max-models · Oct 29, 2026 · Oct 29, 2026
diff --git a/tutorials/01_first_hierarchy.ipynb b/tutorials/01_first_hierarchy.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# A first patch hierarchy\n",
+    "# Patch hierarchy\n",
     "\n",
     "A hierarchy is a coarse base mesh and rectangular patches of finer cells on top of it. This\n",
     "tutorial builds one, shows the rules the patches follow, and puts fields on it."

diff --git a/tutorials/02_cell_centered_poisson.ipynb b/tutorials/02_cell_centered_poisson.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# Poisson's equation on cells\n",
+    "# Cell-centered Poisson\n",
     "\n",
     "`solve_poisson` solves $-\\nabla^2 \\phi = f$ with one value per cell, on all patches at\n",
     "once: a conservative finite-volume scheme in which a coarse cell next to a patch exchanges\n",

diff --git a/tutorials/03_node_centered_poisson.ipynb b/tutorials/03_node_centered_poisson.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# Poisson's equation on nodes\n",
+    "# Node-centered Poisson\n",
     "\n",
     "`NodalPoisson` solves $-\\nabla^2\\phi = f$ with the unknowns on the cell corners. It suits\n",
     "codes whose own grid is node-centered, such as particle-in-cell codes that deposit charge on\n",

diff --git a/tutorials/04_non_rectangular_domains.ipynb b/tutorials/04_non_rectangular_domains.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# Domains that are not rectangles\n",
+    "# Non-rectangular domains\n",
     "\n",
     "The base level can be several boxes of cells instead of the whole rectangle. Their union is\n",
     "the domain: an L, a T, a rectangle with a notch. The edges inside the bounding rectangle are a\n",

diff --git a/tutorials/05_halo_exchange.ipynb b/tutorials/05_halo_exchange.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# Halos: stencils on patches\n",
+    "# Halo exchange\n",
     "\n",
     "A field allocated with `halo=h` has `h` cells (or nodes) around every patch. Fill them with\n",
     "`exchange_halos`, and a finite-difference stencil can be applied to each patch on its own,\n",

diff --git a/tutorials/06_regridding.ipynb b/tutorials/06_regridding.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# Regridding: patches that follow the solution\n",
+    "# Regridding\n",
     "\n",
     "Placing patches by hand works for fixed features such as electrodes. For a feature that moves\n",
     "or that you cannot place in advance, let patchwork place them: tag the cells that need finer\n",

diff --git a/tutorials/07_edge_space.ipynb b/tutorials/07_edge_space.ipynb
@@ -5,7 +5,7 @@
    "id": "0",
    "metadata": {},
    "source": [
-    "# The edge space\n",
+    "# Edge space\n",
     "\n",
     "`CompositeEdges` is the space of an electric field next to the potential's nodes: one value per\n",
     "edge of the leaf cells, the line integral of the field along it. It is the field space of an\n",