# `pymor.analyticalproblems.domaindescriptions`¶

## Module Contents¶

pymor.analyticalproblems.domaindescriptions.KNOWN_BOUNDARY_TYPES[source]
class pymor.analyticalproblems.domaindescriptions.CircleDomain(domain=(0, 1))[source]

Domain with the topology of a circle, i.e. a line with end points identified.

Parameters

domain

List [x_l, x_r] providing the left and right endpoint.

domain[source]

Methods

dim = 1[source]
property width[source]

Describes a circular sector domain of variable radius.

Parameters

angle

The angle between 0 and 2*pi of the circular sector.

The radius of the circular sector.

arc

The boundary type of the arc.

The boundary type of the two radii.

num_points

The number of points of the polygonal chain approximating the circular boundary.

angle[source]
arc[source]
num_points[source]
class pymor.analyticalproblems.domaindescriptions.CylindricalDomain(domain=([0, 0], [1, 1]), top='dirichlet', bottom='dirichlet')[source]

Describes a cylindrical domain.

Boundary types can be associated edgewise.

Parameters

domain

List of two points defining the lower-left and upper-right corner of the domain. The left and right edge are identified.

top

The boundary type of the top edge.

bottom

The boundary type of the bottom edge.

domain[source]
top[source]
bottom[source]
dim = 2[source]
property diameter[source]
property height[source]
property lower_left[source]
property upper_right[source]
property volume[source]
property width[source]

Describes a disc domain of variable radius.

Parameters

boundary

The boundary type of the boundary.

num_points

The number of points of the polygonal chain approximating the boundary.

boundary[source]
num_points[source]
class pymor.analyticalproblems.domaindescriptions.DomainDescription[source]

Describes a geometric domain along with its boundary.

dim[source]

The dimension of the domain

boundary_types[source]

Set of boundary types the domain has.

property has_dirichlet[source]
property has_neumann[source]
property has_robin[source]
class pymor.analyticalproblems.domaindescriptions.LineDomain(domain=(0, 1), left='dirichlet', right='dirichlet')[source]

Describes an interval domain.

Boundary types can be associated edgewise.

Parameters

domain

List [x_l, x_r] providing the left and right endpoint.

left

The boundary type of the left endpoint.

right

The boundary type of the right endpoint.

domain[source]
left[source]
right[source]

Methods

dim = 1[source]
property width[source]
class pymor.analyticalproblems.domaindescriptions.PolygonalDomain(points, boundary_types, holes=None)[source]

Describes a domain with a polygonal boundary and polygonal holes inside the domain.

Parameters

points

List of points [x_0, x_1] that describe the polygonal chain that bounds the domain.

boundary_types

Either a dictionary `{boundary_type: [i_0, ...], boundary_type: [j_0, ...], ...}` with `i_0, ...` being the ids of boundary segments for a given boundary type (`0` is the line connecting point `0` to `1`, `1` is the line connecting point `1` to `2` etc.), or a function that returns the boundary type for a given coordinate.

holes

List of lists of points that describe the polygonal chains that bound the holes inside the domain.

points[source]
boundary_types[source]
holes[source]
dim = 2[source]
class pymor.analyticalproblems.domaindescriptions.RectDomain(domain=([0, 0], [1, 1]), left='dirichlet', right='dirichlet', top='dirichlet', bottom='dirichlet')[source]

Describes a rectangular domain.

Boundary types can be associated edgewise.

Parameters

domain

List of two points defining the lower-left and upper-right corner of the domain.

left

The boundary type of the left edge.

right

The boundary type of the right edge.

top

The boundary type of the top edge.

bottom

The boundary type of the bottom edge.

domain[source]
left[source]
right[source]
top[source]
bottom[source]
dim = 2[source]
property diameter[source]
property height[source]
property lower_left[source]
property upper_right[source]
property volume[source]
property width[source]
class pymor.analyticalproblems.domaindescriptions.TorusDomain(domain=([0, 0], [1, 1]))[source]

Describes a domain with the topology of a torus.

Parameters

domain

List of two points defining the lower-left and upper-right corner of the domain. The left and right edge are identified, as well as the bottom and top edge

domain[source]
dim = 2[source]
property diameter[source]
property height[source]
property lower_left[source]
property upper_right[source]
property volume[source]
property width[source]