You can now solve partial differential equations with 3-D geometry.
To do so, there is a new workflow that combines the geometry, mesh,
and boundary conditions into a `PDEModel`

object.
You can also use this workflow for 2-D geometry. For details, see Solve Problems Using PDEModel Objects.

To specify problem coefficients or boundary conditions in 3-D geometry, you can use strings with a syntax similar to that of a 2-D problem. There is a new way of writing functions for coefficients in 3-D geometries. For details, see PDE Coefficients and Boundary Conditions.

To accommodate both 2-D and 3-D geometry, the format of boundary
condition objects changed from that introduced in R2014b. The new
object is BoundaryCondition Properties,
and calling `pdeBoundaryConditions`

now warns that
it will be removed in a future release. If you saved a `pdeBoundaryConditions`

object
in an R2014b-format MAT file, then loading that file in R2015a can
produce an error. Additionally, the syntax for specifying nonconstant
boundary conditions has changed. Functions written in the previous
syntax continue to work for now.

R2014b Syntax | R2015a Syntax |
---|---|

`function bcMatrix = myfun(problem,region,state)` | `function bcMatrix = myfun(region,state)` |

For details, see Changes to Boundary Conditions Object From R2014b.

The main toolbox solvers now support problems with 3-D geometry.
For a listing of functions that do or do not support 3-D geometry,
see Functions That Support 3-D Geometry. Solvers take
a `model`

argument instead of the previous `b`

, `p`

, `e`

, `t`

arguments.
For details, see the function reference pages.

Import the geometry for a 3-D problem in the STL file format
using the `importGeometry`

function.
For details, see Create and View 3-D Geometry.

Create finite element meshes using the `generateMesh`

function.
For 3-D geometry, the meshes consist of tetrahedra. See Mesh Data for [p,e,t] Triples: 3-D.

The `pdeplot3D`

function plots
solutions on the boundaries of 3-D geometry. For details, see Plot 3-D Solutions.

There are two new featured examples related to linear elasticity that have 3-D geometry:

There is also a new example of plotting slices through a 3-D solution: Contour Slices Through a 3-D Solution.

To run the examples at the MATLAB^{®} command line:

echodemo StrainedBracketExample echodemo Eigenvaluesofa3DPlateExample echodemo ContourSlices3DExample

`pdebound`

and `pdegeom`

reference
pages removedThe `pdebound`

and `pdegeom`

reference
pages have been replaced by the Boundary Conditions and 2-D Geometry documentation
categories.

To specify PDE boundary conditions in a modular fashion, per
edge or set of edges, use a `pdeBoundaryConditions`

specification.
For details, see Steps
to Specify a Boundary Conditions Object.

`pdeInterpolant`

object for solution interpolationInterpolate a PDE solution to a set of points using `evaluate`

on
an interpolant. Create the interpolant using `pdeInterpolant`

.

`hyperbolic`

solverYou can include damping in the `hyperbolic`

solver
in matrix form. There is a new example of dynamics
of a damped cantilever beam that shows how to use this feature.

`hyperbolic`

and `parabolic`

solversYou can disable the display of internal ODE solution details
that the `hyperbolic`

and `parabolic`

solvers
report. To disable the display, set the `Stats`

name-value
pair to `'off'`

.

There is a new example of eigenvalues of a circular membrane. View the example here. To run the example at the MATLAB command line:

`echodemo eigsExample`

The meshing (geometry triangulation) functions in `initmesh`

and `adaptmesh`

provide
an enhancement option for increased meshing speed and robustness.
Choose the enhanced algorithm by setting the `MesherVersion`

name-value
pair to `'R2013a'`

. The default `MesherVersion`

value
of `'preR2013a'`

gives the same mesh as previous
toolbox versions.

The enhancement is available in `pdetool`

in
the **Mesh > Parameters > Mesher version** menu.

There is a new example of heat distribution in a radioactive rod. View the example here. To run the example at the MATLAB command line:

`echodemo radioactiveRod`

You can now solve parabolic and hyperbolic equations whose coefficients
depend on the solution *u* or on the gradient of *u*.
Use the `parabolic`

or `hyperbolic`

commands,
or solve the equations using `pdetool`

. For details,
see the function reference pages.

`pdegplot`

labels edges and subdomains`pdegplot`

now optionally labels:

The edges in the geometry

The subdomains in the geometry

To obtain these labels, set the `edgeLabels`

or `subdomainLabels`

name-value
pairs to `'on'`

. For details, see the `pdegplot`

reference
page.

There is a new example of uniform pressure load on a thin plate. View the example here. To run the example at the MATLAB command line:

`echodemo clampedSquarePlateExample`

There is a new example of nonlinear heat transfer in a thin plate. View the example here. To run the example at the MATLAB command line:

`echodemo heatTransferThinPlateExample`

There is a new example of a system of coupled PDEs. View the example here. To run the example at the MATLAB command line:

`echodemo deflectionPiezoelectricActuator`

`pdesmech`

shear strain calculation change The `pdesmech`

function
now calculates shear strain according to the engineering shear strain
definition. This has always been the documented behavior. However,
the previous calculation was performed according to the tensor shear
strain calculation, which gives half the value of the engineering
shear strain.

`pdesmech`

now returns shear strain values
exactly twice as large as before.

Release | Features or Changes with Compatibility Considerations |
---|---|

R2015a | Equation coefficients and boundary conditions for 3-D problems |

R2014b | None |

R2014a | None |

R2013b | None |

R2013a | None |

R2012b | `pdesmech` shear strain calculation change |

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