Bartels

A lightweight collection of routines for physics simulation .

External Dependencies

Intel MKL (OPTIONAL) Pardiso (OPTIONAL) OpenMP (OPTIONAL)

Included Submodules (Installed Automatically)

1. Libigl https://github.com/libigl/libigl
2. Eigen >= 3.2 (By Default Bartels uses the libigl Eigen install)

To get started: Clone this repository and all its submodule dependencies using:

git clone --recursive https://github.com/dilevin/Bartels.git

Compilation

Bartels is a header only library but includes some things that need to be compiled for use.

Tests

To compile the included tests do the following:

cd ${BARTELS_SOURCE_DIRECTORY}/tests
mkdir build
cd build
cmake ..
make all

MATLAB Interface

Bartels includes MATLAB wrappers for useful functions. To compile the MATLAB wrappers do the following:

cd ${BARTELS_SOURCE_DIRECTORY}/matlab
mkdir build
cd build
cmake ..
make all

To enable Bartels in MATLAB open MATLAB and issue the following commands:

addpath('${BARTELS_SOURCE_DIRECTORY}/matlab')
addpath('${BARTELS_SOURCE_DIRECTORY}/matlab/mex')
savepath

Here is an example of using Bartels to compute the first 20 deformation modes of a Neo-Hookean bunny:

>> [V,T,F] = readMESH('/Users/dilevin/Documents/Research/Development/bartels/data/meshes_mesh/coarser_bunny.mesh');
>> M = linear_tetmesh_mass_matrix(V,T, 0.1*ones(size(T,1),1), vol);
>> YM = 2e6; %in Pascals
>> pr =  0.45
>> [lambda, mu] = emu_to_lame(YM*ones(size(T,1),1), pr*ones(size(T,1),1));
>>  H = linear_tetmesh_neohookean_dq2(V,T, q, dX, vol, [0.5*mu, 0.5*lambda]);
>> [modes, freq] = eigs(-H, M, 20, 'smallestabs');

NOTE: I use GPToolbox by Alec Jacobson for file I/O (i.e readMESH) and geometry processing.

Conventions

I try to obey some naming conventions when I implement new functions in Bartels which makes it, in some sense, self documenting. Below are some of these conventions:

• Finite element methods are prefaced by element type i.e linear_tet_.... indicates this method applies to a single tetrahedral element with linear shape functions.

• There are seperate methods which apply per element functions to an entire computational mesh. These take the form i.e. linear_tetmesh_...

• q refers to the degrees of freedom of a mechanical system, no matter what they are. For FEM they are the vertices of the simulation mesh

• F refers to the deformation gradient at point in space

• psi refers to a potential energy function for a constitutive model

• phi referes to shape functions

• lower case d is used to represent differential operations.

• when taking derivatives with respect to matrix quantities (like F), the matrix quantitiy is flattened to a column vector. *i.e the 3x3 matrix F = [F00 F01 F02; F10 F11 F12; F20 F21 F22] becomes a 9x1 vector [F00 F10 F20 F01 F11 F21 F02 F12 F22]'.

Some examples of putting it all together:

• dpsi_neohookean_dF2 computes the second derivative of the neohookean potential energy, with respect to the deformation gradient.

• linear_tet_dphi_dX computes the derivative of the linear tetrahedron shape functions with respect to the reference space

• linear_tetmesh_dphi_dX computes the above over the entire tetmesh

• linear_tetmesh_neohooken_dq2 computes the sparse Hessian of the neohookean energy over an entire tetmesh

• linear_tetmesh_stvk_dq computes the gradient of the stvk energy over an entire tetmesh

• linear_tetmesh_arap_q computes the energy of the As-Rigid-As-Possible energy over an entire tetmesh

Installation Instructions for Optional Dependencies

OpenMP

Bartels can leverage the OpenMP library for parallelization (though honestly, most functions aren't parallelized yet). On non-OSX computers with an OpenMP compantible compiler, you simply need to call cmake with the bartels_USE_OPENMP option set to on. So, from the build directory:

cmake .. -Dbartels_USE_OPENMP=ON

OpenMP on OSX

IMPORTANT: Requires CMake 3.17 or above

The osx native compiler doesn't support OpenMP by default. Fortunately this support can be added using the Homebrew package manager.

1. Install Homebrew from https://brew.sh
2. Run 'brew install libomp'
3. From the build directory run cmake .. -Dbartels_USE_OPENMP=ON

Pardiso

Bartels now comes with an Eigen wrapper for the open source version of the Pardiso linear systems solver.

To use Pardiso visit the [webpage]((https://pardiso-project.org) and request a license. Once you recieve your license email, download the pardiso library.

1. mkdir ${BARTELS_SOURCE_DIRECTORY}/extern/pardiso
2. Copy libPardiso to ${BARTELS_SOURCE_DIRECTORY}/extern/pardiso
3. Create Pardiso.lic in ${BARTELS_SOURCE_DIRECTORY}/extern/pardiso
4. Paste your license key into Pardiso.lic
5. From ${BARTELS_SOURCE_DIRECTORY}/build run cmake .. -Dbartels_USE_OPENMP=ON -Dbartels_USE_PARDISO=ON

IMPORTANT: Pardiso requires OpenMP

Intel MKL`

Bartels relies on the Eigen library for linear algebra operations. Eigen itself can be accelerated by linking to the Intel Math Kernel Library (MKL). It's available free for academic use. Bartels can be compiled to use MKL to speed up basic linear algebra operations.

1. Download and install the Intel Math Kernel Library (MKL)
2. Set the MKLROOT Environment Variable to the fullpath of the mkl installation directory (on my machine this is /usr/local/opt/intel/compilers_and_libraries_2020.1.216/mac/mkl).
3. From ${BARTELS_SOURCE_DIRECTORY}/build run cmake .. -Dbartels_USE_MKL=ON

IMPORTANT: OpenMP, Pardiso and MKL can all be used together as well by specifying all options as ON.

IMPORTANT 2: MKL is not compatible with MATLAB, if you are building the MATLAB interface, DO NOT turn on MKL.