# Partial Differential Equation Toolbox Functions

## PDE Problem Setup

### PDE Problem Setup Basics

 createpde Create PDE model pdetool Open PDE app PDEModel PDE model container

### 2-D Geometry

 pdetool Open PDE app geometryFromEdges Create 2-D geometry pdegplot Plot PDE geometry pdecirc Draw circle pdeellip Draw ellipse pdepoly Draw polygon pderect Draw rectangle csgchk Check validity of Geometry Description matrix csgdel Delete borders between minimal regions decsg Decompose Constructive Solid Geometry into minimal regions pdearcl Interpolation between parametric representation and arc length wgeom Write geometry specification function AnalyticGeometry Properties 2-D geometry description

### 3-D Geometry

 geometryFromMesh Create 3-D geometry from a triangulated mesh importGeometry Import 3-D geometry pdegplot Plot PDE geometry DiscreteGeometry Properties 3-D geometry description

### Boundary Conditions

 BoundaryCondition Properties Boundary condition for PDE model applyBoundaryCondition Add boundary condition to PDEModel container assemb Assemble boundary condition contributions wbound Write boundary condition specification file pdetool Open PDE app

### Meshing

 generateMesh Create triangular or tetrahedral mesh meshToPet [p,e,t] representation of FEMesh data pdetool Open PDE app initmesh Create initial 2-D mesh adaptmesh Adaptive 2-D mesh generation and PDE solution jigglemesh Jiggle internal points of triangular mesh refinemesh Refine triangular mesh tri2grid Interpolate from PDE triangular mesh to rectangular grid pdemesh Plot PDE mesh pdeadgsc Select triangles using relative tolerance criterion pdeadworst Select triangles relative to worst value pdeent Indices of triangles neighboring given set of triangles pdeintrp Interpolate from node data to triangle midpoint data pdejmps Error estimates for adaptation pdeprtni Interpolate from triangle midpoint data to node data pdesdp Indices of points/edges/triangles in set of subdomains pdesde Indices of points/edges/triangles in set of subdomains pdesdt Indices of points/edges/triangles in set of subdomains pdetrg Triangle geometry data pdetriq Triangle quality measure FEMesh Properties Mesh object

### PDE Solvers

 pdetool Open PDE app assempde Assemble finite element matrices and solve elliptic PDE adaptmesh Adaptive 2-D mesh generation and PDE solution pdejmps Error estimates for adaptation pdenonlin Solve nonlinear elliptic PDE problem hyperbolic Solve hyperbolic PDE problem parabolic Solve parabolic PDE problem pdeeig Solve eigenvalue PDE problem assema Assemble area integral contributions assemb Assemble boundary condition contributions poisolv Fast solution of Poisson's equation on rectangular grid poicalc Fast solver for Poisson's equation on rectangular grid poimesh Make regular mesh on rectangular geometry dst Discrete sine transform idst Discrete sine transform poiasma Boundary point matrix contributions for fast solvers of Poisson's equation poiindex Indices of points in canonical ordering for rectangular grid

## Solution Visualization and Interpolation

 pdegplot Plot PDE geometry pdeplot Plot solution in 2-D geometry pdeplot3D Plot 3-D solution or surface mesh pdecont Shorthand command for contour plot pdemesh Plot PDE mesh pdesurf Shorthand command for surface plot createPDEResults Create PDEResults object pdesmech Calculate structural mechanics tensor functions pdecgrad Flux of PDE solution pdegrad Gradient of PDE solution evaluate Interpolate data to selected locations interpolateSolution Interpolate PDE solution to arbitrary points pdeintrp Interpolate from node data to triangle midpoint data pdeprtni Interpolate from triangle midpoint data to node data tri2grid Interpolate from PDE triangular mesh to rectangular grid pdeInterpolant Interpolant for nodal data to selected locations PDEResults PDE results object

## Electrostatics and Magnetostatics

 pdetool Open PDE app

## Structural Mechanics

 pdetool Open PDE app pdesmech Calculate structural mechanics tensor functions

## AC Power Electromagnetics

 pdetool Open PDE app

## DC Conduction and Elliptic Problems

 pdetool Open PDE app

## Heat Transfer and Diffusion

 pdetool Open PDE app

## Eigenvalue Problems

 pdetool Open PDE app pdeeig Solve eigenvalue PDE problem sptarn Solve generalized sparse eigenvalue problem