Multidomain Geometry Reconstructed from Mesh
This example shows how to split a single-domain block geometry into two domains. The first part of the example generates a mesh and divides the mesh elements into two groups. The second part of the example creates a two-domain geometry based on this division.
Generate Mesh and Split Its Elements into Two Groups
Create a PDE model.
modelSingleDomain = createpde;
Import the geometry.
Generate and plot a mesh.
msh = generateMesh(modelSingleDomain); figure pdemesh(modelSingleDomain)
Obtain the nodes and elements of the mesh.
nodes = msh.Nodes; elements = msh.Elements;
Find the x-coordinates of the geometric centers of all elements of the mesh. First, create an array of the same size as
elements that contains the x-coordinates of the nodes forming the mesh elements. Each column of this vector contains the x-coordinates of 10 nodes that form an element.
elemXCoords = reshape(nodes(1,elements),10,);
Compute the mean of each column of this array to get a vector of the x-coordinates of the element geometric centers.
elemXCoordsGeometricCenter = mean(elemXCoords);
Assume that all elements have the same region ID and create a matrix
ElementIdToRegionId = ones(1,size(elements,2));
Find IDs of all elements for which the x-coordinate of the geometric center exceeds 60.
idx = elemXCoordsGeometricCenter > 60;
For the elements with centers located beyond x = 60, change the region IDs to 2.
ElementIdToRegionId(idx) = 2;
Create Geometry with Two Cells
Create a new PDE model.
modelTwoDomain = createpde;
geometryFromMesh, import the mesh. Assign the elements to two cells based on their IDs.
ans = DiscreteGeometry with properties: NumCells: 2 NumFaces: 56 NumEdges: 121 NumVertices: 68 Vertices: [68x3 double]
Plot the geometry, displaying the cell labels.
Highlight the elements from cell 1 in red and the elements from cell 2 in green.
elementIDsCell1 = findElements(modelTwoDomain.Mesh,"region","Cell",1); elementIDsCell2 = findElements(modelTwoDomain.Mesh,"region","Cell",2); figure pdemesh(modelTwoDomain.Mesh.Nodes, ... modelTwoDomain.Mesh.Elements(:,elementIDsCell1), ... "FaceColor","red") hold on pdemesh(modelTwoDomain.Mesh.Nodes, ... modelTwoDomain.Mesh.Elements(:,elementIDsCell2), ... "FaceColor","green")
When you divide mesh elements into groups and then create a multidomain geometry based on this division, the mesh might be invalid for the multidomain geometry. For example, elements in a cell might be touching by only a node or an edge instead of sharing a face. In this case,
geometryFromMesh throws an error saying that neighboring elements in the mesh are not properly connected.