Geometry and Mesh
Define a geometry using one of these sources:
Decomposed geometry matrix or a handle to a geometry function. See
Basic volumes. See Cuboids, Cylinders, and Spheres.
alphaShapeobject. See Geometry from alphaShape.
PDE Modelerapp for 2-D geometries. See PDE Modeler.
The general PDE workflow, as well as the domain-specific workflows, use a
Typically, you can define these objects using the same sources as for
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.
Creation and Visualization
|Import geometry from STL or STEP file|
|Create 2-D or 3-D geometry from mesh|
|Create 2-D geometry from decomposed geometry matrix|
|Decompose constructive solid 2-D geometry into minimal regions|
|Create geometry formed by several cubic cells|
|Create geometry formed by several cylindrical cells|
|Create geometry formed by several spherical cells|
|Plot PDE geometry|
|Combine two geometries by adding one inside a cell of another (Since R2021a)|
|Fill void regions in 2-D and split cells in 3-D geometry (Since R2020a)|
|Add vertex on geometry boundary (Since R2019b)|
|Create void regions inside 3-D geometry (Since R2021a)|
|Merge geometry cells (Since R2023b)|
|Rotate geometry (Since R2020a)|
|Scale geometry (Since R2020a)|
|Translate geometry (Since R2020a)|
|Vertically extrude 2-D geometry or specified faces of 3-D geometry (Since R2020b)|
|Find edges belonging to boundaries of specified cells (Since R2021a)|
|Find faces belonging to specified cells (Since R2021a)|
|Find edges belonging to specified faces (Since R2021a)|
|Find faces attached to specified edges (Since R2021a)|
|Find edges nearest to specified point (Since R2021a)|
|Find faces nearest to specified point (Since R2021a)|
PDE Modeler App
|Create triangular or tetrahedral mesh|
|Evaluate shape quality of mesh elements|
|Find mesh elements in specified region|
|Find mesh nodes in specified region|
|Area of 2-D mesh elements|
|Volume of 3-D mesh elements|
|Plot PDE mesh|
|Plot solution or mesh for 2-D problem|
|Plot solution or surface mesh for 3-D problem|
|Create and plot PDE visualization object (Since R2021a)|
|Delete boundaries between subdomains|
|Represent arc lengths as parametrized curve|
|Write geometry function to file|
|PDE Modeler||Create complex 2-D geometries by drawing, overlapping, and rotating basic shapes|
- 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®
- Geometry from alphaShape
Reconstruct a geometry from a triangulated surface mesh created by the MATLAB
- 2-D Geometry Creation at Command Line
Use constructive solid geometry (CSG) modeling approach to combine basic shapes at the command line.
- Parametrized Function for 2-D Geometry Creation
Create a 2-D geometry by using a parametrized 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.
- Mesh Data
Recommended workflow uses
FEMeshobjects to represent meshes.
- Generate Mesh
Adjust a mesh by using additional arguments of the
- 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.
- 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