Boundary condition for PDE model
A BoundaryCondition
object specifies the
type of PDE boundary condition on a set of geometry boundaries. A PDEModel
object contains a vector of BoundaryCondition
objects in its BoundaryConditions
property.
Specify boundary conditions for your model using the applyBoundaryCondition
function.
BCType
— Type of boundary condition'dirichlet'
| 'neumann'
| 'mixed'
Boundary type, returned as 'dirichlet'
,
'neumann'
, or 'mixed'
.
Example: applyBoundaryCondition(model,'dirichlet','Face',3,'u',0)
Data Types: char
RegionType
— Geometric region type'Face'
for 3-D geometry | 'Edge'
for 2-D geometryGeometric region type, returned as 'Face'
for 3-D
geometry or 'Edge'
for 2-D geometry.
Example: applyBoundaryCondition(model,'dirichlet','Face',3,'u',0)
Data Types: char
| string
RegionID
— Geometric region IDGeometric region ID, returned as a vector of positive integers. Find the
region IDs by using pdegplot
with the
'FaceLabels'
(3-D) or 'EdgeLabels'
(2-D) value set to 'on'
.
Example: applyBoundaryCondition(model,'dirichlet','Face',3:6,'u',0)
Data Types: double
r
— Dirichlet condition h*u = r
zeros(N,1)
(default) | vector with N elements | function handleDirichlet condition h*u = r
, returned as a vector with
N elements or a function handle. N
is the number of PDEs in the system. For the syntax of the function handle
form of r
, see Nonconstant Boundary Conditions.
Example: 'r',[0;4;-1]
Data Types: double
| function_handle
Complex Number Support: Yes
h
— Dirichlet condition h*u = r
eye(
N)
(default) | N-by-N matrix | vector with N^2 elements | function handleDirichlet condition h*u = r
, returned as an
N-by-N matrix, a vector with
N^2 elements, or a function handle.
N is the number of PDEs in the system. For the syntax
of the function handle form of h
, see Nonconstant Boundary Conditions.
Example: 'h',[2,1;1,2]
Data Types: double
| function_handle
Complex Number Support: Yes
g
— Generalized Neumann condition n·(c×
∇u) + qu = g
zeros(
N,1)
(default) | vector with N elements | function handleGeneralized Neumann condition n·(c×
∇u) + qu =
g
, returned as a vector with N elements or
a function handle. N is the number of PDEs in the system.
For scalar PDEs, the generalized Neumann condition is n·(c
∇u) + qu =
g
. For the syntax of the function handle form of
g
, see Nonconstant Boundary Conditions.
Example: 'g',[3;2;-1]
Data Types: double
| function_handle
Complex Number Support: Yes
q
— Generalized Neumann condition n·(c×
∇u) + qu = g
zeros(
N)
(default) | N-by-N matrix | vector with N^2
elements | function handleGeneralized Neumann condition n·(c×
∇u) + qu =
g
, returned as an N-by-N
matrix, a vector with N^2
elements, or
a function handle. N is the number of PDEs in the system.
For the syntax of the function handle form of q
, see
Nonconstant Boundary Conditions.
Example: 'q',eye(3)
Data Types: double
| function_handle
Complex Number Support: Yes
u
— Dirichlet conditionszeros(
N,1)
(default) | vector of up to N elements | function handleDirichlet conditions, returned as a vector of up to N
elements or as a function handle. If u
has less than
N elements, then you must also use
EquationIndex
. The u
and
EquationIndex
arguments must have the same length. If
u
has N elements, then specifying
EquationIndex
is optional.
For the syntax of the function handle form of u
, see
Nonconstant Boundary Conditions.
Example: applyBoundaryCondition(model,'dirichlet','Face',[2,4,11],'u',0)
Data Types: double
Complex Number Support: Yes
EquationIndex
— Index of the known u
components1:
N (default) | vector of integers with entries from 1
to
NIndex of the known u
components, returned as a vector
of integers with entries from 1
to N.
EquationIndex
and u
must have the
same length.
Example: applyBoundaryCondition(model,'mixed','Face',[2,4,11],'u',[3,-1],'EquationIndex',[2,3])
Data Types: double
Vectorized
— Vectorized function evaluation'off'
(default) | 'on'
Vectorized function evaluation, returned as 'on'
or
'off'
. This evaluation applies when you pass a
function handle as an argument. To save time in function handle evaluation,
specify 'on'
, assuming that your function handle computes
in a vectorized fashion. See Vectorization (MATLAB). For details of
this evaluation, see Nonconstant Boundary Conditions.
Example: applyBoundaryCondition(model,'dirichlet','Face',[2,4,11],'u',@ucalculator,'Vectorized','on')
Data Types: char
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