Polyquad

About

Polyquad is an open-source C++ application for finding symmetric quadrature rules suitable for use with the finite element method. Both the target strength of the quadrature and the number of points are configurable. Polyquad is parallelised using MPI and can refine rules to an arbitrary degree of numerical precision.

Authors

See the AUTHORS file.

License

Polyquad is release under the GNU GPL v3.0 license. Please see COPYING for further details.

Dependencies

In order to build polyquad it is necessary to have first installed:

• CMake 2.8;
• Eigen, preferably the current head revision;
• Boost, specifically
• mpi (optional)
• multiprecision
• program_options
• serialization

If Boost MPI and a suitable compiler are found then polyquad will be able to run on clusters. As polyquad makes use of advanced template metaprogramming features it is important to build it using a compiler that supports the C++17 standard. As of the time of writing the following compilers are known to have successfully built polyquad:

• GCC 9.2;
• Clang 8.

Building polyquad can require in excess of four gigabytes of main memory and several minutes of CPU time.

Building polyquad

After cloning the repository polyquad can be built by issuing the following commands:

$ mkdir build
$ cd build
$ cmake -G"Unix Makefiles" ../
$ make

for further information please consult the CMake documentation and the CMakeLists.txt file.

Running polyquad

Usage instructions can be obtained by running:

$ ./polyquad --help

a simple example we consider using polyquad to search for strength 5 rules inside of a tetrahedron using 15 points:

$ ./polyquad find -s tet -q5 -n15 -V -p > rules.txt

where -V enables verbose output and -p requires all rules to have positive weights. We can then convert the rules from the internal representation used by polyquad to a standard tabular format by issuing:

$ ./polyquad expand -s tet -q5 < rules.txt > rules-tab.txt