Geometry and Mesh

Define a geometry and discretize it using a triangular or tetrahedral mesh

Unified finite element analysis workflow uses an fegeometry object to define a geometry. You can simply assign a geometry to the Geometry property of femodel.

Define a geometry using one of these sources:

STL or STEP file. See fegeometry and importGeometry.
Mesh nodes and elements. See fegeometry and geometryFromMesh.
Decomposed geometry matrix or a handle to a geometry function. See geometryFromEdges.
Triangulation or Delaunay triangulation. See fegeometry and Geometry from polyshape.
Basic volumes. See Cuboids, Cylinders, and Spheres.
alphaShape object. See Geometry from alphaShape.
PDE Modeler app for 2-D geometries. See PDE Modeler.

The general PDE workflow, as well as the domain-specific workflows, use a DiscreteGeometry and AnalyticGeometry objects. Typically, you can define these objects using the same sources as for fegeometry.

Mesh a geometry using the generateMesh function. The toolbox uses the finite element method (FEM) to solve PDEs. For details about meshing, see Mesh Data.

For details about the components of geometries and meshes and the relationships between them, see Geometry and Mesh Components.

Functions

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Geometry

Creation and Visualization

`importGeometry`	Import geometry from STL or STEP file
`geometryFromMesh`	Create 2-D or 3-D geometry from mesh
`geometryFromEdges`	Create 2-D geometry from decomposed geometry matrix
`decsg`	Decompose constructive solid 2-D geometry into minimal regions
`multicuboid`	Create geometry formed by several cubic cells
`multicylinder`	Create geometry formed by several cylindrical cells
`multisphere`	Create geometry formed by several spherical cells
`triangulation`	Create `triangulation` object from `fegeometry` (Since R2023b)
`pdegplot`	Plot PDE geometry

Modification

`addCell`	Combine two geometries by adding one inside a cell of another (Since R2021a)
`addFace`	Fill void regions in 2-D and split cells in 3-D geometry
`addVertex`	Add vertex on geometry boundary
`addVoid`	Create void regions inside 3-D geometry (Since R2021a)
`deleteCell`	Delete geometry cells (Since R2025a)
`extrude`	Vertically extrude 2-D geometry or specified faces of 3-D geometry (Since R2020b)
`intersect`	Boolean intersection between 3-D geometries (Since R2025a)
`mergeCells`	Merge geometry cells (Since R2023b)
`rotate`	Rotate geometry
`subtract`	Boolean subtraction of one 3-D geometry from another (Since R2025a)
`scale`	Scale geometry
`translate`	Translate geometry
`union`	Boolean union of 3-D geometries (Since R2025a)

Queries

`cellEdges`	Find edges belonging to boundaries of specified cells (Since R2021a)
`cellFaces`	Find faces belonging to specified cells (Since R2021a)
`faceEdges`	Find edges belonging to specified faces (Since R2021a)
`facesAttachedToEdges`	Find faces attached to specified edges (Since R2021a)
`findCell`	Find cells by coordinates of points located inside them (Since R2025a)
`nearestEdge`	Find edges nearest to specified point (Since R2021a)
`nearestFace`	Find faces nearest to specified point (Since R2021a)

PDE Modeler App

`pdecirc`	Draw circle in PDE Modeler app
`pdeellip`	Draw ellipse in PDE Modeler app
`pdepoly`	Draw polygon in PDE Modeler app
`pderect`	Draw rectangle in PDE Modeler app

Mesh

`generateMesh`	Create triangular or tetrahedral mesh
`meshQuality`	Evaluate shape quality of mesh elements
`findElements`	Find mesh elements in specified region
`findNodes`	Find mesh nodes in specified region
`area`	Area of 2-D mesh elements
`volume`	Volume of 3-D mesh elements
`pdemesh`	Plot PDE mesh
`pdeplot`	Plot solution or mesh for 2-D problem
`pdeplot3D`	Plot solution or surface mesh for 3-D problem
`pdeviz`	Create and plot PDE visualization object (Since R2021a)

Legacy Functions

Geometry

`csgdel`	Delete boundaries between subdomains
`pdearcl`	Represent arc lengths as parametrized curve
`wgeom`	Write geometry function to file

Mesh

`adaptmesh`	Create adaptive 2-D mesh and solve PDE
`initmesh`	Create initial 2-D mesh
`meshToPet`	`[p,e,t]` representation of `FEMesh` data
`jigglemesh`	(Not recommended) Jiggle internal points of triangular mesh
`refinemesh`	Refine triangular mesh

Objects

`fegeometry`	Geometry object for finite element analysis (Since R2023a)
`DiscreteGeometry`	Discrete 2-D or 3-D geometry description
`AnalyticGeometry`	Analytic 2-D geometry description
`FEMesh`	Mesh object

Properties

PDEVisualization Properties

PDE visualization of mesh and nodal results (Since R2021a)

Apps

PDE Modeler

Create complex 2-D geometries by drawing, overlapping, and rotating basic shapes

Topics

Geometry

Geometry and Mesh Components
Learn about the components of geometries and meshes and the relationships between them within a model object.
STL File Import
Import a 2-D or 3-D geometry from an STL file.
STEP File Import
Import a 3-D geometry from a STEP file.
Geometry from Triangulated Mesh
Reconstruct a geometry from a tetrahedral mesh and from a planar multidomain mesh.
Geometry from polyshape
Reconstruct a geometry from a triangulated mesh created by the MATLAB^® polyshape function.
Geometry from alphaShape
Reconstruct a geometry from a triangulated surface mesh created by the MATLAB alphaShape function.
2-D Geometry Creation at Command Line
Use constructive solid geometry (CSG) modeling approach to combine basic shapes at the command line.
Parameterized Function for 2-D Geometry Creation
Create a 2-D geometry by using a parameterized function.
Cuboids, Cylinders, and Spheres
Create a 3-D geometry by stacking or nesting three basic volumes.
3-D Multidomain Geometry from 2-D Geometry
Extrude a 2-D geometry imported as an STL file into a 3-D geometry.
Multidomain Geometry Reconstructed from Mesh
Split a single-domain block geometry into two domains.
Sphere in Cube
Create a nested multidomain geometry consisting of a unit sphere and a cube.
Battery Module Geometry
Create a battery module geometry consisting of nine cells, connectors at both ends, the casing, and an air gap between the cells and the casing.
Cat Geometry
Create a geometry representing a cat's head by using the geometry creation and modification functions.
Pillow Block Bearing Geometry
Create a geometry of a pillow block bearing by using the MATLAB® functions polyshape and polybuffer, and the geometry modification functions available in Partial Differential Equation™ Toolbox.

Mesh

Mesh Data
Recommended workflow uses FEMesh objects to represent meshes.
Generate Mesh
Adjust meshes by using additional arguments of generateMesh.
Find Mesh Elements and Nodes by Location
Find mesh elements and nodes by their geometric location or proximity to a particular point or node.
Assess Quality of Mesh Elements
Evaluate the shape quality of mesh elements.

Legacy Mesh

Mesh Data as [p,e,t] Triples
Legacy workflow uses [p,e,t] triples to represent meshes.
Poisson's Equation with Point Source and Adaptive Mesh Refinement
Solve a Poisson's equation with a delta-function point source on the unit disk using the adaptmesh function.