Create an Mesh Object

You can create a Mesh object by

mesh = Mesh(v4e, x); % 1D line mesh / v4e: 2 x nrE
mesh = Mesh(v4e, x, y); % 2D triangular mesh / v4e: 3 x nrE
mesh = Mesh(v4e, x, y, z); % 3D tetrahedral mesh / v4e: 4 x nrE

where v4e(:,i) contains vertex index for each element.

Or, you can get uniform mesh by

% 1D uniform mesh in (0,1) with 10 elements.
mesh = line2linemesh(0,1,10);
% 2D uniform mesh in (0,1)x(0,2) with 10 x 20 (x2) elements.
mesh = rect2rectmesh(0,1,0,2,10,20);
% 3D uniform mesh in (0,1)x(0,2)x(0,3) with 10 x 20 x 30 (x6) elements
mesh = cube2cubemesh(0,1,0,2,0,3,10,20,30);

Display Mesh

To show the mesh, you can use show() method.

mesh.show(); % default configuration
mesh.show('FaceColor', 'r'); % change face color
mesh.show(ax, __); % specify target axes

where the optional arguments are from plot for 1D and patch for 2D and 3D

Facet Information

When a Mesh object is created, facet information can be obtained, where

• v4f is the vertex index for each facet
• x4f is the x-coordinate for each facet (or y, z)
• nx4f is the facet normal for each facet (or y, z)
• J4f is the Jacobian for each facet
• e4f is the neighboring elements' index for each facet
• ef4f is the neighboring elements' local facet index for each facet
• fmask and fmask_neg are the local facet vertex index of an element (positive / negative)

All information about facets can be obtained seperately for interior/boundary facets
by changing f to f0 or fb.

If you want to access to the first neighboring element to 10th facet, you can use

mesh.e4f(1,10); % gives the first neighboring element of 10th facet
mesh.ef4f(1,10); % gives the positive element's which facet is 10th facet.

In other words,

mesh.v4f(:,10) == mesh.v4e(mesh.fmask(:,mesh.ef4f(1,10)), mesh.e4f(1,10))

Or, for negative element (the second neighboring element)

mesh.v4f(:,10) == mesh.v4e(mesh.fmask_neg(:,mesh.ef4f(2,10)), mesh.e4f(2,10))

Note that e4fb and ef4fb are 1 x nrfb vectors since there is only one neighboring element.

mesh = rect2trimesh(); % get uniform triangular mesh
figure;
mesh.show(); % display mesh
hold on;
plot(mesh.x4fb, mesh.y4fb, 'r', 'linewidth', 2); % plot boundary edges
plot(mesh.x4f0, mesh.y4f0, 'b', 'linewidth', 1.5); % plot interior edges

Affine Information

In finite element assembly, affine information of physical triangles is often used.

One can access to the affine information by

% dX/dR
mesh.xr, mesh.xs, mesh.xm
mesh.yr, mesh.ys, mesh.ym
mesh.zr, mesh.zs, mesh.zm

% Jacobial
mesh.J

% dR/dX
mesh.rx, mesh.ry, mesh.rz
mesh.sx, mesh.sy, mesh.sz
mesh.mx, mesh.my, mesh.mz

Here, each property is 1 x nrE vector.

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