Summary

This application (based on MFEM's Volta miniapp https://mfem.org/electromagnetics/), solves the electrostatic problem for a substrate that includes an array of ellipsoidal inclusions with a different permittivity. The boundary conditions for this problem are consistent with a uniform background Electric field in the z direction of the coordinate axes.

Build Instructions

• Edit config.sh and provide installation path for MFEM_INSTALL_PATH(location of the MFEM installation), HYPRE_DIR (location of Hypre installation) and METIS_DIR (location of Metis installation)
• mkdir build
• cd build
• source ../config.sh
• make

If things run successfully there should be an executable named inclusion in your build folder.

Note for SCOREC users. All the necessary modules to build this example can be loaded by calling source ../env-setup-scorec.sh, and scorec_config.sh config file is customized for SCOREC.

Note both the build for this example and the build of MFEM have to use consistent dependencies (e.g. the same Hypre, Metis, etc) to avoid build problems.

Example environment and config for build with CUDA enabled in MFEM and Omega_h

environment (SCOREC RHEL7)

module use /opt/scorec/spack/v0132/lmod/linux-rhel7-x86_64/Core
module load gcc mpich cmake hypre parmetis cuda/10.2 

pmetis=${PARMETIS_ROOT}
export CMAKE_PREFIX_PATH=$CMAKE_PREFIX_PATH:$pmetis

export HYPRE_DIR=$HYPRE_ROOT
unset HYPRE_ROOT
export METIS_DIR=$METIS_ROOT
unset METIS_ROOT
export ZLIB_DIR=$ZLIB_ROOT
unset ZLIB_ROOT 

export MPICH_CXX=g++
export CMAKE_PREFIX_PATH=$CMAKE_PREFIX_PATH:/path/to/omegah/install

config.sh

export MFEM_INSTALL_PATH=/path/to/mfem/install/
flags="-g -O0"
cmake $1 \
  -DCMAKE_BUILD_TYPE=Debug \
  -DMFEM_PREFIX=$MFEM_INSTALL_PATH \
  -DCMAKE_VERBOSE_MAKEFILE:BOOL=OFF \
  -DCMAKE_INSTALL_PREFIX:PATH=$PWD/install \
  -DCMAKE_CXX_COMPILER=mpicxx \
  -DCMAKE_CXX_FLAGS="${flags}" \
  -DCMAKE_EXE_LINKER_FLAGS="-lpthread ${flags}" \
  -DINCLUSION_SOLVER_CUDA_ARCH=75

Example Meshes

You can find two example meshes in the folder ./meshes. The first one setup_1x1_global_coarse_template_mesh.mesh has only 1 ellipsoidal inclusion in the substrate. The second one setup_5x5_global_coarse_template_mesh.mesh has a 5by5 array of identical ellipsoidal inclusions in the substrate. Both of these meshes have appropriate classification information.

Running Cases

You can use the executable inclusion as follows:

mpirun -np nnn ./inclusion --mesh path_to_mesh --substrate 'substrate-model-tag-list' --inclusion 'inclusion-model-tag-list' -dbcs 'drichlet-bc-model-tag-list'

• substrate-model-tag-list: space separated list of integers (tags) for the model regions making up the phase 1 or substrate
• inclusion-model-tag-list: space separated list of integers (tags) for the model regions making up the phase 2 or inclusions
• drichlet-bc-model-tag-list: space separated list of integers (tags) for the model faces that needs to be included in the Dirichlet bc.

Specifically for the two meshes provided with this example the command to run looks like

mpirun -np 4 ./inclusion --mesh ../meshes/setup_1x1_global_coarse_template_mesh.mesh --substrate '92' --inclusion '186' -dbcs '24 42 76 78 80 82'

mpirun -np 4 ./inclusion --mesh ../meshes/setup_5x5_global_coarse_template_mesh.mesh --substrate '92' --inclusion '2590 2435 4321 2282 714 2757 875 2918 3862 1823 4494 3711 4184 2145 4031 1992 1366 3409 1527 3570 1060 3103 1221 3264 1696' -dbcs '24 42 76 78 80 82'