diff --git a/Electrostatics/microstrip.pro b/Electrostatics/microstrip.pro index c37beb886192b89ef509c4971ff5b860491d5457..54c453e5dec5e1ebae4cbfce0bd218016ccf8167 100644 --- a/Electrostatics/microstrip.pro +++ b/Electrostatics/microstrip.pro @@ -104,10 +104,10 @@ Group{ FunctionSpace { /* The function space in which we shall pick the electric scalar potential "v" - solution is definied by + solution is defined by - a domain of definition (the "Support": "Dom_Hgrad_v_Ele") - a type ("Form0" means scalar field) - - a set of scalar basis functions ("BF_Node" means nodal basis functions) + - a set of basis functions ("BF_Node" means scalar nodal basis functions) - a set of entities to which the basis functions are associated ("Entity": here all the nodes of the domain of definition "NodesOf[All]") - a constraint (here the Dirichlet boundary conditions) @@ -116,11 +116,11 @@ FunctionSpace { v(x,y) = Sum_k vn_k sn_k(x,y) - where the "vn_k" are the nodal values (connectors) and "sn_k(x,y)" the - nodal basis functions. Not all connectors are unknowns of the FE problem, - due to the "Constraint", which assigns particular values to the nodes of - the Ground and Electrode regions. GetDP deals with that automatically on - basis of the definition of the FunctionSpace. */ + where the "vn_k" coefficients are the nodal values (connectors) and + "sn_k(x,y)" the nodal basis functions. Not all connectors are unknowns of + the FE problem, due to the "Constraint", which assigns particular values to + the nodes of the Ground and Electrode regions. GetDP deals with that + automatically on basis of the definition of the FunctionSpace. */ { Name Hgrad_v_Ele; Type Form0; BasisFunction { @@ -128,7 +128,7 @@ FunctionSpace { Support Dom_Hgrad_v_Ele; Entity NodesOf[ All ]; } // using "NodesOf[All]" instead of "NodesOf[Dom_Hgrad_v_Ele]" is an // optimization, which allows GetDP to not explicitly build the list of - // all nodes + // all the nodes } Constraint { { NameOfCoef vn; EntityType NodesOf; NameOfConstraint Dirichlet_Ele; } @@ -140,8 +140,8 @@ Jacobian { /* Jacobians are used to specify the mapping between elements in the mesh and the reference elements (defined in standardized unit cells) over which integration is performed. "Vol" represents the classical 1-to-1 mapping - between elements of identical geometrical dimension, i.e. in this case a - reference triangle/quadrangle onto triangles/quadrangles in the z=0 plane + between identical spatial dimensions, i.e. in this case a reference + triangle/quadrangle onto triangles/quadrangles in the z=0 plane (2D <-> 2D). "Sur" would be used to map the reference triangle/quadrangle onto triangles/quadrangles in a 3D space (2D <-> 3D), or to map the reference line segment onto segments in 2D space (1D <-> 2D). "Lin" would @@ -178,15 +178,15 @@ Formulation { (-Div(epsilon Grad v) , v')_Vol_Ele = 0 holds for all so-called "test-functions" v', where (.,.)_D denotes an inner - product over the domain D. If the test-functions v' are differentiable, + product over a domain D. If the test-functions v' are differentiable, integration by parts using Green's identity leads to finding v such that (epsilon Grad v, Grad v')_Vol_Ele + (epsilon n.Grad v, v')_Bnd_Vol_Ele = 0 holds for all v', where Bnd_Vol_Ele is the boundary of Vol_Ele. In our - microstrip example this surface term vanishes, as either there is no test - function v' (on the Dirichlet boundary) or the "epsilon n.Grad v" is zero - (on the homogeneous Neumann boundary). We are thus eventually looking for + microstrip example this surface term vanishes, as there is either no test + function v' (on the Dirichlet boundary), or "epsilon n.Grad v" is zero + (on the homogeneous Neumann boundary. We are thus eventually looking for functions v in the function space Hgrad_v_Ele such that (epsilon Grad v, Grad v')_Vol_Ele = 0