.ci/install-for-firedrake.sh

+sudo chmod -R a+rwX /github/home || true
+sudo chmod -R a+rwX /__w || true
+
+sudo apt update
+sudo apt upgrade -y
+sudo apt install time
+
+. "/root/myvenv/bin/activate"
+grep -v loopy requirements.txt > /tmp/myreq.txt
+
+# no need for these in the Firedrake tests
+sed -i "/boxtree/ d" /tmp/myreq.txt
+sed -i "/sumpy/ d" /tmp/myreq.txt
+sed -i "/pytential/ d" /tmp/myreq.txt
+sed -i "/pyopencl/ d" /tmp/myreq.txt
+
+# This shouldn't be necessary, but...
+# https://github.com/inducer/meshmode/pull/48#issuecomment-687519451
+pip install pybind11
+pip install pytest
+pip install -r /tmp/myreq.txt
+pip install pyopencl[pocl]
+
+# Context: https://github.com/OP2/PyOP2/pull/605
+python -m pip install --force-reinstall git+https://github.com/inducer/pytools.git
+
+# bring in up-to-date loopy
+pip uninstall -y loopy
+pip install "git+https://github.com/inducer/loopy.git#egg=loopy"
+
+pip install .

.ci/run_firedrake_examples.sh

+cd examples
+for i in $(find . -name '*firedrake*.py' -exec grep -q __main__ '{}' \; -print ); do
+    echo "-----------------------------------------------------------------------"
+    echo "RUNNING $i"
+    echo "-----------------------------------------------------------------------"
+    dn=$(dirname "$i")
+    bn=$(basename "$i")
+    (cd $dn; time python3 "$bn")
+done

.editorconfig

+# https://editorconfig.org/
+# https://github.com/editorconfig/editorconfig-vim 
+# https://github.com/editorconfig/editorconfig-emacs 
+
+root = true
+
+[*]
+indent_style = space
+end_of_line = lf
+charset = utf-8
+trim_trailing_whitespace = true
+insert_final_newline = true
+
+[*.py]
+indent_size = 4
+
+[*.rst]
+indent_size = 4
+
+[*.cpp]
+indent_size = 2
+
+[*.hpp]
+indent_size = 2
+
+# There may be one in doc/
+[Makefile]
+indent_style = tab
+
+# https://github.com/microsoft/vscode/issues/1679
+[*.md]
+trim_trailing_whitespace = false

.github/dependabot.yml

+version: 2
+updates:
+    # Set update schedule for GitHub Actions
+    - package-ecosystem: "github-actions"
+      directory: "/"
+      schedule:
+          interval: "weekly"
+
+# vim: sw=4

.github/workflows/autopush.yml

+name: Gitlab mirror
+on:
+    push:
+        branches:
+        - main
+
+jobs:
+    autopush:
+        name: Automatic push to gitlab.tiker.net
+        if: startsWith(github.repository, 'inducer/')
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   run: |
+                curl -L -O https://tiker.net/ci-support-v0
+                . ./ci-support-v0
+                mirror_github_to_gitlab
+
+            env:
+                GITLAB_AUTOPUSH_KEY: ${{ secrets.GITLAB_AUTOPUSH_KEY }}
+
+# vim: sw=4

.github/workflows/ci.yml

+name: CI
+on:
+    push:
+        branches:
+        - main
+    pull_request:
+    schedule:
+        - cron:  '17 3 * * 0'
+
+concurrency:
+    group: ${{ github.head_ref || github.ref_name }}
+    cancel-in-progress: true
+
+jobs:
+    typos:
+        name: Typos
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   uses: crate-ci/typos@master
+
+    ruff:
+        name: Ruff
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   uses: actions/setup-python@v5
+        -   name: "Main Script"
+            run: |
+                pip install ruff
+                ruff check
+
+    pylint:
+        name: Pylint
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   name: "Main Script"
+            run: |
+                echo "- scipy" >> .test-conda-env-py3.yml
+                USE_CONDA_BUILD=1
+                curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-pylint.sh
+                . ./prepare-and-run-pylint.sh "$(basename $GITHUB_REPOSITORY)" examples/*.py test/test_*.py
+
+    mypy:
+        name: Mypy
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   name: "Main Script"
+            run: |
+                curl -L -O https://tiker.net/ci-support-v0
+                . ./ci-support-v0
+                build_py_project_in_conda_env
+                python -m pip install mypy
+                ./run-mypy.sh
+
+    pytest3:
+        name: Pytest Conda Py3
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   name: "Main Script"
+            run: |
+                sudo apt update && sudo apt install octave
+
+                export MPLBACKEND=Agg
+                curl -L -O https://tiker.net/ci-support-v0
+                . ./ci-support-v0
+                build_py_project_in_conda_env
+                test_py_project
+
+    firedrake:
+        name: Pytest Firedrake
+        runs-on: ubuntu-latest
+        container:
+            image: 'firedrakeproject/firedrake'
+        steps:
+        -   name: "Checkout"
+            run: |
+                cd /root
+                mkdir meshmode
+                cd meshmode
+                git init
+
+                git remote add origin "https://github.com/$GITHUB_REPOSITORY.git"
+                git fetch origin "$GITHUB_REF"
+                git checkout FETCH_HEAD
+
+        -   name: "Make a venv"
+            run: |
+                cd /root
+                python3 -m venv --system-site-packages myvenv
+
+        -   name: "Dependencies"
+            run: |
+                cd /root/meshmode
+                . .ci/install-for-firedrake.sh
+
+        -   name: "Test"
+            run: |
+                cd /root/meshmode
+                . /root/myvenv/bin/activate
+                cd test
+                python -m pytest --tb=native -rxsw test_firedrake_interop.py
+
+    firedrake_examples:
+        name: Examples Firedrake
+        runs-on: ubuntu-latest
+        container:
+            image: 'firedrakeproject/firedrake'
+        steps:
+        -   name: "Checkout"
+            run: |
+                cd /root
+                mkdir meshmode
+                cd meshmode
+                git init
+
+                git remote add origin "https://github.com/$GITHUB_REPOSITORY.git"
+                git fetch origin "$GITHUB_REF"
+                git checkout FETCH_HEAD
+
+        -   name: "Make a venv"
+            run: |
+                cd /root
+                python3 -m venv --system-site-packages myvenv
+
+        -   name: "Dependencies"
+            run: |
+                cd /root/meshmode
+                . .ci/install-for-firedrake.sh
+
+        -   name: "Examples"
+            run: |
+                cd /root/meshmode
+                . /root/myvenv/bin/activate
+                . ./.ci/run_firedrake_examples.sh
+
+    examples3:
+        name: Examples Conda Py3
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   name: "Main Script"
+            run: |
+                export MPLBACKEND=Agg
+                USE_CONDA_BUILD=1
+                curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/build-py-project-and-run-examples.sh
+                . ./build-py-project-and-run-examples.sh
+
+
+                # Test lazy eval
+                rm -f *.vtu
+                python simple-dg.py --lazy
+
+    docs:
+        name: Documentation
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -
+            uses: actions/setup-python@v5
+            with:
+                python-version: '3.x'
+        -   name: "Main Script"
+            run: |
+                # texlive is needed for sphinxcontrib-tikz
+                sudo apt-get update
+                sudo apt-get install -y --no-install-recommends \
+                    texlive-pictures texlive-latex-extra graphviz pdf2svg
+
+                curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/ci-support.sh
+                . ci-support.sh
+
+                # https://github.com/sphinx-contrib/tikz/issues/21
+                export EXTRA_INSTALL="sphinxcontrib-tikz!=0.4.18"
+                build_py_project_in_conda_env
+
+                # Work around
+                # intersphinx inventory 'https://firedrakeproject.org/objects.inv' not fetchable
+                # by deleting all the Firedrake stuff
+                rm -Rf meshmode/interop/firedrake
+                sed -i '/firedrakeproject/d' doc/conf.py
+                sed -i '/interop/d' doc/index.rst
+                rm doc/interop.rst
+
+                build_docs
+
+    downstream_tests:
+        strategy:
+            fail-fast: false
+            matrix:
+                downstream_project: [grudge, pytential, mirgecom, mirgecom_examples]
+        name: Tests for downstream project ${{ matrix.downstream_project }}
+        runs-on: ubuntu-latest
+        steps:
+        -   uses: actions/checkout@v4
+        -   name: "Main Script"
+            env:
+                DOWNSTREAM_PROJECT: ${{ matrix.downstream_project }}
+            run: |
+                curl -L -O https://tiker.net/ci-support-v0
+                . ./ci-support-v0
+                if [[ "$DOWNSTREAM_PROJECT" == "grudge" && "$GITHUB_HEAD_REF" == "group-constr-drop-index" ]]; then
+                    DOWNSTREAM_PROJECT=https://github.com/inducer/grudge.git@grad-test-overint
+                fi
+                test_downstream "$DOWNSTREAM_PROJECT"
+
+# vim: sw=4

.gitignore

@@ -13,5 +13,16 @@ distribute*egg
 distribute*tar.gz
 a.out
 *.vtu
+*.pvtu
+*.h5
+*.xmf
+*.hdf
+*.pdf
+*.stl
 
 .cache
+.pytest_cache
+.pylintrc.yml
+.run-pylint.py
+
+test/nodal-dg

.gitlab-ci.yml

-Python 2.7 AMD CPU:
-  script:
-  - export PY_EXE=python2.7
-  - export PYOPENCL_TEST=amd:pu
-  - export EXTRA_INSTALL="numpy mako"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
-  - ". ./build-and-test-py-project.sh"
-  tags:
-  - python2.7
-  - amd-cl-cpu
+Python 3 POCL:
+  script: |
+    export PY_EXE=python3
+    export PYOPENCL_TEST=portable:cpu
+    # cython is here because pytential (for now, for TS) depends on it
+    export EXTRA_INSTALL="pybind11 cython numpy mako mpi4py h5py oct2py"
+    curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/build-and-test-py-project.sh
+    . ./build-and-test-py-project.sh
+  tags:
+  - python3
+  - pocl
+  - mpi
   except:
   - tags
-Python 2.7 POCL:
-  script:
-  - export PY_EXE=python2.7
-  - export PYOPENCL_TEST=portable
-  - export EXTRA_INSTALL="numpy mako"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
-  - ". ./build-and-test-py-project.sh"
+  artifacts:
+    reports:
+      junit: test/pytest.xml
+
+Python 3 Nvidia Titan V:
+  script: |
+    export PY_EXE=python3
+    export PYOPENCL_TEST=nvi:titan
+    export EXTRA_INSTALL="pybind11 cython numpy mako oct2py"
+    # cython is here because pytential (for now, for TS) depends on it
+    curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/build-and-test-py-project.sh
+    . ./build-and-test-py-project.sh
   tags:
-  - python2.7
-  - pocl
+  - python3
+  - nvidia-titan-v
   except:
   - tags
-Python 3.5 POCL:
+  artifacts:
+    reports:
+      junit: test/pytest.xml
+
+Python 3 POCL Examples:
   script:
-  - export PY_EXE=python3.5
-  - export PYOPENCL_TEST=portable
-  - export EXTRA_INSTALL="numpy mako"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-and-test-py-project.sh
-  - ". ./build-and-test-py-project.sh"
+  - test -n "$SKIP_EXAMPLES" && exit
+  - export PY_EXE=python3
+  - export PYOPENCL_TEST=portable:cpu
+  # cython is here because pytential (for now, for TS) depends on it
+  - export EXTRA_INSTALL="pybind11 cython numpy mako matplotlib"
+  - curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/build-py-project-and-run-examples.sh
+  - ". ./build-py-project-and-run-examples.sh"
   tags:
-  - python3.5
+  - python3
   - pocl
+  - large-node
   except:
   - tags
+
+# The machine shop is too old for the Firedrake container.
+# Lawrence Mitchell says that they likely build PETSc with -march=native
+# on something like Skylake.
+#
+# Python 3 POCL Firedrake:
+#   tags:
+#   - "docker-runner"
+#   image: "firedrakeproject/firedrake"
+#   script:
+#   - . .ci/install-for-firedrake.sh
+#   - cd test
+#   - python -m pytest --tb=native --junitxml=pytest.xml -rxsw test_firedrake_interop.py
+#   artifacts:
+#     reports:
+#       junit: test/pytest.xml
+#
+# Python 3 POCL Firedrake Examples:
+#   tags:
+#   - "docker-runner"
+#   image: "firedrakeproject/firedrake"
+#   script:
+#   - . .ci/install-for-firedrake.sh
+#   - . ./.ci/run_firedrake_examples.sh
+#   artifacts:
+#     reports:
+#       junit: test/pytest.xml
+
+Python 3 Conda:
+  script: |
+    export PYOPENCL_TEST=portable:cpu
+    export MPLBACKEND=Agg
+    curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/build-and-test-py-project-within-miniconda.sh
+    . ./build-and-test-py-project-within-miniconda.sh
+  tags:
+  # - docker-runner
+  - linux
+  - large-node
+  except:
+  - tags
+
 Documentation:
   script:
-  - EXTRA_INSTALL="numpy"
-  - curl -L -O -k https://gitlab.tiker.net/inducer/ci-support/raw/master/build-docs.sh
-  - ". ./build-docs.sh"
+  # https://github.com/sphinx-contrib/tikz/issues/21
+  - EXTRA_INSTALL="pybind11 cython numpy sphinxcontrib-tikz!=0.4.18"
+  - curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/main/build-docs.sh
+  - . ./build-docs.sh
+  tags:
+  - python3
+
+Ruff:
+  script: |
+    pipx install ruff
+    ruff check
+  tags:
+  - docker-runner
+  except:
+  - tags
+
+Pylint:
+  script: |
+    export PY_EXE=python3
+    EXTRA_INSTALL="Cython pybind11 numpy mako matplotlib scipy mpi4py h5py oct2py"
+    curl -L -O https://gitlab.tiker.net/inducer/ci-support/raw/master/prepare-and-run-pylint.sh
+    . ./prepare-and-run-pylint.sh "$CI_PROJECT_NAME" examples/*.py test/test_*.py
+  tags:
+  - python3
+  except:
+  - tags
+
+Mypy:
+  script: |
+    EXTRA_INSTALL="Cython mpi4py"
+    curl -L -O https://tiker.net/ci-support-v0
+    . ./ci-support-v0
+    build_py_project_in_venv
+    python -m pip install mypy
+    ./run-mypy.sh
+  tags:
+  - python3
+  except:
+  - tags
+
+Downstream:
+  parallel:
+    matrix:
+    - DOWNSTREAM_PROJECT: [grudge, pytential, mirgecom, mirgecom_examples]
   tags:
-  - python3.5
-  only:
-  - master
+  - large-node
+  - "docker-runner"
+  script: |
+    curl -L -O https://tiker.net/ci-support-v0
+    . ./ci-support-v0
+    test_downstream "$DOWNSTREAM_PROJECT"
+
+# vim: sw=2

.pylintrc-local.yml

+- arg: py-version
+  val: '3.10'
+
+- arg: ignore
+  val:
+    - firedrake
+    - to_firedrake.py
+    - from_firedrake.py
+    - test_firedrake_interop.py
+- arg: extension-pkg-whitelist
+  val: mayavi

.test-conda-env-py3.yml

+name: test-conda-env
+channels:
+- conda-forge
+- nodefaults
+
+dependencies:
+- python=3
+- git
+- libhwloc=2
+- numpy
+# 3.1 needed for SVM functionality
+- pocl>=3.1
+- mako
+- pyopencl
+- islpy
+- gmsh
+
+# Needed for nodal-DG interop
+- oct2py
+
+# for Pytential
+- cython
+
+# for pymetis
+- pybind11
+
+# for MPI-based tests
+- openmpi
+- mpi4py
+
+# for xdmf/hdf5 visualizer
+- h5py=*=mpi_openmpi*
+
+# Only needed to make pylint succeed
+- matplotlib-base
+
+- pip

README.rst

-meshmode
-========
+meshmode: High-Order Meshes and Discontinuous Function Spaces
+=============================================================
 
-* `Source code on Github <https://github.com/inducer/meshmode>`_
-* `Documentation <https://documen.tician.de/meshmode>`_
+.. image:: https://gitlab.tiker.net/inducer/meshmode/badges/main/pipeline.svg
+    :alt: Gitlab Build Status
+    :target: https://gitlab.tiker.net/inducer/meshmode/commits/main
+.. image:: https://github.com/inducer/meshmode/actions/workflows/ci.yml/badge.svg
+    :alt: Github Build Status
+    :target: https://github.com/inducer/meshmode/actions/workflows/ci.yml
+.. image:: https://badge.fury.io/py/meshmode.svg
+    :alt: Python Package Index Release Page
+    :target: https://pypi.org/project/meshmode/
 
-.. TODO
+Meshmode provides the "boring bits" of high-order unstructured discretization,
+for simplices (triangles, tetrahedra) and tensor products (quads, hexahedra).
+Features:
+
+- 1/2/3D, line/surface/volume discretizations in each, curvilinear supported.
+- "Everything is a (separate) discretization." (mesh boundaries are, element surfaces are,
+  refined versions of the same mesh are) "Connections" transfer information
+  between discretizations.
+- Periodic connectivity.
+- Mesh partitioning (not just) for distributed execution (e.g. via MPI).
+- Interpolatory, quadrature (overintegration), and modal element-local discretizations.
+- Independent of execution environment (GPU/CPU, numpy, ...)
+  via `array contexts <https://github.com/inducer/arraycontext/>`__.
+- Simple mesh refinement (via bisection). Adjacency currently only
+  maintained if conforming.
+- Input from Gmsh, Visualization to Vtk (both high-order curvilinear).
+- Easy data exchange with `Firedrake <https://www.firedrakeproject.org/>`__.
+
+Meshmode emerged as the shared discretization layer for `pytential
+<https://github.com/inducer/pytential/>`__ (layer potentials) and `grudge
+<https://github.com/inducer/grudge>`__ (discontinuous Galerkin).
+
+Places on the web related to meshmode:
+
+* `Source code on Github <https://github.com/inducer/meshmode>`__
+* `Documentation <https://documen.tician.de/meshmode>`__

doc/Makefile

-# Makefile for Sphinx documentation
+# Minimal makefile for Sphinx documentation
 #
 
-# You can set these variables from the command line.
-SPHINXOPTS    =
-SPHINXBUILD   = sphinx-build
-PAPER         =
+# You can set these variables from the command line, and also
+# from the environment for the first two.
+SPHINXOPTS    ?= -n
+SPHINXBUILD   ?= python $(shell which sphinx-build)
+SOURCEDIR     = .
 BUILDDIR      = _build
 
-# User-friendly check for sphinx-build
-ifeq ($(shell which $(SPHINXBUILD) >/dev/null 2>&1; echo $$?), 1)
-$(error The '$(SPHINXBUILD)' command was not found. Make sure you have Sphinx installed, then set the SPHINXBUILD environment variable to point to the full path of the '$(SPHINXBUILD)' executable. Alternatively you can add the directory with the executable to your PATH. If you don't have Sphinx installed, grab it from http://sphinx-doc.org/)
-endif
-
-# Internal variables.
-PAPEROPT_a4     = -D latex_paper_size=a4
-PAPEROPT_letter = -D latex_paper_size=letter
-ALLSPHINXOPTS   = -d $(BUILDDIR)/doctrees $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
-# the i18n builder cannot share the environment and doctrees with the others
-I18NSPHINXOPTS  = $(PAPEROPT_$(PAPER)) $(SPHINXOPTS) .
-
-.PHONY: help clean html dirhtml singlehtml pickle json htmlhelp qthelp devhelp epub latex latexpdf text man changes linkcheck doctest gettext
-
+# Put it first so that "make" without argument is like "make help".
 help:
-	@echo "Please use \`make <target>' where <target> is one of"
-	@echo "  html       to make standalone HTML files"
-	@echo "  dirhtml    to make HTML files named index.html in directories"
-	@echo "  singlehtml to make a single large HTML file"
-	@echo "  pickle     to make pickle files"
-	@echo "  json       to make JSON files"
-	@echo "  htmlhelp   to make HTML files and a HTML help project"
-	@echo "  qthelp     to make HTML files and a qthelp project"
-	@echo "  devhelp    to make HTML files and a Devhelp project"
-	@echo "  epub       to make an epub"
-	@echo "  latex      to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
-	@echo "  latexpdf   to make LaTeX files and run them through pdflatex"
-	@echo "  latexpdfja to make LaTeX files and run them through platex/dvipdfmx"
-	@echo "  text       to make text files"
-	@echo "  man        to make manual pages"
-	@echo "  texinfo    to make Texinfo files"
-	@echo "  info       to make Texinfo files and run them through makeinfo"
-	@echo "  gettext    to make PO message catalogs"
-	@echo "  changes    to make an overview of all changed/added/deprecated items"
-	@echo "  xml        to make Docutils-native XML files"
-	@echo "  pseudoxml  to make pseudoxml-XML files for display purposes"
-	@echo "  linkcheck  to check all external links for integrity"
-	@echo "  doctest    to run all doctests embedded in the documentation (if enabled)"
-
-clean:
-	rm -rf $(BUILDDIR)/*
-
-html:
-	$(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
-	@echo
-	@echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
-
-dirhtml:
-	$(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
-	@echo
-	@echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
-
-singlehtml:
-	$(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
-	@echo
-	@echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
-
-pickle:
-	$(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
-	@echo
-	@echo "Build finished; now you can process the pickle files."
-
-json:
-	$(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
-	@echo
-	@echo "Build finished; now you can process the JSON files."
-
-htmlhelp:
-	$(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
-	@echo
-	@echo "Build finished; now you can run HTML Help Workshop with the" \
-	      ".hhp project file in $(BUILDDIR)/htmlhelp."
-
-qthelp:
-	$(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
-	@echo
-	@echo "Build finished; now you can run "qcollectiongenerator" with the" \
-	      ".qhcp project file in $(BUILDDIR)/qthelp, like this:"
-	@echo "# qcollectiongenerator $(BUILDDIR)/qthelp/meshmode.qhcp"
-	@echo "To view the help file:"
-	@echo "# assistant -collectionFile $(BUILDDIR)/qthelp/meshmode.qhc"
-
-devhelp:
-	$(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
-	@echo
-	@echo "Build finished."
-	@echo "To view the help file:"
-	@echo "# mkdir -p $$HOME/.local/share/devhelp/meshmode"
-	@echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/meshmode"
-	@echo "# devhelp"
-
-epub:
-	$(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
-	@echo
-	@echo "Build finished. The epub file is in $(BUILDDIR)/epub."
-
-latex:
-	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
-	@echo
-	@echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
-	@echo "Run \`make' in that directory to run these through (pdf)latex" \
-	      "(use \`make latexpdf' here to do that automatically)."
-
-latexpdf:
-	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
-	@echo "Running LaTeX files through pdflatex..."
-	$(MAKE) -C $(BUILDDIR)/latex all-pdf
-	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
-
-latexpdfja:
-	$(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
-	@echo "Running LaTeX files through platex and dvipdfmx..."
-	$(MAKE) -C $(BUILDDIR)/latex all-pdf-ja
-	@echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
-
-text:
-	$(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text
-	@echo
-	@echo "Build finished. The text files are in $(BUILDDIR)/text."
-
-man:
-	$(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man
-	@echo
-	@echo "Build finished. The manual pages are in $(BUILDDIR)/man."
-
-texinfo:
-	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
-	@echo
-	@echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
-	@echo "Run \`make' in that directory to run these through makeinfo" \
-	      "(use \`make info' here to do that automatically)."
-
-info:
-	$(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
-	@echo "Running Texinfo files through makeinfo..."
-	make -C $(BUILDDIR)/texinfo info
-	@echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
-
-gettext:
-	$(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale
-	@echo
-	@echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
-
-changes:
-	$(SPHINXBUILD) -b changes $(ALLSPHINXOPTS) $(BUILDDIR)/changes
-	@echo
-	@echo "The overview file is in $(BUILDDIR)/changes."
-
-linkcheck:
-	$(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
-	@echo
-	@echo "Link check complete; look for any errors in the above output " \
-	      "or in $(BUILDDIR)/linkcheck/output.txt."
-
-doctest:
-	$(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
-	@echo "Testing of doctests in the sources finished, look at the " \
-	      "results in $(BUILDDIR)/doctest/output.txt."
+	@$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
 
-xml:
-	$(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml
-	@echo
-	@echo "Build finished. The XML files are in $(BUILDDIR)/xml."
+.PHONY: help Makefile
 
-pseudoxml:
-	$(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml
-	@echo
-	@echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml."
+# Catch-all target: route all unknown targets to Sphinx using the new
+# "make mode" option.  $(O) is meant as a shortcut for $(SPHINXOPTS).
+%: Makefile
+	@$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)

doc/array.rst

+DOF (Degree-of-Freedom) Arrays
+==============================
+
+.. automodule:: meshmode.dof_array
+
+Array Contexts
+==============
+
+.. automodule:: meshmode.array_context
+
+Metadata for Program Transformation
+===================================
+
+.. automodule:: meshmode.transform_metadata

doc/conf.py

-# -*- coding: utf-8 -*-
-#
-# meshmode documentation build configuration file, created by
-# sphinx-quickstart on Thu Jun  5 15:22:45 2014.
-#
-# This file is execfile()d with the current directory set to its
-# containing dir.
-#
-# Note that not all possible configuration values are present in this
-# autogenerated file.
-#
-# All configuration values have a default; values that are commented out
-# serve to show the default.
-
-import sys
-import os
-
-# If extensions (or modules to document with autodoc) are in another directory,
-# add these directories to sys.path here. If the directory is relative to the
-# documentation root, use os.path.abspath to make it absolute, like shown here.
-#sys.path.insert(0, os.path.abspath('.'))
-
-# -- General configuration ------------------------------------------------
-
-# If your documentation needs a minimal Sphinx version, state it here.
-#needs_sphinx = '1.0'
-
-# Add any Sphinx extension module names here, as strings. They can be
-# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
-# ones.
-extensions = [
-    'sphinx.ext.autodoc',
-    'sphinx.ext.doctest',
-    'sphinx.ext.intersphinx',
-    'sphinx.ext.mathjax',
-]
-
-# Add any paths that contain templates here, relative to this directory.
-templates_path = ['_templates']
-
-# The suffix of source filenames.
-source_suffix = '.rst'
-
-# The encoding of source files.
-#source_encoding = 'utf-8-sig'
-
-# The master toctree document.
-master_doc = 'index'
-
-# General information about the project.
-project = u'meshmode'
-copyright = u'2014, Andreas Klöckner'
-
-# The version info for the project you're documenting, acts as replacement for
-# |version| and |release|, also used in various other places throughout the
-# built documents.
-#
-# The short X.Y version.
-ver_dic = {}
-exec(compile(open("../meshmode/version.py").read(), "../meshmode/version.py", 'exec'), ver_dic)
-version = ".".join(str(x) for x in ver_dic["VERSION"])
-# The full version, including alpha/beta/rc tags.
-release = ver_dic["VERSION_TEXT"]
-
-# The language for content autogenerated by Sphinx. Refer to documentation
-# for a list of supported languages.
-#language = None
-
-# There are two options for replacing |today|: either, you set today to some
-# non-false value, then it is used:
-#today = ''
-# Else, today_fmt is used as the format for a strftime call.
-#today_fmt = '%B %d, %Y'
-
-# List of patterns, relative to source directory, that match files and
-# directories to ignore when looking for source files.
-exclude_patterns = ['_build']
-
-# The reST default role (used for this markup: `text`) to use for all
-# documents.
-#default_role = None
-
-# If true, '()' will be appended to :func: etc. cross-reference text.
-#add_function_parentheses = True
-
-# If true, the current module name will be prepended to all description
-# unit titles (such as .. function::).
-#add_module_names = True
-
-# If true, sectionauthor and moduleauthor directives will be shown in the
-# output. They are ignored by default.
-#show_authors = False
-
-# The name of the Pygments (syntax highlighting) style to use.
-pygments_style = 'sphinx'
-
-# A list of ignored prefixes for module index sorting.
-#modindex_common_prefix = []
-
-# If true, keep warnings as "system message" paragraphs in the built documents.
-#keep_warnings = False
-
-
-# -- Options for HTML output ----------------------------------------------
-
-html_theme = "alabaster"
-
-html_theme_options = {
-        "extra_nav_links": {
-            "🚀 Github": "https://github.com/inducer/meshmode",
-            "💾 Download Releases": "https://pypi.python.org/pypi/meshmode",
-            }
-        }
-
-html_sidebars = {
-    '**': [
-        'about.html',
-        'navigation.html',
-        'relations.html',
-        'searchbox.html',
-    ]
+from importlib import metadata
+from urllib.request import urlopen
+
+
+_conf_url = \
+        "https://raw.githubusercontent.com/inducer/sphinxconfig/main/sphinxconfig.py"
+with urlopen(_conf_url) as _inf:
+    exec(compile(_inf.read(), _conf_url, "exec"), globals())
+
+extensions.extend([  # noqa: F821
+    "sphinx.ext.graphviz",
+    "sphinxcontrib.tikz",
+])
+
+tikz_tikzlibraries = "decorations.markings"
+
+copyright = "2014-2024, Meshmode contributors"
+release = metadata.version("meshmode")
+version = ".".join(release.split(".")[:2])
+
+intersphinx_mapping = {
+    "arraycontext": ("https://documen.tician.de/arraycontext", None),
+    "fenics": ("https://fenics.readthedocs.io/projects/fiat/en/latest", None),
+    "FInAT": ("https://finat.github.io/FInAT/", None),
+    "firedrake": ("https://www.firedrakeproject.org", None),
+    "gmsh_interop": ("https://documen.tician.de/gmsh_interop", None),
+    "h5py": ("https://docs.h5py.org/en/stable", None),
+    "loopy": ("https://documen.tician.de/loopy", None),
+    "meshpy": ("https://documen.tician.de/meshpy", None),
+    "modepy": ("https://documen.tician.de/modepy", None),
+    "mpi4py": ("https://mpi4py.readthedocs.io/en/stable", None),
+    "numpy": ("https://numpy.org/doc/stable", None),
+    "pymetis": ("https://documen.tician.de/pymetis", None),
+    "pyopencl": ("https://documen.tician.de/pyopencl", None),
+    "python": ("https://docs.python.org/3", None),
+    "pytools": ("https://documen.tician.de/pytools", None),
+    "recursivenodes": ("https://tisaac.gitlab.io/recursivenodes", None),
 }
 
 
-# Add any paths that contain custom themes here, relative to this directory.
-#html_theme_path = []
-
-# The name for this set of Sphinx documents.  If None, it defaults to
-# "<project> v<release> documentation".
-#html_title = None
-
-# A shorter title for the navigation bar.  Default is the same as html_title.
-#html_short_title = None
-
-# The name of an image file (relative to this directory) to place at the top
-# of the sidebar.
-#html_logo = None
-
-# The name of an image file (within the static path) to use as favicon of the
-# docs.  This file should be a Windows icon file (.ico) being 16x16 or 32x32
-# pixels large.
-#html_favicon = None
-
-# Add any paths that contain custom static files (such as style sheets) here,
-# relative to this directory. They are copied after the builtin static files,
-# so a file named "default.css" will overwrite the builtin "default.css".
-html_static_path = ['_static']
-
-# Add any extra paths that contain custom files (such as robots.txt or
-# .htaccess) here, relative to this directory. These files are copied
-# directly to the root of the documentation.
-#html_extra_path = []
-
-# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
-# using the given strftime format.
-#html_last_updated_fmt = '%b %d, %Y'
-
-# If true, SmartyPants will be used to convert quotes and dashes to
-# typographically correct entities.
-#html_use_smartypants = True
-
-# Custom sidebar templates, maps document names to template names.
-#html_sidebars = {}
-
-# Additional templates that should be rendered to pages, maps page names to
-# template names.
-#html_additional_pages = {}
-
-# If false, no module index is generated.
-#html_domain_indices = True
-
-# If false, no index is generated.
-#html_use_index = True
-
-# If true, the index is split into individual pages for each letter.
-#html_split_index = False
-
-# If true, links to the reST sources are added to the pages.
-#html_show_sourcelink = True
-
-# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
-#html_show_sphinx = True
-
-# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
-#html_show_copyright = True
-
-# If true, an OpenSearch description file will be output, and all pages will
-# contain a <link> tag referring to it.  The value of this option must be the
-# base URL from which the finished HTML is served.
-#html_use_opensearch = ''
-
-# This is the file name suffix for HTML files (e.g. ".xhtml").
-#html_file_suffix = None
-
-# Output file base name for HTML help builder.
-htmlhelp_basename = 'meshmodedoc'
-
-
-# -- Options for LaTeX output ---------------------------------------------
-
-latex_elements = {
-# The paper size ('letterpaper' or 'a4paper').
-#'papersize': 'letterpaper',
-
-# The font size ('10pt', '11pt' or '12pt').
-#'pointsize': '10pt',
-
-# Additional stuff for the LaTeX preamble.
-#'preamble': '',
-}
-
-# Grouping the document tree into LaTeX files. List of tuples
-# (source start file, target name, title,
-#  author, documentclass [howto, manual, or own class]).
-latex_documents = [
-  ('index', 'meshmode.tex', u'meshmode Documentation',
-   u'Andreas Klöckner', 'manual'),
-]
-
-# The name of an image file (relative to this directory) to place at the top of
-# the title page.
-#latex_logo = None
-
-# For "manual" documents, if this is true, then toplevel headings are parts,
-# not chapters.
-#latex_use_parts = False
-
-# If true, show page references after internal links.
-#latex_show_pagerefs = False
-
-# If true, show URL addresses after external links.
-#latex_show_urls = False
-
-# Documents to append as an appendix to all manuals.
-#latex_appendices = []
-
-# If false, no module index is generated.
-#latex_domain_indices = True
-
-
-# -- Options for manual page output ---------------------------------------
-
-# One entry per manual page. List of tuples
-# (source start file, name, description, authors, manual section).
-man_pages = [
-    ('index', 'meshmode', u'meshmode Documentation',
-     [u'Andreas Klöckner'], 1)
-]
-
-# If true, show URL addresses after external links.
-#man_show_urls = False
-
-
-# -- Options for Texinfo output -------------------------------------------
-
-# Grouping the document tree into Texinfo files. List of tuples
-# (source start file, target name, title, author,
-#  dir menu entry, description, category)
-texinfo_documents = [
-  ('index', 'meshmode', u'meshmode Documentation',
-   u'Andreas Klöckner', 'meshmode', 'One line description of project.',
-   'Miscellaneous'),
-]
-
-# Documents to append as an appendix to all manuals.
-#texinfo_appendices = []
-
-# If false, no module index is generated.
-#texinfo_domain_indices = True
-
-# How to display URL addresses: 'footnote', 'no', or 'inline'.
-#texinfo_show_urls = 'footnote'
-
-# If true, do not generate a @detailmenu in the "Top" node's menu.
-#texinfo_no_detailmenu = False
+# Some modules need to import things just so that sphinx can resolve symbols in
+# type annotations. Often, we do not want these imports (e.g. of PyOpenCL) when
+# in normal use (because they would introduce unintended side effects or hard
+# dependencies). This flag exists so that these imports only occur during doc
+# build. Since sphinx appears to resolve type hints lexically (as it should),
+# this needs to be cross-module (since, e.g. an inherited arraycontext
+# docstring can be read by sphinx when building meshmode, a dependent package),
+# this needs a setting of the same name across all packages involved, that's
+# why this name is as global-sounding as it is.
+import sys
 
 
-# Example configuration for intersphinx: refer to the Python standard library.
-intersphinx_mapping = {'http://docs.python.org/': None}
+sys._BUILDING_SPHINX_DOCS = True

doc/connection.rst

+Connections: Interpolating between Discretizations
+==================================================
+
+.. automodule:: meshmode.discretization.connection

doc/discretization.rst

@@ -6,16 +6,11 @@ Abstract interface
 
 .. automodule:: meshmode.discretization
 
-Composite polynomial discretization
------------------------------------
+Element Groups for Composite Polynomial Discretization
+------------------------------------------------------
 
 .. automodule:: meshmode.discretization.poly_element
 
-Connection/interpolation
-------------------------
-
-.. automodule:: meshmode.discretization.connection
-
 Visualization
 -------------
 

doc/distributed.rst

+Distributed memory
+==================
+
+.. automodule:: meshmode.distributed

doc/index.rst

@@ -7,8 +7,14 @@ Contents:
    :maxdepth: 2
 
    mesh
+   array
    discretization
+   connection
+   distributed
+   interop
    misc
+   🚀 Github <https://github.com/inducer/meshmode>
+   💾 Download Releases <https://pypi.org/project/meshmode>
 
 Indices and tables
 ==================

doc/interop.rst

+Interoperability with Other Discretization Packages
+===================================================
+
+Functionality in this subpackage helps import and export data to/from other
+pieces of software, typically PDE solvers.
+
+Nodal DG
+--------
+
+.. automodule:: meshmode.interop.nodal_dg
+
+Firedrake
+---------
+
+Function Spaces/Discretizations
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Users wishing to interact with :mod:`meshmode` from :mod:`firedrake`
+will create a
+:class:`~meshmode.interop.firedrake.connection.FiredrakeConnection`
+using :func:`~meshmode.interop.firedrake.connection.build_connection_from_firedrake`,
+while users wishing
+to interact with :mod:`firedrake` from :mod:`meshmode` will use
+will create a
+:class:`~meshmode.interop.firedrake.connection.FiredrakeConnection`
+using :func:`~meshmode.interop.firedrake.connection.build_connection_to_firedrake`.
+It is not recommended to create a
+:class:`~meshmode.interop.firedrake.connection.FiredrakeConnection` directly.
+
+.. automodule:: meshmode.interop.firedrake.connection
+
+Meshes
+^^^^^^
+
+.. automodule:: meshmode.interop.firedrake.mesh
+
+Reference Cells
+^^^^^^^^^^^^^^^
+
+.. automodule:: meshmode.interop.firedrake.reference_cell
+
+
+Implementation Details
+^^^^^^^^^^^^^^^^^^^^^^
+
+Converting between :mod:`firedrake` and :mod:`meshmode` is in general
+straightforward. Some language is different:
+
+* In a mesh, a :mod:`meshmode` "element" is a :mod:`firedrake` "cell"
+* A :class:`~meshmode.discretization.Discretization` is a :mod:`firedrake`
+  :class:`~firedrake.functionspaceimpl.WithGeometry`, usually
+  created by calling the function :func:`~firedrake.functionspace.FunctionSpace`
+  and referred to as a "function space"
+* In a mesh, any vertices, faces, cells, etc. are :mod:`firedrake`
+  "entities" (see `the PETSc documentation on DMPLEX <https://petsc.org/release/manualpages/DMPlex/>`__
+  for more info on how topological mesh information is stored
+  in :mod:`firedrake`).
+
+Other than carefully tabulating how and which vertices/faces
+correspond to other vertices/faces/cells, there are two main difficulties.
+
+1. :mod:`meshmode` has discontinuous polynomial function spaces
+   which may use different unit nodes than :mod:`firedrake`.
+2. :mod:`meshmode` requires that all mesh elements be positively oriented,
+   :mod:`firedrake` does not. Meanwhile, when :mod:`firedrake` creates
+   a mesh, it changes the element ordering and the local vertex ordering.
+
+(1.) is easily handled by insisting that the :mod:`firedrake`
+:class:`~firedrake.functionspaceimpl.WithGeometry` uses polynomial elements
+and that the group of the :class:`~meshmode.discretization.Discretization`
+being converted is a
+:class:`~meshmode.discretization.poly_element.InterpolatoryQuadratureSimplexElementGroup`
+of the same order. Then, on each element, the function space being
+represented is the same in :mod:`firedrake` and :mod:`meshmode`.
+We may simply resample to one system or another's unit nodes.
+
+To handle (2.),
+once we associate a :mod:`meshmode`
+element to the correct :mod:`firedrake` cell, we have something
+like this picture:
+
+.. graphviz::
+
+    digraph{
+        // created with graphviz2.38 dot
+        // NODES
+
+        mmNodes [label="Meshmode\nnodes"];
+        mmRef   [label="Meshmode\nunit nodes"];
+        fdRef   [label="Firedrake\nunit nodes"];
+        fdNodes [label="Firedrake\nnodes"];
+
+        // EDGES
+
+        mmRef -> mmNodes [label=" f "];
+        fdRef -> fdNodes [label=" g "];
+    }
+
+(Assume we have already
+ensured that :mod:`meshmode` and :mod:`firedrake` use the
+same reference element by mapping :mod:`firedrake`'s reference
+element onto :mod:`meshmode`'s).
+If :math:`f=g`, then we can resample function values from
+one node set to the other. However, if :mod:`firedrake`
+has reordered the vertices or if we flipped their order to
+ensure :mod:`meshmode` has positively-oriented elements,
+there is some map :math:`A` applied to the reference element
+which implements this permutation of barycentric coordinates.
+In this case, :math:`f=g\circ A`. Now, we have a connected diagram:
+
+.. graphviz::
+
+    digraph{
+        // created with graphviz2.38 dot
+        // NODES
+
+        mmNodes [label="Meshmode\nnodes"];
+        mmRef   [label="Meshmode\nunit nodes"];
+        fdRef   [label="Firedrake\nunit nodes"];
+        fdRef2  [label="Firedrake\nunit nodes"];
+        fdNodes [label="Firedrake\nnodes"];
+
+        // EDGES
+
+        {rank=same; mmRef; fdRef;}
+        {rank=same; mmNodes; fdNodes;}
+        mmRef -> fdRef [label="Resampling", dir="both"];
+        mmRef -> mmNodes [label=" f "];
+        fdRef -> fdRef2 [label=" A "];
+        fdRef2 -> fdNodes [label=" g "];
+    }
+
+In short, once we reorder the :mod:`firedrake` nodes so
+that the mapping from the :mod:`meshmode` and :mod:`firedrake`
+reference elements are the same, we can resample function values
+at nodes from one set of unit nodes to another (and then undo
+the reordering if converting function values
+from :mod:`meshmode` to :mod:`firedrake`). The
+information for this whole reordering process is
+stored in
+:attr:`~meshmode.interop.firedrake.connection.FiredrakeConnection.mm2fd_node_mapping`,
+an array which associates each :mod:`meshmode` node
+to the :mod:`firedrake` node found by tracing the
+above diagram (i.e. it stores
+:math:`g\circ A\circ \text{Resampling} \circ f^{-1}`).
+
+For Developers: Firedrake Function Space Design Crash Course
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In Firedrake, meshes and function spaces have a close relationship.
+In particular, this is  due to some structure described in this
+`Firedrake pull request <https://github.com/firedrakeproject/firedrake/pull/627>`_.
+If you wish to develop on / add to the implementation of conversion
+between :mod:`meshmode` and :mod:`firedrake`, you will need
+to understand their design style. Below is a crash course.
+
+In short, it is the idea
+that every function space should have a mesh, and the coordinates of the mesh
+should be representable as a function on that same mesh, which must live
+on some function space on the mesh... etc.
+Under the hood, we divide between topological and geometric objects,
+roughly as so:
+
+(1) A reference element defined using :mod:`finat` and :mod:`FIAT`
+    is used to define what meshmode calls the unit nodes and unit
+    vertices. It is worth noting that :mod:`firedrake` does
+    not require a positive orientation of elements and that its
+    reference triangle is different than specified in :mod:`modepy`.
+
+(2) A `~firedrake.mesh.MeshTopology`
+    which holds information about connectivity
+    and other topological properties, but nothing about geometry/coordinates
+    etc.
+
+(3) A class :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    created from a :mod:`finat` element and a
+    `~firedrake.mesh.MeshTopology` which allows us to
+    define functions mapping the nodes (defined by the
+    :mod:`finat` element) of each element in the
+    `~firedrake.mesh.MeshTopology` to some values.
+    Note that the function :func:`~firedrake.functionspace.FunctionSpace`
+    in the firedrake API is used to create objects of class
+    :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    and :class:`~firedrake.functionspaceimpl.WithGeometry` (see
+    (6)).
+
+(4) A `~firedrake.function.CoordinatelessFunction`
+    (in the sense that its *domain* has no coordinates)
+    which is a function in a
+    :class:`~firedrake.functionspaceimpl.FunctionSpace`.
+
+(5) A `~firedrake.mesh.MeshGeometry` created from a
+    :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    and a `~firedrake.function.CoordinatelessFunction`
+    in that :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    which maps each dof to its geometric coordinates.
+
+(6) A :class:`~firedrake.functionspaceimpl.WithGeometry` which is a
+    :class:`~firedrake.functionspaceimpl.FunctionSpace` together
+    with a `~firedrake.mesh.MeshGeometry`.
+    This is the object returned
+    usually returned to the user by a call
+    to the :mod:`firedrake` function
+    :func:`~firedrake.functionspace.FunctionSpace`.
+
+(7) A :class:`~firedrake.function.Function` is defined on a
+    :class:`~firedrake.functionspaceimpl.WithGeometry`.
+
+Thus, by the coordinates of a mesh geometry we mean
+
+(a) On the hidden back-end: a `~firedrake.function.CoordinatelessFunction`
+    *f* on some function space defined only on the mesh topology.
+(b) On the front-end: A :class:`~firedrake.function.Function`
+    with the values of *f* but defined
+    on a :class:`~firedrake.functionspaceimpl.WithGeometry`
+    created from the :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    *f* lives in and the `~firedrake.mesh.MeshGeometry` *f* defines.
+
+Basically, it's this picture (where :math:`a\to b` if :math:`b` depends on :math:`a`)
+
+.. warning::
+
+    In general, the :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    of the coordinates function
+    of a :class:`~firedrake.functionspaceimpl.WithGeometry` may not be the same
+    :class:`~firedrake.functionspaceimpl.FunctionSpace`
+    as for functions which live in the
+    :class:`~firedrake.functionspaceimpl.WithGeometry`.
+    This picture
+    only shows how the class definitions depend on each other.
+
+
+.. graphviz::
+
+    digraph{
+        // created with graphviz2.38 dot
+        // NODES
+
+        top [label="Topological\nMesh"];
+        ref [label="Reference\nElement"];
+        fspace [label="Function Space"];
+        coordless [label="Coordinateless\nFunction"];
+        geo [label="Geometric\nMesh"];
+        withgeo [label="With\nGeometry"];
+
+        // EDGES
+
+        top -> fspace;
+        ref -> fspace;
+
+        fspace -> coordless;
+
+        top -> geo;
+        coordless -> geo [label="Mesh\nCoordinates"];
+
+        fspace -> withgeo;
+        geo -> withgeo;
+    }

doc/mesh.rst

@@ -2,19 +2,89 @@ Common infrastructure
 =====================
 
 .. automodule:: meshmode
+.. automodule:: meshmode.mesh.tools
 
 Mesh management
 ===============
 
-.. automodule:: meshmode.mesh
+.. currentmodule:: meshmode.mesh
+
+Design of the Data Structure
+----------------------------
+
+Why does a :class:`Mesh` need to be broken into :class:`MeshElementGroup` instances?
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Elements can be of different types (e.g. triangle, quadrilateral,
+tetrahedron, what have you). In addition, elements may vary in the
+polynomial degree used to represent them (see also below).
+
+All these bits of information could in principle be stored by element,
+but having large, internally homogeneous groups is a good thing from an
+efficiency standpoint. (So that you can, e.g., launch one GPU kernel to
+deal with all order-3 triangles, instead of maybe having to dispatch
+based on type and size inside the kernel)
+
+What is the difference between 'vertices' and 'nodes'?
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+Nodes exist mainly to represent the (potentially non-affine) deformation of
+each element, by a one-to-one correspondence with
+:attr:`MeshElementGroup.unit_nodes`.  They are unique to each element. Vertices
+on the other hand exist to clarify whether or not a point shared by two
+elements is actually identical (or just happens to be "close"). This is done by
+assigning (single, globally shared) vertex numbers and having elements refer to
+them.
+
+Consider the following picture:
+
+.. tikz:: Mesh nodes and vertices
+    :libs: decorations.markings
+    :align: center
+    :xscale: 60
+
+    \tikzset{-node-/.style={decoration={
+        markings,
+        mark=at position #1 with {
+            \draw[fill=green!60!black, line width=0.4] circle [radius=0.1];}},
+        postaction={decorate}}}
+
+    \draw [thick, -node-=.33,-node-=0.66] (0, 0) to (3, 0);
+    \draw [thick, -node-=.33,-node-=0.66] (3, 0) to (0, 3);
+    \draw [thick, -node-=.33,-node-=0.66] (0, 3) to (0, 0);
+    \draw [fill=green!60!black] (0, 0) circle [radius=0.1];
+    \draw [fill=green!60!black] (3, 0) circle [radius=0.1];
+    \draw [fill=green!60!black] (0, 3) circle [radius=0.1];
+    \draw [fill=green!60!black] (1, 1) circle [radius=0.1];
+
+    \draw [ultra thick,bend left,->] (1.5, 2.5) to (3.5, 2.5);
 
-.. autoclass:: MeshElementGroup
-    :members:
-    :undoc-members:
+    \begin{scope}[shift={(4, 2)},rotate=-47]
+    \draw [thick, -node-=.33,-node-=0.66] (0, 0) to [bend left] (3, 0);
+    \draw [thick, -node-=.33,-node-=0.66] (3, 0) to [bend right] (0, 3);
+    \draw [thick, -node-=.33,-node-=0.66] (0, 3) to [bend right] (0, 0);
+    \draw [dashed] (3, 0) to [bend left] (5, 3);
+    \draw [dashed] (5, 3) to [bend right] (0, 3);
 
-.. autoclass:: Mesh
-    :members:
-    :undoc-members:
+    \draw [fill=magenta!60] (0, 0) circle [radius=0.15];
+    \draw [fill=magenta!60] (0, 3) circle [radius=0.15];
+    \draw [fill=magenta!60] (3, 0) circle [radius=0.15];
+    \draw [fill=green!60!black] (0.75, 1.5) circle [radius=0.1];
+    \end{scope}
+
+    \node at (1.5, -0.5) [below] {Reference Element};
+    \draw [fill=green!60!black] (0.25, -1.5) circle [radius=0.1]
+        node [right] {~ unit nodes};
+    \node at (6.5, -0.5) [below] {Mesh Element};
+    \draw [fill=green!60!black] (5.5, -1.5) circle [radius=0.1]
+        node [right] {~ nodes (unique)};
+    \draw [fill=magenta!60] (5.5, -2) circle [radius=0.15]
+        node [right] {~ vertices (shared)};
+
+Mesh Data Structure
+-------------------
+
+.. automodule:: meshmode.mesh
 
 Mesh generation
 ---------------
@@ -27,8 +97,18 @@ Mesh input/output
 .. automodule:: meshmode.mesh.io
 
 Mesh processing
------------------
+---------------
 
 .. automodule:: meshmode.mesh.processing
 
+Mesh refinement
+---------------
+
+.. automodule:: meshmode.mesh.refinement
+
+Mesh visualization
+------------------
+
+.. automodule:: meshmode.mesh.visualization
+
 .. vim: sw=4