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+ | ===== ===== | ||

+ | ==== General Information ==== | ||

+ | |||

+ | * **Solver Fortran File:** ''Compute2DNodalGradient.F90'' | ||

+ | * **Solver Name:** ''ElmerIce_MeshAdapt2D(Compute2DNodalGradient)'' | ||

+ | * **Required Output Variable(s):** | ||

+ | * (1) ''g'' (dofs=2) | ||

+ | * **Required Input Variable(s):** | ||

+ | * (1) ''v'' | ||

+ | * **Optional Output Variable(s):** None | ||

+ | * **Optional Input Variable(s):** None | ||

+ | |||

+ | ==== General Description ==== | ||

+ | This is a pseudo solver (i.e. it is not solving an equation). This solver compute the nodal 2D gradient vector <m>g_i={{\partial v}/{\partial x_i}}</m> of a variable //v//. | ||

+ | |||

+ | This is used for example by the mesh adaptation procedure to compute the hessian of //v// ([[mesh:meshadaptation|Mesh Adaptation]]). | ||

+ | |||

+ | By default (//FE consistent average = Logical True//), this is done using a //L²//-projection on the FE mesh; If //FE consistent average = False//, at a given node the derivative is simply the average of the derivatives evaluated at the node in each elements sharing the node. | ||

+ | |||

+ | ==== SIF contents ==== | ||

+ | <code> | ||

+ | |||

+ | Solver 2 | ||

+ | Equation = "Nodal Gradient" | ||

+ | Variable = -dofs 2 "g" | ||

+ | Procedure = "ElmerIce_MeshAdapt2D" "Compute2DNodalGradient" | ||

+ | |||

+ | Optimize Bandwidth = False | ||

+ | |||

+ | Variable Name = string "v" | ||

+ | FE consistent average = Logical True | ||

+ | End | ||

+ | |||

+ | </code> | ||

+ | |||

+ | |||

+ | ==== Example ==== | ||

+ | Examples for anisotropic mesh adaptation can be found under ''[ELMER_TRUNK]/elmerice/Tests/MMG2D_Aniso1'' and ''[ELMER_TRUNK]/elmerice/Tests/MMG2D_Aniso2'', where the mesh size is adapted using 1 or 2 variables (i.e. combining metric informations), respectively. | ||