[benchmark] add bm for testing prj_python_script

inst/extdata/benchmarks/square_1x1_SteadyStateDiffusion_Python/bcs_laplace_eq.py

+import OpenGeoSys
+from math import pi, sin, cos, sinh, cosh
+
+a = 2.0 * pi / 3.0
+
+# analytical solution used to set the Dirichlet BCs
+def solution(x, y):
+    return sin(a * x) * sinh(a * y)
+
+
+# gradient of the analytical solution used to set the Neumann BCs
+def grad_solution(x, y):
+    return a * cos(a * x) * sinh(a * y), a * sin(a * x) * cosh(a * y)
+
+
+# Dirichlet BCs
+class BCTop(OpenGeoSys.BoundaryCondition):
+    def getDirichletBCValue(self, t, coords, node_id, primary_vars):
+        x, y, z = coords
+        assert y == 1.0 and z == 0.0
+        value = solution(x, y)
+        return (True, value)
+
+
+class BCLeft(OpenGeoSys.BoundaryCondition):
+    def getDirichletBCValue(self, t, coords, node_id, primary_vars):
+        x, y, z = coords
+        assert x == 0.0 and z == 0.0
+        value = solution(x, y)
+        return (True, value)
+
+
+class BCBottom(OpenGeoSys.BoundaryCondition):
+    def getDirichletBCValue(self, t, coords, node_id, primary_vars):
+        x, y, z = coords
+        assert y == 0.0 and z == 0.0
+        value = solution(x, y)
+        return (True, value)
+
+
+# Neumann BC
+class BCRight(OpenGeoSys.BoundaryCondition):
+    def getFlux(self, t, coords, primary_vars):
+        x, y, z = coords
+        assert x == 1.0 and z == 0.0
+        value = grad_solution(x, y)[0]
+        Jac = [0.0]  # value does not depend on primary variable
+        return (True, value, Jac)
+
+
+# instantiate BC objects referenced in OpenGeoSys' prj file
+bc_top = BCTop()
+bc_right = BCRight()
+bc_bottom = BCBottom()
+bc_left = BCLeft()

inst/extdata/benchmarks/square_1x1_SteadyStateDiffusion_Python/square_1e3_laplace_eq.prj

+<?xml version="1.0" encoding="ISO-8859-1"?>
+<OpenGeoSysProject>
+    <mesh>square_1x1_quad_1e3.vtu</mesh>
+    <geometry>square_1x1.gml</geometry>
+    <python_script>bcs_laplace_eq.py</python_script>
+    <media>
+        <medium id="0">
+            <phases/>
+            <properties>
+                <property>
+                    <name>diffusion</name>
+                    <type>Constant</type>
+                    <value>1</value>
+                </property>
+                <property>
+                    <name>reference_temperature</name>
+                    <type>Constant</type>
+                    <value>293.15</value>
+                </property>
+            </properties>
+        </medium>
+    </media>
+    <processes>
+        <process>
+            <name>SteadyStateDiffusion</name>
+            <type>STEADY_STATE_DIFFUSION</type>
+            <integration_order>2</integration_order>
+            <process_variables>
+                <process_variable>pressure</process_variable>
+            </process_variables>
+            <secondary_variables>
+                <secondary_variable internal_name="darcy_velocity" output_name="v"/>
+            </secondary_variables>
+            <jacobian_assembler>
+                <type>CentralDifferences</type>
+            </jacobian_assembler>
+        </process>
+    </processes>
+    <time_loop>
+        <processes>
+            <process ref="SteadyStateDiffusion">
+                <nonlinear_solver>basic_newton</nonlinear_solver>
+                <convergence_criterion>
+                    <type>DeltaX</type>
+                    <norm_type>NORM2</norm_type>
+                    <abstol>1.e-6</abstol>
+                </convergence_criterion>
+                <time_discretization>
+                    <type>BackwardEuler</type>
+                </time_discretization>
+                <time_stepping>
+                    <type>SingleStep</type>
+                </time_stepping>
+            </process>
+        </processes>
+        <output>
+            <type>VTK</type>
+            <prefix>square_1e3_neumann</prefix>
+            <variables>
+                <variable> pressure </variable>
+                <variable> v      </variable>
+            </variables>
+            <suffix>_ts_{:timestep}_t_{:time}</suffix>
+        </output>
+    </time_loop>
+    <parameters>
+        <parameter>
+            <name>zero</name>
+            <type>Constant</type>
+            <value>0</value>
+        </parameter>
+    </parameters>
+    <process_variables>
+        <process_variable>
+            <name>pressure</name>
+            <components>1</components>
+            <order>1</order>
+            <initial_condition>zero</initial_condition>
+            <boundary_conditions>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>left</geometry>
+                    <type>Python</type>
+                    <bc_object>bc_left</bc_object>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>right</geometry>
+                    <type>Python</type>
+                    <bc_object>bc_right</bc_object>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>top</geometry>
+                    <type>Python</type>
+                    <bc_object>bc_top</bc_object>
+                </boundary_condition>
+                <boundary_condition>
+                    <geometrical_set>square_1x1_geometry</geometrical_set>
+                    <geometry>bottom</geometry>
+                    <type>Python</type>
+                    <bc_object>bc_bottom</bc_object>
+                </boundary_condition>
+            </boundary_conditions>
+        </process_variable>
+    </process_variables>
+    <nonlinear_solvers>
+        <nonlinear_solver>
+            <name>basic_newton</name>
+            <type>Newton</type>
+            <max_iter>10</max_iter>
+            <linear_solver>general_linear_solver</linear_solver>
+        </nonlinear_solver>
+    </nonlinear_solvers>
+    <linear_solvers>
+        <linear_solver>
+            <name>general_linear_solver</name>
+            <lis>-i cg -p jacobi -tol 1e-16 -maxiter 10000</lis>
+            <eigen>
+                <solver_type>CG</solver_type>
+                <precon_type>DIAGONAL</precon_type>
+                <max_iteration_step>10000</max_iteration_step>
+                <error_tolerance>1e-16</error_tolerance>
+            </eigen>
+            <petsc>
+                <prefix>gw</prefix>
+                <parameters>-gw_ksp_type cg -gw_pc_type bjacobi -gw_ksp_rtol 1e-16 -gw_ksp_max_it 10000</parameters>
+            </petsc>
+        </linear_solver>
+    </linear_solvers>
+</OpenGeoSysProject>

inst/extdata/benchmarks/square_1x1_SteadyStateDiffusion_Python/square_1x1.gml

+<?xml version="1.0" encoding="ISO-8859-1"?>
+<?xml-stylesheet type="text/xsl" href="OpenGeoSysGLI.xsl"?>
+
+<OpenGeoSysGLI xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="http://www.opengeosys.org/images/xsd/OpenGeoSysGLI.xsd" xmlns:ogs="http://www.opengeosys.org">
+    <name>square_1x1_geometry</name>
+    <points>
+        <point id="0" x="0" y="0" z="0" name="ll"/>
+        <point id="1" x="0" y="1" z="0" name="lr"/>
+        <point id="2" x="1" y="0" z="0" name="ul"/>
+        <point id="3" x="1" y="1" z="0" name="ur"/>
+        <point id="4" x="0.5" y="0.5" z="0" name="middle_point"/>
+    </points>
+
+    <polylines>
+        <polyline id="0" name="left">
+            <pnt>0</pnt>
+            <pnt>1</pnt>
+        </polyline>
+        <polyline id="1" name="right">
+            <pnt>2</pnt>
+            <pnt>3</pnt>
+        </polyline>
+        <polyline id="2" name="bottom">
+            <pnt>0</pnt>
+            <pnt>2</pnt>
+        </polyline>
+        <polyline id="3" name="top">
+            <pnt>1</pnt>
+            <pnt>3</pnt>
+        </polyline>
+    </polylines>
+</OpenGeoSysGLI>