# Documentation

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# 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

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

### 3-D Geometry

 `geometryFromMesh` Create 3-D geometry from a triangulated mesh `importGeometry` Import 3-D geometry `pdegplot` Plot PDE geometry

### Boundary Conditions

 `applyBoundaryCondition` Add boundary condition to PDEModel container `findBoundaryConditions` Find boundary condition assignment for a geometric region

### PDE Coefficients

 `findCoefficients` Locate active PDE coefficients `specifyCoefficients` Specify coefficients in a PDE model

### Meshing

 `generateMesh` Create triangular or tetrahedral mesh `pdemesh` Plot PDE mesh `adaptmesh` Adaptive 2-D mesh generation and PDE solution `initmesh` Create initial 2-D mesh `meshToPet` [p,e,t] representation of FEMesh data `jigglemesh` Jiggle internal points of triangular mesh `refinemesh` Refine triangular mesh `pdeent` Indices of triangles neighboring given set of triangles `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

### Initial Conditions

 `findInitialConditions` Locate active initial conditions `setInitialConditions` Give initial conditions or initial solution

### PDE Solvers

 `assembleFEMatrices` Assemble finite element matrices `solvepde` Solve PDE specified in a PDEModel `solvepdeeig` Solve PDE eigenvalue problem specified in a PDEModel `adaptmesh` Adaptive 2-D mesh generation and PDE solution

## Solution Visualization and Interpolation

 `evaluateGradient` Evaluate gradients of PDE solutions at arbitrary points `evaluateCGradient` Evaluate flux of PDE solution `interpolateSolution` Interpolate PDE solution to arbitrary points `pdeplot` Plot solution in 2-D geometry `pdeplot3D` Plot 3-D solution or surface mesh `createPDEResults` Create solution object `evaluate` Interpolate data to selected locations `pdecont` Shorthand command for contour plot `pdecgrad` Flux of PDE solution `pdegrad` Gradient of PDE solution `pdesurf` Shorthand command for surface plot `EigenResults` Contain PDE eigenvalue solution and derived quantities `StationaryResults` Contain time-independent PDE solution and derived quantities `TimeDependentResults` Contain time-dependent PDE solution and derived quantities `pdeInterpolant` Interpolant for nodal data to selected locations