Partial Differential Equations Toolbox

Reference

This chapter contains detailed descriptions of most of the functions in the Partial Differential Equation (PDE) Toolbox. Some of the functions that are used by the graphical user interface (GUI) function pdetool are not listed in this chapter because they are not supposed to be used
directly -- they are called from pdetool.

Commands Grouped by Function

PDE Algorithms

Function	Purpose
adaptmesh	Adaptive mesh generation and PDE solution.
assema	Assemble area integral contributions.
assemb	Assemble boundary condition contributions
assempde	Assemble the stiffness matrix and right-hand side of a PDE problem.
hyperbolic	Solve hyperbolic PDE problem.
parabolic	Solve parabolic PDE problem.
pdeeig	Solve eigenvalue PDE problem.
pdenonlin	Solve nonlinear PDE problem.
poisolv	Fast solution of Poisson's equation on a rectangular grid.

Function	Purpose
pdecirc	Draw circle.
pdeellip	Draw ellipse.
pdemdlcv	Convert PDE Toolbox 1.0 Model M-files
pdepoly	Draw polygon.
pderect	Draw rectangle.
pdetool	PDE Toolbox graphical user interface (GUI).

User Interface Algorithms

Geometry Algorithms

Function	Purpose
csgchk	Check validity of Geometry Description Matrix.
csgdel	Delete borders between minimal regions.
decsg	Decompose Constructive Solid Geometry into minimal regions.
initmesh	Create initial triangular mesh.
jigglemesh	Jiggle internal points of a triangular mesh.
pdearcl	Interpolation between parametric representation and arc length.
poimesh	Make regular mesh on a rectangular geometry.
refinemesh	Refine a triangular mesh.
wbound	Write boundary condition specification file.
wgeom	Write geometry specification function.

Plot Functions

Function	Purpose
pdecont	Shorthand command for contour plot.
pdegplot	Plot a PDE geometry.
pdemesh	Plot a PDE triangular mesh.
pdeplot	Generic PDE Toolbox plot function.
pdesurf	Shorthand command for surface plot.

Function	Purpose
dst	Discrete sine transform.
idst	Inverse discrete sine transform.
pdeadgsc	Select triangles using a relative tolerance criterion.
pdeadworst	Select triangles relative to the worst value.
pdecgrad	The flux of a PDE solution.
pdeent	Indices of triangles neighboring a given set of triangles.
pdegrad	The gradient of a PDE solution.
pdeintrp	Interpolate from node data to triangle midpoint data.
pdejmps	Error estimates for adaption.
pdeprtni	Interpolate from triangle midpoint data to node data.
pdesde	Indices of edges in a set of subdomains.
pdesdp	Indices of points in a set of subdomains.
pdesdt	Indices of triangles in a set of subdomains.
pdesmech	Calculate structural mechanics tensor functions.
pdetrg	Triangle geometry data.
pdetriq	Triangle quality measure.
poiasma	Boundary point matrix contributions for fast solvers of Poisson's equation.
poicalc	Fast solver for Poisson's equation on a rectangular grid.
poiindex	Indices of points in canonical ordering for rectangular grid.
sptarn	Solve generalized sparse eigenvalue problem.
tri2grid	Interpolate from PDE triangular mesh to rectangular grid.

Function	Purpose
pdebound	Boundary M-file.
pdegeom	Geometry M-file.

User Defined Algorithms

Demonstration Programs

Function	Purpose
pdedemo1	Exact solution of Poisson's equation on unit disk.
pdedemo2	Solve Helmholtz's equation and study the reflected waves.
pdedemo3	Solve a minimal surface problem.
pdedemo4	Solve PDE problem using subdomain decomposition.
pdedemo5	Solve a parabolic PDE (the heat equation).
pdedemo6	Solve a hyperbolic PDE (the wave equation).
pdedemo7	Adaptive solution with point source.
pdedemo8	Solve Poisson's equation on rectangular grid.

Partial Differential Equations Toolbox Reference

adaptmesh