[web] Added all elliptic benchmarks.

ProcessLib/GroundwaterFlow/CMakeLists.txt

@@ -34,8 +34,6 @@ foreach(mesh_size 1e0 1e1 1e2 1e3)
         ABSTOL 1e-1 RELTOL 1e-1
         DIFF_DATA
         cube_1x1x1_hex_${mesh_size}.vtu cube_${mesh_size}_neumann_pcs_0_ts_1_t_1.000000.vtu D1_left_front_N1_right pressure
-        VIS
-        cube_${mesh_size}_neumann_pcs_0_ts_1_t_1.000000.vtu
     )
 endforeach()
 
@@ -90,6 +88,7 @@ foreach(mesh_size 1e0 1e1 1e2 1e3 1e4)
         ABSTOL 1e-1 RELTOL 1e-1
         DIFF_DATA
         square_1x1_quad_${mesh_size}.vtu square_${mesh_size}_neumann_pcs_0_ts_1_t_1.000000.vtu D1_left_bottom_N1_right pressure
+        VIS square_${mesh_size}_neumann_pcs_0_ts_1_t_1.000000.vtu
     )
 endforeach()
 

web/content/docs/benchmarks/elliptic/groundwater-flow-dirichlet.md

++++
+date = "2017-02-15T11:17:39+01:00"
+title = "Groundwater Flow (Dirichlet)"
+project = "Elliptic/square_1x1_GroundWaterFlow/square_1e2.prj"
+author = "Dmitri Naumov"
+
+[menu]
+  [menu.benchmarks]
+    weight = 1
+    parent = "elliptic"
+
++++
+
+{{< project-link >}}
+
+## Equations
+
+We start with simple linear homogeneous elliptic problem:
+$$
+\begin{equation}
+k\; \Delta h = 0 \quad \text{in }\Omega
+\end{equation}$$
+w.r.t boundary conditions
+$$
+\eqalign{
+h(x) = g_D(x) &\quad \text{on }\Gamma_D,\cr
+k\;{\partial h(x) \over \partial n} = g_N(x) &\quad \text{on }\Gamma_N,
+}$$
+
+where $h$ could be hydraulic head, the subscripts $D$ and $N$ denote the Dirichlet- and Neumann-type boundary conditions, $n$ is the normal vector pointing outside of $\Omega$, and $\Gamma = \Gamma_D \cup \Gamma_N$ and $\Gamma_D \cap \Gamma_N = \emptyset$.
+
+## Problem specification and analytical solution
+
+We solve the Laplace equation on a square domain $[0\times 1]^2$ with $k = 1$ w.r.t. the specific boundary conditions:
+$$
+\eqalign{
+h(x,y) = 1 &\quad \text{on } (x=0,y) \subset \Gamma_D,\cr
+h(x,y) = -1 &\quad \text{on } (x=1,y) \subset \Gamma_D,\cr
+k\;{\partial h(x,y) \over \partial n} = 0 &\quad \text{on }\Gamma_N.
+}$$
+The solution of this problem is
+$$
+h(x,y) = 1 - 2x.
+$$
+
+## Input files
+
+TODO: {asset:247:link}
+
+The main project file is `square_1e2.prj`. It describes the processes to be solved and the related process variables together with their initial and boundary conditions. It also references the mesh and geometrical objects defined on the mesh.
+
+As of now a small portion of possible inputs is implemented; one can change:
+ - the mesh file
+ - the geometry file
+ - introduce more/different Dirichlet boundary conditions (different geometry or values)
+
+The geometries used to specify the boundary conditions are given in the `square_1x1.gml` file.
+
+The input mesh `square_1x1_quad_1e2.vtu` is stored in the VTK file format and can be directly visualized in Paraview for example.
+
+## Running simulation
+
+To start the simulation (after successful compilation) run:
+```bash
+$ ogs square_1e2.prj
+```
+
+It will produce some output and write the computed result into the `square_1e2_result.dat`, which is a simple list of values for every node of the mesh.
+
+The output on the console will be similar to the following one (ignore the spurious error messages "Could not find POINT..."):
+```
+error: GEOObjects::getGeoObject(): Could not find POINT "left" in geometry.
+error: GEOObjects::getGeoObject(): Could not find POINT "right" in geometry.
+info: Initialize processes.
+info: Solve processes.
+info: -> max. absolute value of diagonal entries = 2.666667e-06
+info: -> penalty scaling = 1.000000e+10
+info: ------------------------------------------------------------------
+info: *** LIS solver computation
+info: -> solve
+initial vector x      : user defined
+precision             : double
+linear solver         : CG
+preconditioner        : none
+convergence condition : ||b-Ax||_2 <= 1.0e-16 * ||b-Ax_0||_2
+matrix storage format : CSR
+linear solver status  : normal end
+
+info:    iteration: 28/1000000
+
+info:    residual: 3.004753e-17
+
+info: ------------------------------------------------------------------
+
+```
+
+A major part of the output was produced by the linear equation solver (LIS in this case).
+
+## Results and evaluation
+
+{{< vis path="Elliptic/square_1x1_GroundWaterFlow/square_1e2_pcs_0_ts_1_t_1.000000.vtu" >}}
+
+The result, written in the `square_1e2_result.dat`, can be visualized with Paraview, for example, by including the values into the `square_1x1_quad_1e2.vtu` file in the `PointData` section:
+```
+...
+
+
+1
+0.8
+0.6
+0.4
+0.2
+...
+-0.6
+-0.8
+-1
+
+
+```
+(The next releases shall simplify this procedure.)

web/content/docs/benchmarks/elliptic/groundwater-flow-neumann.md

@@ -2,13 +2,14 @@
 date = "2017-01-31T14:27:10+01:00"
 author = "Dmitri Naumov"
 title = "Groundwater flow (Neumann)"
+project = "Elliptic/square_1x1_GroundWaterFlow/square_1e2_neumann.prj"
 
 aliases = [ "/docs/benchmarks/" ] # First benchmark page
 
 [menu]
   [menu.benchmarks]
     parent = "elliptic"
-    weight = 0
+    weight = 2
 +++
 
 ## Equations
@@ -112,7 +113,7 @@ A last major part of the output was produced by the linear equation solver (LIS
 
 ## Results and evaluation
 
-{{< vis path="Elliptic/square_1x1_GroundWaterFlow/square_1e2_pcs_0_ts_1_t_1.000000.vtu" >}}
+{{< vis path="Elliptic/square_1x1_GroundWaterFlow/square_1e2_neumann_pcs_0_ts_1_t_1.000000.vtu" >}}
 
 Compared to the analytical solution presented above the results are very good but in a single point:
 

web/content/docs/benchmarks/elliptic/groundwater-flow-robin.md

++++
+date = "2017-02-15T11:46:49+01:00"
+title = "Groundwater Flow (Robin)"
+project = "Elliptic/line_1_GroundWaterFlow/line_1e1_robin_left_picard.prj"
+author = "Dmitri Naumov"
+
+[menu]
+
+  [menu.benchmarks]
+    weight = 3
+    parent = "elliptic"
+
++++
+
+{{< project-link >}}
+
+## Equations
+
+We start with simple linear homogeneous elliptic problem:
+$$
+\begin{equation}
+k\; \Delta h = 0 \quad \text{in }\Omega
+\end{equation}$$
+w.r.t boundary conditions
+$$
+\eqalign{
+h(x) = g_D(x) &\quad \text{on }\Gamma_D,\cr
+k{\partial h(x) \over \partial n} = g_N(x) &\quad \text{on }\Gamma_N,
+}$$
+where $h$ could be hydraulic head, the subscripts $D$ and $N$ denote the Dirichlet- and Neumann-type boundary conditions, $n$ is the normal vector pointing outside of $\Omega$, and $\Gamma = \Gamma_D \cup \Gamma_N$ and $\Gamma_D \cap \Gamma_N = \emptyset$.
+
+## Problem specification and analytical solution
+
+We solve the Laplace equation on a line domain $[0\times 1]^2$ with $k = 1$ w.r.t. the specific boundary conditions:
+
+$$
+\eqalign{
+h(x,y) = 1 &\quad \text{on } (x=0,y) \subset \Gamma_D,\cr
+h(x,y) = 1 &\quad \text{on } (x,y=0) \subset \Gamma_D,\cr
+k {\partial h(x,y) \over \partial n} = 1 &\quad \text{on } (x=1,y) \subset \Gamma_N,\cr
+k {\partial h(x,y) \over \partial n} = 0 &\quad \text{on } (x,y=1) \subset \Gamma_N.
+}$$
+
+The solution of this problem is
+$$
+\begin{equation}
+h(x,y) = 1 + \sum_{k=1}^\infty A_k \sin\bigg(C_k y\bigg) \sinh\bigg(C_k x\bigg),
+\end{equation}
+$$

web/layouts/shortcodes/project-link.html

+<a href="https://github.com/ufz/ogs-data/blob/master/{{ .Page.Params.project }}">
+  Project file on GitHub &nbsp; <i class="fi-arrow-right"></i> &nbsp;
+</a>