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Wraps the fastlap BEM (boundary element method aka BIE boundary integral equations) + FMM (fast multipole method) + Laplace kernel implementation from http://www.rle.mit.edu/cpg/research_codes.htm The original code is in doc/fastlap_fl-2.0-22oct96 for reference.

03/2019 Wance Wang

Create a python environment "ele36" for bem package:

$ conda create -n ele36 python=3.6 $ conda install -n ele36 jupyter scipy matplotlib cython cvxopt apptools envisage $ source activate ele36 $ pip install mayavi

Or you can reproduce my environment by using file ele36pip_2019.yml.

$ conda env create -f ele36pip_2019.yml $ source activate ele36

For building fastlap and triangle C extensions:

$ python setup.py build_ext --inplace

(When you want to rebuild it, add a --force option.)

• The revised workflow for 3D electrostatics is currently in the "big_rewrite" branch in svn. It may move to trunk later.
• Most of the bugs and problems mentioned in "BEM software -Development" on the wiki are solved.
• The old .cpx "init" style configuration file is gone. Replaced with Python code. More flexible, less coding overhead when implementing new features. Compare the old cpx with the new python example.
• The input geometry is not the inventor-meshed .cpy file anymore but the face loops .ele or .trap or inventor exported .stl. You need to re-export your files or write a cpy-to-trap convertor (should not be too difficult).
• The meshing is now done preferably with Jonathan Shewchuk's triangle code. It is integrated into the Python package and compiled into a python module, see triangle and pytriangle.pyx
• The Fastlap code is also integrated and compiled into a python module (see fastlap/ and fastlap.pyx and called directly without exporting and importing intermediate file formats.
• The meshing can be adaptive: for a given potential configuration, the charge distribution for a small initial mesh is solved and the mesh is refined such that each triangle in the final mesh contributes equally to the field at the observation point (since the triangles are also constrained by the geometry, min angle etc, the final number of triangles is typically larger than the desired one).
• Triangle areas can also be constrained via differently shaped constraint fields (Box, Sphere, Cylinder or BYO).

Ryan Bowler, 2014

If you wish to generate your own STL for the SimpleTrap, there are some important features. The code scales the trap as if it is in units if microns, so when exporting to STL in Inventor, be sure to choose microns for the Units. There are no curved surfaces, so Surface and Normal deviations are not important. Set max edge length to something reasonable or else triangles are too small or large (40 microns, the ion height from the surface, is a good choice). Choose a low aspect ratio and make sure to export the colors.

Old notes regarding multipole expansion and jumps in potentials/fields:

The 'slfcc - Precise.exe' version is meant to solve the following problem. It can happen that the center of your trapping region is right on the boundary between two "cells" of the tree structure built by FastLap for the multipole-accelerated algorithm. In this case the calculated potentials and fields will show tiny "jumps" in their values when going across this boundary. This has usually no noticeable effect on potentials, but can be noticeable on the field and hence pseudopotential.

One way to solve this problem is to add dummy electrodes on the side of your real electrodes, so that the spatial structure of the tree is shifted a bit. This would displace the cell boundary out of the center of your trap.

The other way is using 'slfcc - Precise.exe', which skips the multipole acceleration procedure when calculating potentials and fields. In other words, it does an exact calculation based on the solved charge distribution, without using any tree structure. This increases the computing time and memory requirements, but yields a slightly more precise result. Note that the charge solving part of the algorithm is not modified (= it uses multipole acceleration, with a depth set in script 'runBEM.py').

-> In the new python code this is achieved by passing "num_lev=1" to Job.simulate().

The cpx&cpy.reg file assumes a root directory C:BEMcode The vtk.reg file assumes a directory C:Program FilesParaView ExamplesTesSphere_1mm 1mm tessellated sphere ExamplesSimpleTrap Simple Signe style trap ExamplesSkull trap Skull trap outline to test Inventor import macros