second plot. The run time was 5 seconds for Fb = 1. It increased to 103 seconds with Fb = 100. To get the same statistics for the bremsstrahlung spectrum with Fb = 1, we would need to increase the number of showers by a factor of 100, giving a run time of about 500 seconds. In this case, interaction forcing reduces the run time to achieve a given statistical accuracy by about a factor of 5.

We recently released GamBet 3.0 with support for parallel processing. We anticipate that users will set up large production runs with a high number of showers for improved statistics.  The corresponding larger escape files would take longer to load in GenDist. In extensive calculations to study rare events, the bulk of the particles recorded in the escape would not be of interest.

To increase efficiency, we added the option for escape particle filtering in GamBet 3.0. Filters may be applied to limit particles recorded in the escape file by species, exit position and kinetic energy. The procedure to define a filter is relatively easy. There is a new command of the form

ESCAPEFILTER Condition1 Condition2 Condition3 ...

A condition is short string with no delimiters. Multiple conditions are separated by spaces. Any number of conditions may be included in the line. The following conditions determine the included particle types:

ElecP  PhotP  PosiP  ElecS  PhotS  PosiS

Here the letters P and S designate primary and secondary. If the EscapeFilter command appears, the initial condition is that no particle species passes the filter. If one or more of the conditions appears, only the specified types are included. For example, this command includes only secondary electrons and photons:

ESCAPEFILTER ElecS PhotS

The following expression types define pass conditions for particles according to their exit positions:

  X>10.56  Y<1.0E-8  Z>15  R>30.5, ....

The conditions begin with a character to define the coordinate axis: X, Y, Z or R. The quantity R is given by R^2 = X^2 + Y^2. Position conditions act differently from species conditions. In the absence of a condition, all particles pass the filter. The expression Z>33.5 means that 1) only particles with final z coordinate greater than 33.5 are included and 2) particles with all values of x and y are included. As an example, the command

ESCAPEFILTER X>0.0 Y>0.0

passes only particles that exit in the first quadrant of the x-y plane. In this case, no filtering is applied in z. Finally, conditions of the form

T<5.0E6, T>1500,....

pass particles according to their kinetic energy. To illustrate a complex filter, consider a 500 keV photon beam passing through a slab of material with Zmax = 60.0 mm. To calculate the attenuation coefficient, we want to find the number of full-energy, primary photons that emerge from the exit face. The appropriate filter command is:

ESCAPEFILTER PhotP T>4.999E5 Z>59.999

• Definition of 3D geometries in an interactive graphical-user-interface with the option for import from SolidWorks.
• Dose records on conformal 3D meshes for accuracy
• Option to add 3D electric and magnetic fields from HiPhi and Magnum
• Import of electron distributions from Trak and OmniTrak.
• Export deposited energy for thermal calculations in TDiff and HeatWave.

In a conversation with a friend who is power-user of GamBet, he stated that these features were nice but that all he cared about was speed and accuracy. Thanks to that bracing insight, we decided to proceed with a long-planned upgrade of the GamBet numerical engine. We addressed the accuracy issue by upgrading the collision physics engine to the latest version of Penelope, one of the highest-rated package for X-ray science (for a review, see the reference M.Vilches, et.al., Monte Carlo simulation of the electron transport through thin slabs: A comparative study of penelope, geant3, geant4, egsnrc and mcnpx (Nucl. Instrum. and Methods 254, 219, 2007) available at this link:  http://arxiv.org/pdf/physics/0612044). The expanded database supports particle interactions as low as 50 eV.

Parallel processing is clearly the key to the speed issue. Our emphasis is on Windows-based computers with multiple processors or multi-core chips — a shared memory architecture. Accordingly, we have integrated OpenMP in our field solution programs (HiPhi, Magnum, …). In these programs, the matrix-inversion process that occupies the bulk of the computing time is relative easy to parallelize. Threads work on separated parts of the matrix so there is no problem with conflicts. Although at first glance a Monte Carlo code would seem to be a good candidates for parallel operation, there were potential thread conflicts in GamBet:

• Primary and secondary particles update deposited dose on a single conformal mesh. Because of the complexity of trajectories, it would be impossible to ensure that particles from simultaneous showers are not in the same cell.
• Penelope is not written for parallel operation, and there are potential shared resource like the secondary stack. I felt it would be foolhardy to make fundamental changes to the structure of the package.

For these reasons, we decided to take a distributed memory approach with GamBet. In this case, multiple instances of the program with independent storage run in individual threads controlled by the operating system. The resulting data files are combined at the end to a single representation with improved statistics. This approach is easily-implemented in modern Windows computers where the standard memory is 4 GB or more. The additional advantage is that GamBet can easily be adapted to large cluster computers. We would be interested in working with researchers running such machines.

As a reference for users of GamBet 3.0, here is how we have implemented parallel operation:

1) Parallel operation is initiated with the new command

PARALLEL NProc [NWait]

in the PROCESS section of the input script. The integer parameter NProc is the number of threads to initiate, less than or equal to the maximum number of threads on the Windows machine. For a Core i7 processor, the maximum value is 8. The parameter NWait is the maximum number of seconds to wait for a child process to complete before going on to the next one.

2) The primary process is handled by the program gambet.exe, which may be run in an interactive window or in the background under batch file control. In the absence of the PARALLEL command, the program runs serially as before. If the command is present, the primary process creates a common Penelope material input file and then initiates (NProc-1) instances of the program gambetmp.exe. This program is a background version of gambet.exe that sends start and end signals. The control program sends the following information in the command line: the script prefix FPREFIX and a process number in the range 1 <= NP <= (NProc-1).

3) There are shared input resources that could cause conflicts (e.g., the control script, the Penelope material file and the geometry mesh). A child process reads the information, closes the files and then sends a start signal (i.e., creates a file with a name FPREFIX01.START, FPREFIX02.START,…). The control program waits until the start signal is detected before starting the next child process.

4) When all child processes are running, the control program proceeds with its own calculation, issuing standard screen messages.

5) When the calculation is complete, the control program checks that all child processes have sent an end signal (i.e., created a file with a name FPREFIX01.END, FPREFIX02.END,…). The program waits a maximum of NWait seconds for each process before going on to the next.

6) The data of the primary process and successful child processes are combined. Start and end signals and unnecessary files are deleted.

The following type of data combination are performed:

• The primary process and each child process creates an escape file listing parameters of particles that escape from the solution volume. Data lines from the child files are appended to the primary escape file.
• Data from all 2D or 3D dose files are read, averaged and written to the primary dose file. For an 8-thread machine, random statistical variations are reduced by a factor of about 2.83.
• Statistical, flux and energy conservation quantities in the listing file are read, average and recorded in the primary listing file. Other information is unchanged.

Here are some concluding notes on parallel operation:

• Although the input and output operations are involved, everything is handled by the code. The user need only include the PARALLEL command in the control script.
• The serial input and data combination operations take only a few seconds. Therefore, a quad-core computer can handle four times the number of showers in almost the same time as a serial run.
• GamBet can generate plots of sample electron, photon and positron orbits. To avoid monster files, generation of such data is best done in a serial run. Therefore, the PLOTON command is deactivated in a parallel run.
• The programs gambet.exe and gambetmp.exe have been modified to ensure that there is a unique random number seed for the primary process and each child process. Otherwise, each process would generate identical information that would be summed and then divided by NProc. Without a unique seed, there would be no point to a parallel run.

Usage history for a six-thread run

Creating a movie in AVI format is easy and takes just a few minutes. Here’s how it works:

1) Add the MOVIE command to a working input script. The command has the format

MOVIE NFrames  [NH  NV  QMin  QMax]
MOVIE 100 640 480 0.0 100.0

The integer quantity NFrames is the approximate number of frames. I say approximate because TDiff and Pulse employ a variable time step. In this case, the code does its best to create NFrames plot files at equal time intervals. The integer quantities NH and NV are the number of horizontal and vertical pixels in the output graphics files. The default is 1024 × 768. I picked 640 × 480 for the example included for a good display on the Internet.

2) Run the simulation. The new feature is compatible with solution display, so you can monitor the plots during the run. The program generates approximately NFrames files in BMP format, at an interval oTMax/NFrames starting at t = 0. If the input script has the name FPrefix.TIN, the graphics files have names FPrefix000.BMP, FPrefix001.BMP, ….

3) Run our free movie-generation program CECIL_B, available at http://www.fieldp.com/cecil_b.html. Navigate to the directory that contains the BMP images and point to any file in the set. CECIL_B automatically orders the files and combines them into an AVI movie. The program uses defaults or the frames/second and codec of your choice.

The following example was created with TDiff in the dynamic mode. The run generated about 100 frames. They are projected at 10 frames/second.