diff --git a/Electrostatics/microstrip.pro b/Electrostatics/microstrip.pro index 27fee8211cbce18252da9b31ad9cec4cb9e1baf6..7da07c2340e4734ef3cd91d8d8b85268a5e8effe 100644 --- a/Electrostatics/microstrip.pro +++ b/Electrostatics/microstrip.pro @@ -35,12 +35,13 @@ (called "Electrode" below) and to 0 V on the ground. A homogeneous Neumann boundary condition (zero flux of the displacement field, i.e. n.d = 0) is imposed on the left boundary of the domain to account for the symmetry of the - problem, as well as on the top and right boundaries that truncate the - simulation domain. */ + problem. The domain is truncated on the top and right with a homogeneous + Dirichlet boundary condition (v = 0), assumed to be imposed sufficiently far + away from the microstrip. */ Group { /* One starts by giving explicit meaningful names to the Physical regions - defined in the "microstrip.msh" mesh file. This model comprises only + defined in the "microstrip.msh" mesh file. This model comprises only 2 volume regions and 2 surface regions. */ Air = Region[101]; @@ -48,6 +49,7 @@ Group { Ground = Region[120]; Electrode = Region[121]; + SurfInf = Region[130]; /* We now define abstract regions to be used below in the definition of the scalar electric potential formulation: @@ -61,9 +63,9 @@ Group { Since there are no non-homogeneous Neumann conditions in this particular example, Sur_Neu_Ele is defined as empty. - - Note that volume elements are those that correspond to the higher dimension - of the model at hand (2D elements here), surface elements correspond to the + + Note that volume elements are those that correspond to the higher dimension + of the model at hand (2D elements here), surface elements correspond to the higher dimension of the model minus one (1D elements here). */ @@ -82,7 +84,7 @@ Function { } Constraint { - /* The Dirichlet boundary condition is also defined piecewise. + /* The Dirichlet boundary condition is also defined piecewise. The constraint "Dirichlet_Ele" is invoked in the FunctionSpace below. */ @@ -90,6 +92,7 @@ Constraint { Case { { Region Ground; Value 0.; } { Region Electrode; Value 1.e-3; } + { Region SurfInf; Value 0; } } } } @@ -131,7 +134,7 @@ FunctionSpace { { Name sn; NameOfCoef vn; Function BF_Node; Support Dom_Hgrad_v_Ele; Entity NodesOf[ All ]; } // using "NodesOf[All]" instead of "NodesOf[Dom_Hgrad_v_Ele]" is an - // optimization, which avoids explicitly building the list of + // optimization, which avoids explicitly building the list of // all the nodes } Constraint { @@ -234,7 +237,7 @@ Formulation { expressions than the second one. In our case it should be expressed in terms of the FE expansion of "v" at the present system solution, i.e. when the coefficients vn_k in the expansion of "v = Sum_k vn_k sn_k" are - unknown. This is indicated by prefixing the braces with "Dof" (degrees of + unknown. This is indicated by prefixing the braces with "Dof" (degrees of freedom), which leads to the following density: [ epsilon[] * Dof{d v} , {d v} ], @@ -252,7 +255,7 @@ Formulation { a so-called linear term that contributes to the right-hand side of the linear system. - Both choices are commonly used in different contexts, and we shall often + Both choices are commonly used in different contexts, and we shall often come back in subsequent tutorials. */ { Name Electrostatics_v; Type FemEquation; @@ -270,13 +273,13 @@ Formulation { Integral { [ nd[] , {v} ]; In Sur_Neu_Ele; Jacobian Sur; Integration Int; } - All the terms in the Equation environment are added, + All the terms in the Equation environment are added, and an implicit "= 0" is considered at the end. */ } } } -/* In the Resolution environment we specify what to do with a weak formulation: +/* In the Resolution environment we specify what to do with a weak formulation: here we simply generate a linear system, solve it and save the solution (.res file) to disk. */ diff --git a/ElectrostaticsFloating/floating.pro b/ElectrostaticsFloating/floating.pro index 040a4ee1db8f8e20387e3492f86cf81be76a6dcb..290bba93bf22ffa08f5d1c74f8e8b757b8b756c0 100644 --- a/ElectrostaticsFloating/floating.pro +++ b/ElectrostaticsFloating/floating.pro @@ -85,11 +85,13 @@ Function { } Constraint { - /* The Dirichlet boundary condition on the local electric potential is no - longer used. The microstrip and the ground are herein treated as electrodes, - whose voltage is imposed with the "SetGlobalPotential" constraint below. */ + /* The Dirichlet boundary condition on the local electric potential is only + used for the homogeneous condition on the top and right boundaries. The + microstrip and the ground are now treated as electrodes, whose voltage is + imposed with the "SetGlobalPotential" constraint below. */ { Name Dirichlet_Ele; Type Assign; Case { + { Region SurfInf; Value 0; } } }