Mesh

A background mesh and a background grid are often used interchangeably in MPM literature, but Tesserae keeps them separate. A mesh stores the geometry of the background domain, while a grid is a state container generated from that mesh. Grid fields such as mass, momentum, velocity, and force live on the grid; coordinates and spacing come from the mesh.

A simulation typically shares one mesh between the grid, particles, and basis weights. This keeps coordinates and particle-grid connectivity consistent across the calculation.

Info

MPM workflows currently use CartesianMesh. FEMesh is used for finite-element calculations; IGAMesh is used for isogeometric calculations. See Finite element calculations and Isogeometric analysis calculations.

Cartesian mesh

Tesserae.CartesianMesh — Type

CartesianMesh([T,] h, (xmin, xmax), (ymin, ymax)...; warn=true, block_size_log2=Val(2))

Construct a uniform Cartesian mesh with scalar spacing h (same in all directions). If an axis length is not divisible by h, the upper bound is expanded to cover the requested domain. Set warn=false to suppress the expansion warning. block_size_log2 sets the block decomposition used by ThreadPartition and SpArray grids generated from this mesh.

Examples

julia> CartesianMesh(1.0, (0,3), (1,4))
4×4 CartesianMesh{2, Float64, Vector{Float64}, 2}:
 [0.0, 1.0]  [0.0, 2.0]  [0.0, 3.0]  [0.0, 4.0]
 [1.0, 1.0]  [1.0, 2.0]  [1.0, 3.0]  [1.0, 4.0]
 [2.0, 1.0]  [2.0, 2.0]  [2.0, 3.0]  [2.0, 4.0]
 [3.0, 1.0]  [3.0, 2.0]  [3.0, 3.0]  [3.0, 4.0]

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Tesserae.spacing — Function

spacing(::CartesianMesh)

Return the spacing of the mesh.

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Tesserae.volume — Function

volume(::CartesianMesh)

Return the volume of the mesh.

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Tesserae.extract — Method

extract(mesh::CartesianMesh, (xmin, xmax), (ymin, ymax)...)

Extract a portion of the mesh. The extracted mesh retains the original origin and spacing.

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Tesserae.isinside — Function

isinside(x::Vec, mesh::CartesianMesh)

Check if x is inside the mesh.

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Tesserae.findcell — Function

findcell(x::Vec, mesh::CartesianMesh)

Return the cell index where x is located.

Examples

julia> mesh = CartesianMesh(1, (0,5), (0,5))
6×6 CartesianMesh{2, Float64, Vector{Float64}, 2}:
 [0.0, 0.0]  [0.0, 1.0]  [0.0, 2.0]  [0.0, 3.0]  [0.0, 4.0]  [0.0, 5.0]
 [1.0, 0.0]  [1.0, 1.0]  [1.0, 2.0]  [1.0, 3.0]  [1.0, 4.0]  [1.0, 5.0]
 [2.0, 0.0]  [2.0, 1.0]  [2.0, 2.0]  [2.0, 3.0]  [2.0, 4.0]  [2.0, 5.0]
 [3.0, 0.0]  [3.0, 1.0]  [3.0, 2.0]  [3.0, 3.0]  [3.0, 4.0]  [3.0, 5.0]
 [4.0, 0.0]  [4.0, 1.0]  [4.0, 2.0]  [4.0, 3.0]  [4.0, 4.0]  [4.0, 5.0]
 [5.0, 0.0]  [5.0, 1.0]  [5.0, 2.0]  [5.0, 3.0]  [5.0, 4.0]  [5.0, 5.0]

julia> findcell(Vec(1.5, 1.5), mesh)
CartesianIndex(2, 2)

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