new HodgeDecomposition(geometry)
This class computes the hodge decomposition of a vector field on a surface mesh.
Parameters:
| Name | Type | Description |
|---|---|---|
geometry |
module:Core.Geometry | The input geometry of the mesh this class acts on. |
Properties:
| Name | Type | Description |
|---|---|---|
edgeIndex |
Object | A dictionary mapping each edge of the input mesh to a unique index. |
hodge1 |
module:LinearAlgebra.SparseMatrix | The hodge star 1-form matrix of the input mesh. |
hodge2 |
module:LinearAlgebra.SparseMatrix | The hodge star 2-form matrix of the input mesh. |
d0 |
module:LinearAlgebra.SparseMatrix | The exterior derivaitve 0-form matrix of the input mesh. |
d1 |
module:LinearAlgebra.SparseMatrix | The exterior derivaitve 1-form matrix of the input mesh. |
hodge1Inv |
module:LinearAlgebra.SparseMatrix | The inverse hodge star 1-form matrix of the input mesh. |
hodge2Inv |
module:LinearAlgebra.SparseMatrix | The inverse hodge star 2-form matrix of the input mesh. |
d0T |
module:LinearAlgebra.SparseMatrix | Transpose of the exterior derivaitve 0-form matrix of the input mesh. |
d1T |
module:LinearAlgebra.SparseMatrix | Transpose of the exterior derivaitve 1-form matrix of the input mesh. |
A |
module:LinearAlgebra.SparseMatrix | The 0-form laplace matrix d0^T star1 d0 of the input mesh. |
B |
module:LinearAlgebra.SparseMatrix | The 2-form matrix d1 star1^-1 d1^T of the input mesh. |
Methods
-
computeExactComponent(omega)
-
Computes the 0-form potential α by solving the system 𝛿dα = 𝛿ω.
Parameters:
Name Type Description omegamodule:LinearAlgebra.DenseMatrix A 1-form on the edges of the input mesh.
Returns:
The exact component dα of ω.
-
computeCoExactComponent(omega)
-
Computes the 2-form potential β by solving the system d𝛿β = dω.
Parameters:
Name Type Description omegamodule:LinearAlgebra.DenseMatrix A 1-form on the edges of the input mesh.
Returns:
The coexact component 𝛿β of ω.
-
computeHarmonicComponent(omega, dAlpha, deltaBeta)
-
Computes the harmonic component γ = ω - dα - 𝛿β of ω.
Parameters:
Name Type Description omegamodule:LinearAlgebra.DenseMatrix A 1-form on the edges of the input mesh.
dAlphamodule:LinearAlgebra.DenseMatrix The exact component of ω.
deltaBetamodule:LinearAlgebra.DenseMatrix The coexact component of ω.
Returns: