From c9d1f46d998f5a3df5ac88b762eba0be3b5296af Mon Sep 17 00:00:00 2001
From: Christophe Geuzaine <cgeuzaine@ulg.ac.be>
Date: Thu, 15 Mar 2018 18:35:36 +0100
Subject: [PATCH] Update microstrip.pro
---
Electrostatics/microstrip.pro | 648 +++++++++++++++++-----------------
1 file changed, 324 insertions(+), 324 deletions(-)
diff --git a/Electrostatics/microstrip.pro b/Electrostatics/microstrip.pro
index f194945..e3524fe 100644
--- a/Electrostatics/microstrip.pro
+++ b/Electrostatics/microstrip.pro
@@ -1,324 +1,324 @@
-/* -------------------------------------------------------------------
- Tutorial 1 : electrostatic field of a microstrip
-
- Features:
- - Physical and abstract regions
- - Scalar FunctionSpace with Dirichlet constraint
- - Galerkin term for stiffness matrix
-
- To compute the solution in a terminal:
- getdp microstrip -solve EleSta_v
- getdp microstrip -pos Map
- getdp microstrip -pos Cut
-
- To compute the solution interactively from the Gmsh GUI:
- File > Open > microstrip.pro
- Run (button at the bottom of the left panel)
- ------------------------------------------------------------------- */
-
-/* In this first tutorial we consider the calculation of the electric field
- given a static distribution of electric potential. This corresponds to an
- "electrostatic" physical model, obtained by combining the time-invariant
- Maxwell-Ampere equation (Curl e = 0, with e the electric field) with Gauss'
- law (Div d = rho, with d the displacement field and rho the charge density)
- and the dielectric constitutive law (d = epsilon e, with epsilon the
- dielectric permittivity).
-
- Since Curl e = 0, e can be derived from a scalar electric potential v, such
- that e = -Grad v. Plugging this potential in Gauss' law and using the
- constitutive law leads to a scalar Poisson equation in terms of the electric
- potential: -Div(epsilon Grad v) = rho.
-
- We consider here the special case where rho = 0, to model a conducting
- microstrip line on top of a dielectric substrate. A Dirichlet boundary
- condition sets the potential to 1 mV on the boundary of the microstrip line
- (called "Electrode" below) and 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
- modelling domain. */
-
-Group {
- /* One starts by giving explicit meaningful names to the Physical regions
- defined in the "microstrip.msh" mesh file. We only use 2 volume regions and
- 2 surface regions in this model. */
-
- Air = Region[101];
- Diel1 = Region[111];
-
- Ground = Region[120];
- Electrode = Region[121];
-
- /* We now define abstract regions to be used below in the definition of the
- scalar electric potential formulation:
-
- Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
- Sur_Neumann_Ele: surface where non homogeneous Neumann boundary conditions
- (on n.d == epsilon n.Grad v) are imposed
-
- Vol_xxx groups contain only volume elements of the mesh (triangles here).
- Sur_xxx groups contain only surface elements of the mesh (lines here).
-
- Since there are no non-homogeneous Neumann conditions in the model,
- Sur_Neumann_Ele is defined as empty.
- */
-
- Vol_Ele = Region[ {Air, Diel1} ];
- Sur_Neumann_Ele = Region[ {} ];
-}
-
-Function {
- /* Material laws (here the dielectric permittivity) are defined as piecewise
- functions (note the square brackets), in terms of the above defined
- physical regions. */
-
- eps0 = 8.854187818e-12;
- epsilon[Air] = 1. * eps0;
- epsilon[Diel1] = 9.8 * eps0;
-}
-
-Constraint {
- /* As for material laws, the Dirichlet boundary condition is defined
- piecewise. The constraint "Dirichlet_Ele" is invoked in the FunctionSpace
- below. */
-
- { Name Dirichlet_Ele; Type Assign;
- Case {
- { Region Ground; Value 0.; }
- { Region Electrode; Value 1.e-3; }
- }
- }
-}
-
-Group{
- /* The domain of definition of a FunctionSpace lists all regions on which a
- field is defined.
-
- Contrary to Vol_xxx and Sur_xxx regions, which contain only volume or
- surface regions, resp., domains of definition Dom_xxx regions may contain
- both volume and surface regions. Hence the use of the prefixes Vol_, Sur_
- and Dom_ to avoid confusions.*/
-
- Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neumann_Ele} ];
-}
-
-FunctionSpace {
- /* The function space in which we shall pick the electric scalar potential "v"
- solution is definied 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 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)
-
- The FE expansion of the unknown field "v" reads
-
- 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. */
-
- { Name Hgrad_v_Ele; Type Form0;
- BasisFunction {
- { 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 allows GetDP to not explicitly build the list of
- // all nodes
- }
- Constraint {
- { NameOfCoef vn; EntityType NodesOf; NameOfConstraint Dirichlet_Ele; }
- }
- }
-}
-
-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
- (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
- be used to map the reference line segment onto segments in 3D space (1D <->
- 3D). */
-
- { Name Vol ;
- Case {
- { Region All ; Jacobian Vol ; }
- }
- }
-}
-
-Integration {
- /* A Gauss quadrature rule with 4 points is used for all integrations below. */
-
- { Name Int ;
- Case { { Type Gauss ;
- Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
- { GeoElement Quadrangle ; NumberOfPoints 4 ; } }
- }
- }
- }
-}
-
-Formulation {
- /* The syntax of the Formulation section is a harder nut to crack. So let's
- deal with it carefully.
-
- A GetDP Formulation encodes a so-called weak formulation of the original
- partial differential equation, i.e. of -Div(epsilon Grad v) = 0. This weak
- formulation involves finding v such that
-
- (-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,
- 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
- functions v in the function space Hgrad_v_Ele such that
-
- (epsilon Grad v, Grad v')_Vol_Ele = 0
-
- holds for all v'. Finally, our choice here is to use a Gakerkin method,
- where the test functions v' are the same basis functions ("sn_k") as the
- ones used to interpolate the unknown potential v.
-
- The "Integral" statement in the Formulation is a symbolic representation of
- this weak formulation. It has got 4 semicolon separated arguments:
- * the density [.,.] to be integrated (note the square brackets instead of
- the parentheses), with the test-functions (always) after the comma
- * the domain of integration,
- * the Jacobian of the transformation reference element <-> real element,
- * the integration method to be used.
-
- In the density, braces around a quantity (such as "{v}") indicate that this
- quantity belongs to a FunctionSpace. Differential operators can be applied
- within braces (such as "{Grad v}"); in particular the symbol "d" represents
- the exterior derivative, and it is a synonym of "Grad" when applied to a
- scalar function (such as "{d v}").
-
- What can be a bit confusing is that the two comma-separated terms of the
- density are not interpreted exactly in the same way. Let us unravel this in
- detail.
-
- As the Galerkin method uses as test functions the same basis functions
- "sn_k" as for the unknown field "v", the second term in the density should
- be something like this [ ... , basis_functions_of {d v} ]. However, since
- the second term is always devoted to test functions, the operator
- "basis_functions_of" would always be there. It can therefore be made
- implicit, and, according to the GetDP syntax, it is omitted. So, one writes
- simply [ ... , {d v} ].
-
- The first term, on the other hand, can contain a much wider variety of
- 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", which leads
- to the following density:
-
- [ epsilon[] * Dof{d v} , {d v} ],
-
- a so-called bilinear term that will contribute to the stiffness matrix of
- the electrostatic problem at hand.
-
- Another option, which would not work here, is to evaluate the first
- argument with the last available already computed solution, i.e. simply
- perform the interpolation with known coefficients vn_k. For this the Dof
- prefix operator would be omitted and we would have:
-
- [ epsilon[] * {d v} , {d v} ],
-
- a so-called linear term that will contribute to the right-hand side of the
- linear system.
-
- Both choices are commonly used in different contexts, and we shall come
- back on this often in subsequent tutorials. */
- { Name Electrostatics_v; Type FemEquation;
- Quantity {
- { Name v; Type Local; NameOfSpace Hgrad_v_Ele; }
- }
- Equation {
- Integral { [ epsilon[] * Dof{d v} , {d v} ];
- In Vol_Ele; Jacobian Vol; Integration Int; }
- }
- }
-}
-
-Resolution {
- { Name EleSta_v;
- System {
- { Name Sys_Ele; NameOfFormulation Electrostatics_v; }
- }
- Operation {
- Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
- }
- }
-}
-
-/* Post-processing is done in two parts.
-
- The first part defines, in terms of the Formulation, which itself refers to
- the FunctionSpace, a number of quantities that can be evaluated at the
- postprocessing stage. The three quantities defined here are:
- - the scalar vector potential,
- - the electric field,
- - the electric displacement.
-
- The second part consists in defining groups of post-processing operations,
- which can be invoked separately. The first group is invoked by default when
- Gmsh is run interactively. Each Operation specifies
- - a quantity to be eveluated,
- - the region on which the evaluation is done,
- - the name of the output file.
- The generated post-processing files are automatically displayed by Gmsh if
- the "Merge result automatically" option is enabled (which is the default). */
-
-PostProcessing {
- { Name EleSta_v; NameOfFormulation Electrostatics_v;
- Quantity {
- { Name v; Value {
- Local { [ {v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
- }
- }
- { Name e; Value {
- Local { [ -{d v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
- }
- }
- { Name d; Value {
- Local { [ -epsilon[] * {d v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
- }
- }
- }
- }
-}
-
-e = 1.e-7; // tolerance to ensure that the cut is inside the simulation domain
-h = 2.e-3; // vertical position of the cut
-
-PostOperation {
- { Name Map; NameOfPostProcessing EleSta_v;
- Operation {
- Print [ v, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_v.pos" ];
- Print [ e, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_e.pos" ];
- Print [ e, OnLine {{e,h,0}{14.e-3,h,0}}{60}, File "Cut_e.pos" ];
- }
- }
- { Name Cut; NameOfPostProcessing EleSta_v;
- // same cut as above, with more points and exported in raw text format
- Operation {
- Print [ e, OnLine {{e,e,0}{14.e-3,e,0}} {500}, Format TimeTable, File "Cut_e.txt" ];
- }
- }
-}
+/* -------------------------------------------------------------------
+ Tutorial 1 : electrostatic field of a microstrip
+
+ Features:
+ - Physical and abstract regions
+ - Scalar FunctionSpace with Dirichlet constraint
+ - Galerkin term for stiffness matrix
+
+ To compute the solution in a terminal:
+ getdp microstrip -solve EleSta_v
+ getdp microstrip -pos Map
+ getdp microstrip -pos Cut
+
+ To compute the solution interactively from the Gmsh GUI:
+ File > Open > microstrip.pro
+ Run (button at the bottom of the left panel)
+ ------------------------------------------------------------------- */
+
+/* In this first tutorial we consider the calculation of the electric field
+ given a static distribution of electric potential. This corresponds to an
+ "electrostatic" physical model, obtained by combining the time-invariant
+ Faraday equation (Curl e = 0, with e the electric field) with Gauss'
+ law (Div d = rho, with d the displacement field and rho the charge density)
+ and the dielectric constitutive law (d = epsilon e, with epsilon the
+ dielectric permittivity).
+
+ Since Curl e = 0, e can be derived from a scalar electric potential v, such
+ that e = -Grad v. Plugging this potential in Gauss' law and using the
+ constitutive law leads to a scalar Poisson equation in terms of the electric
+ potential: -Div(epsilon Grad v) = rho.
+
+ We consider here the special case where rho = 0, to model a conducting
+ microstrip line on top of a dielectric substrate. A Dirichlet boundary
+ condition sets the potential to 1 mV on the boundary of the microstrip line
+ (called "Electrode" below) and 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
+ modelling domain. */
+
+Group {
+ /* One starts by giving explicit meaningful names to the Physical regions
+ defined in the "microstrip.msh" mesh file. We only use 2 volume regions and
+ 2 surface regions in this model. */
+
+ Air = Region[101];
+ Diel1 = Region[111];
+
+ Ground = Region[120];
+ Electrode = Region[121];
+
+ /* We now define abstract regions to be used below in the definition of the
+ scalar electric potential formulation:
+
+ Vol_Ele : volume where -Div(epsilon Grad v) = 0 is solved
+ Sur_Neumann_Ele: surface where non homogeneous Neumann boundary conditions
+ (on n.d == epsilon n.Grad v) are imposed
+
+ Vol_xxx groups contain only volume elements of the mesh (triangles here).
+ Sur_xxx groups contain only surface elements of the mesh (lines here).
+
+ Since there are no non-homogeneous Neumann conditions in the model,
+ Sur_Neumann_Ele is defined as empty.
+ */
+
+ Vol_Ele = Region[ {Air, Diel1} ];
+ Sur_Neumann_Ele = Region[ {} ];
+}
+
+Function {
+ /* Material laws (here the dielectric permittivity) are defined as piecewise
+ functions (note the square brackets), in terms of the above defined
+ physical regions. */
+
+ eps0 = 8.854187818e-12;
+ epsilon[Air] = 1. * eps0;
+ epsilon[Diel1] = 9.8 * eps0;
+}
+
+Constraint {
+ /* As for material laws, the Dirichlet boundary condition is defined
+ piecewise. The constraint "Dirichlet_Ele" is invoked in the FunctionSpace
+ below. */
+
+ { Name Dirichlet_Ele; Type Assign;
+ Case {
+ { Region Ground; Value 0.; }
+ { Region Electrode; Value 1.e-3; }
+ }
+ }
+}
+
+Group{
+ /* The domain of definition of a FunctionSpace lists all regions on which a
+ field is defined.
+
+ Contrary to Vol_xxx and Sur_xxx regions, which contain only volume or
+ surface regions, resp., domains of definition Dom_xxx regions may contain
+ both volume and surface regions. Hence the use of the prefixes Vol_, Sur_
+ and Dom_ to avoid confusions.*/
+
+ Dom_Hgrad_v_Ele = Region[ {Vol_Ele, Sur_Neumann_Ele} ];
+}
+
+FunctionSpace {
+ /* The function space in which we shall pick the electric scalar potential "v"
+ solution is definied 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 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)
+
+ The FE expansion of the unknown field "v" reads
+
+ 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. */
+
+ { Name Hgrad_v_Ele; Type Form0;
+ BasisFunction {
+ { 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 allows GetDP to not explicitly build the list of
+ // all nodes
+ }
+ Constraint {
+ { NameOfCoef vn; EntityType NodesOf; NameOfConstraint Dirichlet_Ele; }
+ }
+ }
+}
+
+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
+ (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
+ be used to map the reference line segment onto segments in 3D space (1D <->
+ 3D). */
+
+ { Name Vol ;
+ Case {
+ { Region All ; Jacobian Vol ; }
+ }
+ }
+}
+
+Integration {
+ /* A Gauss quadrature rule with 4 points is used for all integrations below. */
+
+ { Name Int ;
+ Case { { Type Gauss ;
+ Case { { GeoElement Triangle ; NumberOfPoints 4 ; }
+ { GeoElement Quadrangle ; NumberOfPoints 4 ; } }
+ }
+ }
+ }
+}
+
+Formulation {
+ /* The syntax of the Formulation section is a harder nut to crack. So let's
+ deal with it carefully.
+
+ A GetDP Formulation encodes a so-called weak formulation of the original
+ partial differential equation, i.e. of -Div(epsilon Grad v) = 0. This weak
+ formulation involves finding v such that
+
+ (-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,
+ 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
+ functions v in the function space Hgrad_v_Ele such that
+
+ (epsilon Grad v, Grad v')_Vol_Ele = 0
+
+ holds for all v'. Finally, our choice here is to use a Gakerkin method,
+ where the test functions v' are the same basis functions ("sn_k") as the
+ ones used to interpolate the unknown potential v.
+
+ The "Integral" statement in the Formulation is a symbolic representation of
+ this weak formulation. It has got 4 semicolon separated arguments:
+ * the density [.,.] to be integrated (note the square brackets instead of
+ the parentheses), with the test-functions (always) after the comma
+ * the domain of integration,
+ * the Jacobian of the transformation reference element <-> real element,
+ * the integration method to be used.
+
+ In the density, braces around a quantity (such as "{v}") indicate that this
+ quantity belongs to a FunctionSpace. Differential operators can be applied
+ within braces (such as "{Grad v}"); in particular the symbol "d" represents
+ the exterior derivative, and it is a synonym of "Grad" when applied to a
+ scalar function (such as "{d v}").
+
+ What can be a bit confusing is that the two comma-separated terms of the
+ density are not interpreted exactly in the same way. Let us unravel this in
+ detail.
+
+ As the Galerkin method uses as test functions the same basis functions
+ "sn_k" as for the unknown field "v", the second term in the density should
+ be something like this [ ... , basis_functions_of {d v} ]. However, since
+ the second term is always devoted to test functions, the operator
+ "basis_functions_of" would always be there. It can therefore be made
+ implicit, and, according to the GetDP syntax, it is omitted. So, one writes
+ simply [ ... , {d v} ].
+
+ The first term, on the other hand, can contain a much wider variety of
+ 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", which leads
+ to the following density:
+
+ [ epsilon[] * Dof{d v} , {d v} ],
+
+ a so-called bilinear term that will contribute to the stiffness matrix of
+ the electrostatic problem at hand.
+
+ Another option, which would not work here, is to evaluate the first
+ argument with the last available already computed solution, i.e. simply
+ perform the interpolation with known coefficients vn_k. For this the Dof
+ prefix operator would be omitted and we would have:
+
+ [ epsilon[] * {d v} , {d v} ],
+
+ a so-called linear term that will contribute to the right-hand side of the
+ linear system.
+
+ Both choices are commonly used in different contexts, and we shall come
+ back on this often in subsequent tutorials. */
+ { Name Electrostatics_v; Type FemEquation;
+ Quantity {
+ { Name v; Type Local; NameOfSpace Hgrad_v_Ele; }
+ }
+ Equation {
+ Integral { [ epsilon[] * Dof{d v} , {d v} ];
+ In Vol_Ele; Jacobian Vol; Integration Int; }
+ }
+ }
+}
+
+Resolution {
+ { Name EleSta_v;
+ System {
+ { Name Sys_Ele; NameOfFormulation Electrostatics_v; }
+ }
+ Operation {
+ Generate[Sys_Ele]; Solve[Sys_Ele]; SaveSolution[Sys_Ele];
+ }
+ }
+}
+
+/* Post-processing is done in two parts.
+
+ The first part defines, in terms of the Formulation, which itself refers to
+ the FunctionSpace, a number of quantities that can be evaluated at the
+ postprocessing stage. The three quantities defined here are:
+ - the scalar vector potential,
+ - the electric field,
+ - the electric displacement.
+
+ The second part consists in defining groups of post-processing operations,
+ which can be invoked separately. The first group is invoked by default when
+ Gmsh is run interactively. Each Operation specifies
+ - a quantity to be eveluated,
+ - the region on which the evaluation is done,
+ - the name of the output file.
+ The generated post-processing files are automatically displayed by Gmsh if
+ the "Merge result automatically" option is enabled (which is the default). */
+
+PostProcessing {
+ { Name EleSta_v; NameOfFormulation Electrostatics_v;
+ Quantity {
+ { Name v; Value {
+ Local { [ {v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
+ }
+ }
+ { Name e; Value {
+ Local { [ -{d v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
+ }
+ }
+ { Name d; Value {
+ Local { [ -epsilon[] * {d v} ]; In Dom_Hgrad_v_Ele; Jacobian Vol; }
+ }
+ }
+ }
+ }
+}
+
+e = 1.e-7; // tolerance to ensure that the cut is inside the simulation domain
+h = 2.e-3; // vertical position of the cut
+
+PostOperation {
+ { Name Map; NameOfPostProcessing EleSta_v;
+ Operation {
+ Print [ v, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_v.pos" ];
+ Print [ e, OnElementsOf Dom_Hgrad_v_Ele, File "mStrip_e.pos" ];
+ Print [ e, OnLine {{e,h,0}{14.e-3,h,0}}{60}, File "Cut_e.pos" ];
+ }
+ }
+ { Name Cut; NameOfPostProcessing EleSta_v;
+ // same cut as above, with more points and exported in raw text format
+ Operation {
+ Print [ e, OnLine {{e,e,0}{14.e-3,e,0}} {500}, Format TimeTable, File "Cut_e.txt" ];
+ }
+ }
+}
--
GitLab