This page is based on a Jupyter notebook.

Problem description

Static fracture opening under a constant pressure

Consider a line fracture $[-a_0, a_0] \times \{0\}$ ($a_0$ = 0.1) with no external loading and an internal fluid pressure of $p=1$ was applied to the fracture surfaces. The results are compared to the analytical solution (Sneddon et al., 1969) for the fracture half-opening: \begin{eqnarray} u(x,0) = \frac{2 p a_0}{ E’} \sqrt{1-(x/a_0)^2} , \label{eq:sneddon_2D_static} \end{eqnarray}

where $u$ is the displacement $E'$ is the plane strain Young’s modulus ($E' = E/(1-\nu^2)$) with $\nu$ is Poisson`s ratio, $p$ is the fluid pressure inside the fracture. To account for the infinite boundaries in the closed-form solution, we considered a large finite domain $ [-10a_o,10a_o] \times [-10a_o,10a_o]$. The effective element size, $h$, is $1\times10^{-2}$.

Schematic view of Sneddon problem and Boundary conditions.

In order to have a static pressurized fracture, add, $\texttt{static}$ in the project file. It’s important to note that static pressurized fracture implementation assumes $p=1$. Yoshioka et al., 2019 discussed using real material properties and rescaling the phase-field energy functional.

Input data

The material and geometrical properties are listed in the Table below. It’s worth noting that the properties are dimensionless and scaled.

Name	Value	Symbol
Young’s modulus	1	$E$
Poisson’s ratio	0.15	$\nu$
Fracture toughness	1	$G_{c}$
Regularization parameter	2$h$	$\ell_s$
Pressure	1	$p$
Length	2	$L$
Height	2	$H$
Initial crack length	0.2	$2a_0$

import math… (click to toggle)

import math
import os
import time
from pathlib import Path
from subprocess import run

import gmsh
import matplotlib.pyplot as plt
import numpy as np
import ogstools as ot
import pyvista as pv
from ogstools.msh2vtu import msh2vtu

… (click to toggle)

pi = math.pi
plt.rcParams["text.usetex"] = True

E = 1.0… (click to toggle)

E = 1.0
nu = 0.15
Gc = 1.0
P = 1.0
h = 0.01


Orientation = 0
a0 = 0.1  # half of the initial crack length
n_slices = (
    2 * (round(3.0 * a0 / h)) + 1
)  # number of slices for calcute width of fracture

phasefield_model = "AT1"

h_list = [0.01]  # list of mesh sizes (h)
# h_list =[0.01, 0.005, 0.0025]  # list of mesh sizes (h), for mesh sensitivity

Output directory and project file

# file's name… (click to toggle)

# file's name
prj_name = "Kregime_Static.prj"
meshname = "mesh_full_pf"

out_dir = Path(os.environ.get("OGS_TESTRUNNER_OUT_DIR", "_out"))
if not out_dir.exists():
    out_dir.mkdir(parents=True)

Mesh generation

def mesh_generation(lc, lc_fine):… (click to toggle)

def mesh_generation(lc, lc_fine):
    """
    lc ... characteristic length for coarse meshing
    lc_fine ... characteristic length for fine meshing
    """
    L = 4.0  # Length
    H = 4.0  # Height
    b = 0.4  # Length/Height of subdomain with fine mesh

    # Before using any functions in the Python API, Gmsh must be initialized
    gmsh.initialize()
    gmsh.option.setNumber("General.Terminal", 1)
    gmsh.model.add("rectangle")

    # Dimensions
    dim1 = 1
    dim2 = 2

    # Points
    gmsh.model.geo.addPoint(-L / 2, -H / 2, 0, lc, 1)
    gmsh.model.geo.addPoint(L / 2, -H / 2, 0, lc, 2)
    gmsh.model.geo.addPoint(L / 2, H / 2, 0, lc, 3)
    gmsh.model.geo.addPoint(-L / 2, H / 2, 0, lc, 4)
    gmsh.model.geo.addPoint(-b, -b - lc_fine / 2, 0, lc_fine, 5)
    gmsh.model.geo.addPoint(b, -b - lc_fine / 2, 0, lc_fine, 6)
    gmsh.model.geo.addPoint(b, b + lc_fine / 2, 0, lc_fine, 7)
    gmsh.model.geo.addPoint(-b, b + lc_fine / 2, 0, lc_fine, 8)

    # Lines
    gmsh.model.geo.addLine(1, 2, 1)
    gmsh.model.geo.addLine(2, 3, 2)
    gmsh.model.geo.addLine(3, 4, 3)
    gmsh.model.geo.addLine(4, 1, 4)
    gmsh.model.geo.addLine(5, 6, 5)
    gmsh.model.geo.addLine(6, 7, 6)
    gmsh.model.geo.addLine(7, 8, 7)
    gmsh.model.geo.addLine(8, 5, 8)

    # Line loops
    gmsh.model.geo.addCurveLoop([1, 2, 3, 4], 1)
    gmsh.model.geo.addCurveLoop([5, 6, 7, 8], 2)

    # Add plane surfaces defined by one or more curve loops.
    gmsh.model.geo.addPlaneSurface([1, 2], 1)
    gmsh.model.geo.addPlaneSurface([2], 2)

    gmsh.model.geo.synchronize()

    # Prepare structured grid
    gmsh.model.geo.mesh.setTransfiniteCurve(
        6, math.ceil(2 * b / lc_fine + 2), "Progression", 1
    )
    gmsh.model.geo.mesh.setTransfiniteCurve(
        8, math.ceil(2 * b / lc_fine + 2), "Progression", 1
    )
    gmsh.model.geo.mesh.setTransfiniteSurface(2, "Alternate")

    gmsh.model.geo.mesh.setRecombine(dim2, 1)
    gmsh.model.geo.mesh.setRecombine(dim2, 2)

    gmsh.model.geo.synchronize()

    # Physical groups
    Bottom = gmsh.model.addPhysicalGroup(dim1, [1])
    gmsh.model.setPhysicalName(dim1, Bottom, "Bottom")

    Right = gmsh.model.addPhysicalGroup(dim1, [2])
    gmsh.model.setPhysicalName(dim1, Right, "Right")

    Top = gmsh.model.addPhysicalGroup(dim1, [3])
    gmsh.model.setPhysicalName(dim1, Top, "Top")

    Left = gmsh.model.addPhysicalGroup(dim1, [4])
    gmsh.model.setPhysicalName(dim1, Left, "Left")

    Computational_domain = gmsh.model.addPhysicalGroup(dim2, [1, 2])
    gmsh.model.setPhysicalName(dim2, Computational_domain, "Computational_domain")
    gmsh.model.geo.synchronize()

    output_file = f"{out_dir}/" + meshname + ".msh"
    gmsh.model.mesh.generate(dim2)
    gmsh.write(output_file)
    gmsh.finalize()

Pre process

def pre_processing(h, a0):… (click to toggle)

def pre_processing(h, a0):
    mesh = pv.read(f"{out_dir}/mesh_full_pf_domain.vtu")
    phase_field = np.ones((len(mesh.points), 1))
    pv.set_plot_theme("document")

    for node_id, x in enumerate(mesh.points):
        if (
            (mesh.center[0] - x[0]) <= a0 + 0.001 * h
            and (mesh.center[0] - x[0]) >= -a0 - 0.001 * h
            and (mesh.center[1] - x[1]) < h / 2 + 0.001 * h
            and (mesh.center[1] - x[1]) > -h / 2 - 0.001 * h
        ):
            phase_field[node_id] = 0.0

    mesh.point_data["phase-field"] = phase_field
    mesh.save(f"{out_dir}/mesh_full_pf_OGS_pf_ic.vtu")

Run the simulation

pv.set_plot_theme("document")… (click to toggle)

pv.set_plot_theme("document")
pv.set_jupyter_backend("static")


def sneddon_numerical(h):
    # mesh properties
    ls = 2 * h
    # generate prefix from properties
    filename = f"results_h_{h:0.4f}"
    mesh_generation(0.1, h)
    # Convert GMSH (.msh) meshes to VTU meshes appropriate for OGS simulation.
    input_file = f"{out_dir}/" + meshname + ".msh"
    msh2vtu(filename=input_file, output_path=out_dir, keep_ids=True)
    # As a preprocessing step, define the initial phase-field (crack).
    pre_processing(h, a0)
    # change properties in prj file #For more information visit: https://ogstools.opengeosys.org/stable/reference/ogstools.ogs6py.html
    model = ot.Project(
        input_file=prj_name,
        output_file=f"{out_dir}/{prj_name}",
        MKL=True,
        args=f"-o {out_dir}",
    )

    gml_file = Path("./Kregime_Static.gml").resolve()

    model.replace_parameter_value(name="ls", value=ls)
    model.replace_text(gml_file, xpath="./geometry")
    model.replace_text(filename, xpath="./time_loop/output/prefix")
    model.write_input()
    # run simulation with ogs
    t0 = time.time()
    print(">>> OGS started execution ... <<<")
    run(
        f"ogs {out_dir}/{prj_name} -o {out_dir} -m {out_dir} > {out_dir}/ogs-out.txt",
        shell=True,
        check=True,
    )
    tf = time.time()
    print(">>> OGS terminated execution  <<< Elapsed time: ", round(tf - t0, 2), " s.")

for h_j in h_list:
    sneddon_numerical(h=h_j)

Info    : Meshing 1D...
Info    : [  0%] Meshing curve 1 (Line)
Info    : [ 20%] Meshing curve 2 (Line)
Info    : [ 30%] Meshing curve 3 (Line)
Info    : [ 40%] Meshing curve 4 (Line)
Info    : [ 60%] Meshing curve 5 (Line)
Info    : [ 70%] Meshing curve 6 (Line)
Info    : [ 80%] Meshing curve 7 (Line)
Info    : [ 90%] Meshing curve 8 (Line)
Info    : Done meshing 1D (Wall 0.000526017s, CPU 0.000902s)
Info    : Meshing 2D...
Info    : [  0%] Meshing surface 1 (Plane, Frontal-Delaunay)

Info    : [  0%] Blossom: 24032 internal 482 closed

INFO:root:Output: mesh_full_pf

INFO:root:Original mesh (read)

INFO:root:<meshio mesh object>
  Number of points: 14439
  Number of cells:
    line: 40
    line: 40
    line: 40
    line: 40
    quad: 7878
    quad: 6480
  Cell sets: Bottom, Right, Top, Left, Computational_domain, gmsh:bounding_entities
  Point data: gmsh:dim_tags
  Cell data: gmsh:physical, gmsh:geometrical
  Field data: Bottom, Right, Top, Left, Computational_domain

INFO:root:Detected mesh dimension: 2

INFO:root:##

INFO:root:Domain mesh (written)

INFO:root:14439 points in 3 dimensions

INFO:root:cells: 14358 quad

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

INFO:root:Boundary mesh (written)

INFO:root:160 points in 3 dimensions

INFO:root:cells: 160 line

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

INFO:root:Submesh Bottom (written)

INFO:root:41 points in 3 dimensions

INFO:root:cells: 40 line

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

INFO:root:Submesh Right (written)

INFO:root:41 points in 3 dimensions

INFO:root:cells: 40 line

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

INFO:root:Submesh Top (written)

INFO:root:41 points in 3 dimensions

INFO:root:cells: 40 line

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

INFO:root:Submesh Left (written)

INFO:root:41 points in 3 dimensions

INFO:root:cells: 40 line

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

Info    : [  0%] Blossom recombination completed (Wall 0.399129s, CPU 0.400634s): 7878 quads, 0 triangles, 0 invalid quads, 0 quads with Q < 0.1, avg Q = 0.793024, min Q = 0.371315
Info    : [ 60%] Meshing surface 2 (Transfinite)
Info    : Done meshing 2D (Wall 0.603961s, CPU 0.605542s)
Info    : 14439 nodes 14848 elements
Info    : Writing '/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/Tests/Data/PhaseField/kregime_jupyter_notebook/Kregime_Static_jupyter/mesh_full_pf.msh'...
Info    : Done writing '/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/Tests/Data/PhaseField/kregime_jupyter_notebook/Kregime_Static_jupyter/mesh_full_pf.msh'

INFO:root:Submesh Computational_domain (written)

INFO:root:14439 points in 3 dimensions

INFO:root:cells: 14358 quad

INFO:root:point_data=['gmsh:dim_tags']

INFO:root:cell_data=['gmsh:physical']

INFO:root:cell_sets=[]

INFO:root:##

>>> OGS started execution ... <<<

>>> OGS terminated execution  <<< Elapsed time:  6.13  s.

Post processing

# As a post-process, we calculate the fracture opening.… (click to toggle)

# As a post-process, we calculate the fracture opening.
def width_calculation(filename):
    reader = pv.get_reader(f"{out_dir}/{filename}.pvd")
    # --------------------------------------------------------------------------------
    # Active the results of last time step
    # --------------------------------------------------------------------------------
    reader.set_active_time_value(reader.time_values[-1])
    mesh = reader.read()[0]
    # --------------------------------------------------------------------------------
    # define grad d
    # --------------------------------------------------------------------------------
    mesh_d = mesh.compute_derivative(scalars="phasefield")
    mesh_d["gradient"]

    def gradients_to_dict(arr):
        """A helper method to label the gradients into a dictionary."""
        keys = np.array(
            ["grad_dx", "grad_dy", "grad_dz", "grad_dx", "grad_dy", "grad_dz"]
        )
        keys = keys.reshape((2, 3))[:, : arr.shape[1]].ravel()
        return dict(zip(keys, mesh_d["gradient"].T))

    gradients_d = gradients_to_dict(mesh_d["gradient"])
    mesh.point_data.update(gradients_d)
    # --------------------------------------------------------------------------------
    # define width at nodes
    # --------------------------------------------------------------------------------
    disp = mesh.point_data["displacement"]
    grad_dx = mesh.point_data["grad_dx"]
    grad_dy = mesh.point_data["grad_dy"]
    num_points = disp.shape
    Wnode = np.zeros(num_points[0])
    for i, _x in enumerate(mesh.points):
        u_x = disp[i][0]
        u_y = disp[i][1]
        gd_x = grad_dx[i]
        gd_y = grad_dy[i]

        Wnode[i] = 0.5 * (u_x * gd_x + u_y * gd_y)
    mesh.point_data["Wnode"] = Wnode
    # --------------------------------------------------------------------------------
    # define width at nodes
    # --------------------------------------------------------------------------------
    # Normalize the vector
    normal = [np.cos(Orientation), np.sin(Orientation), 0]
    # Make points along that vector for the extent of your slices
    point_a = mesh.center + np.array([1.5 * a0, 0, 0])
    point_b = mesh.center + np.array([-1.5 * a0, 0, 0])
    dist_a_b = ((point_b[0] - point_a[0]) ** 2 + (point_b[1] - point_a[1]) ** 2) ** 0.5
    # Define the line/points for the slices
    line = pv.Line(point_a, point_b, n_slices)
    width_line = np.zeros(len(line.points))
    r_i = np.zeros(len(line.points))
    # Generate all of the slices
    slices = pv.MultiBlock()

    for i, point in enumerate(line.points):
        slices.append(mesh.slice(normal=normal, origin=point))
        slice_mesh = mesh.slice(normal=normal, origin=point)
        y_slice = slice_mesh.points[:, 1]
        Wnode_slice = slice_mesh.point_data["Wnode"]
        width_i = np.trapz(Wnode_slice, x=y_slice)  # noqa: NPY201
        if width_i >= 0:
            width_line[i] = width_i
        r_i[i] = (
            (point[0] - point_a[0]) ** 2 + (point[1] - point_a[1]) ** 2
        ) ** 0.5 - dist_a_b / 2

    return r_i, width_line

Sneddon

def sneddon(h, ls, phasefield_model):… (click to toggle)

def sneddon(h, ls, phasefield_model):
    # Effective a for AT1/A2
    if phasefield_model == "AT1":
        a_eff = a0 * (1 + pi * ls / (4.0 * a0 * (3 * h / 8.0 / ls + 1.0)))
    elif phasefield_model == "AT2":
        a_eff = a0 * (1 + pi * ls / (4.0 * a0 * (h / (2.0 * ls) + 1.0)))

    x = np.linspace(-1.0 * a_eff, a_eff, 40)
    uy = []
    for i in range(len(x)):
        uy.append(
            2 * a_eff * (1 - nu**2) * P / E * math.sqrt(1.0 - ((x[i]) / (a_eff)) ** 2)
        )

    return x, uy, a_eff

Opening profile

color = ["-.k", "ko", "-.r", "ro", "-.b", "bo", "-.g", "go"]… (click to toggle)

color = ["-.k", "ko", "-.r", "ro", "-.b", "bo", "-.g", "go"]
Label = ["Closed form solution", "VPF-FEM"]
lineWIDTH = [1.5, 1.5, 1.5]

for j, h_j in enumerate(h_list):
    r_i_num = []
    width_line_num = []
    filename = f"results_h_{h_j:0.4f}"
    print(filename)
    width_calculation(filename)
    r_i_num = width_calculation(filename)[0]
    width_line_num = width_calculation(filename)[1]
    ls = 2 * h_j

    x_Sneddon = sneddon(h_j, ls, phasefield_model)[0]
    uy_Sneddon = sneddon(h_j, ls, phasefield_model)[1]
    a_eff_Sneddon = sneddon(h_j, ls, phasefield_model)[2]
    plt.plot(
        np.array(x_Sneddon[:]),
        np.array(uy_Sneddon[:]),
        color[2 * j],
        fillstyle="none",
        markersize=0,
        linewidth=lineWIDTH[0],
        label=f"Closed form solution - $h= ${h_j:0.4f}",
    )
    plt.plot(
        np.array(r_i_num[:]),
        np.array(width_line_num[:]),
        color[2 * j + 1],
        fillstyle="none",
        markersize=6,
        linewidth=lineWIDTH[1],
        label=f"VPF - $h =${h_j:0.4f}",
    )
    # ------------------------------------------------------------------------
plt.rcParams["figure.figsize"] = [40, 20]
plt.rcParams["figure.dpi"] = 1600
plt.ylabel("$w_n$ [m]", fontsize=14)
plt.xlabel("$r$ [m]", fontsize=14)
plt.grid(linestyle="dashed")
plt.title(f"{phasefield_model}")

legend = plt.legend(bbox_to_anchor=(1.04, 1), loc="upper left")
plt.show()

results_h_0.0100

DEBUG:matplotlib.pyplot:Loaded backend module://matplotlib_inline.backend_inline version unknown.

DEBUG:matplotlib.pyplot:Loaded backend module://matplotlib_inline.backend_inline version unknown.

DEBUG:matplotlib.font_manager:findfont: Matching sans\-serif:style=normal:variant=normal:weight=normal:stretch=normal:size=10.0.

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmr10.ttf', name='cmr10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSans-Bold.ttf', name='DejaVu Sans', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 0.33499999999999996

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizOneSymBol.ttf', name='STIXSizeOneSym', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSans.ttf', name='DejaVu Sans', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 0.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmss10.ttf', name='cmss10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSansMono-BoldOblique.ttf', name='DejaVu Sans Mono', style='oblique', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSansMono-Bold.ttf', name='DejaVu Sans Mono', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXGeneralItalic.ttf', name='STIXGeneral', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSerif.ttf', name='DejaVu Serif', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXNonUni.ttf', name='STIXNonUnicode', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSerif-Bold.ttf', name='DejaVu Serif', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXGeneral.ttf', name='STIXGeneral', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizThreeSymBol.ttf', name='STIXSizeThreeSym', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmtt10.ttf', name='cmtt10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSansMono.ttf', name='DejaVu Sans Mono', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmex10.ttf', name='cmex10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXGeneralBolIta.ttf', name='STIXGeneral', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizOneSymReg.ttf', name='STIXSizeOneSym', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSans-Oblique.ttf', name='DejaVu Sans', style='oblique', variant='normal', weight=400, stretch='normal', size='scalable')) = 1.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizFourSymReg.ttf', name='STIXSizeFourSym', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXGeneralBol.ttf', name='STIXGeneral', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizTwoSymBol.ttf', name='STIXSizeTwoSym', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXNonUniBol.ttf', name='STIXNonUnicode', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmmi10.ttf', name='cmmi10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSans-BoldOblique.ttf', name='DejaVu Sans', style='oblique', variant='normal', weight=700, stretch='normal', size='scalable')) = 1.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSerifDisplay.ttf', name='DejaVu Serif Display', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSerif-Italic.ttf', name='DejaVu Serif', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmb10.ttf', name='cmb10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSerif-BoldItalic.ttf', name='DejaVu Serif', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSansDisplay.ttf', name='DejaVu Sans Display', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizTwoSymReg.ttf', name='STIXSizeTwoSym', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSansMono-Oblique.ttf', name='DejaVu Sans Mono', style='oblique', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizThreeSymReg.ttf', name='STIXSizeThreeSym', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXNonUniIta.ttf', name='STIXNonUnicode', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizFourSymBol.ttf', name='STIXSizeFourSym', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXSizFiveSymReg.ttf', name='STIXSizeFiveSym', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/cmsy10.ttf', name='cmsy10', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/STIXNonUniBolIta.ttf', name='STIXNonUnicode', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/D050000L.otf', name='D050000L', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/C059-BdIta.otf', name='C059', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-Semibold.otf', name='Source Code Pro', style='normal', variant='normal', weight=600, stretch='normal', size='scalable')) = 10.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWGothic-Demi.otf', name='URW Gothic', style='normal', variant='normal', weight=600, stretch='normal', size='scalable')) = 10.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/P052-Roman.otf', name='P052', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeMonoOblique.otf', name='FreeMono', style='oblique', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWBookman-LightItalic.otf', name='URW Bookman', style='italic', variant='normal', weight=300, stretch='normal', size='scalable')) = 11.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/P052-Italic.otf', name='P052', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/C059-Italic.otf', name='C059', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/Z003-MediumItalic.otf', name='Z003', style='italic', variant='normal', weight=500, stretch='normal', size='scalable')) = 11.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSerifBold.otf', name='FreeSerif', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSerif.otf', name='FreeSerif', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSans.otf', name='FreeSans', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSansBold.otf', name='FreeSans', style='normal', variant='normal', weight=600, stretch='normal', size='scalable')) = 10.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSansOblique.otf', name='FreeSans', style='oblique', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusMonoPS-Regular.otf', name='Nimbus Mono PS', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSansBoldOblique.otf', name='FreeSans', style='oblique', variant='normal', weight=600, stretch='normal', size='scalable')) = 11.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWBookman-Demi.otf', name='URW Bookman', style='normal', variant='normal', weight=600, stretch='normal', size='scalable')) = 10.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSansNarrow-Oblique.otf', name='Nimbus Sans Narrow', style='oblique', variant='normal', weight=400, stretch='condensed', size='scalable')) = 11.25

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWBookman-Light.otf', name='URW Bookman', style='normal', variant='normal', weight=300, stretch='normal', size='scalable')) = 10.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-MediumIt.otf', name='Source Code Pro', style='italic', variant='normal', weight=500, stretch='normal', size='scalable')) = 11.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-ExtraLightIt.otf', name='Source Code Pro', style='italic', variant='normal', weight=200, stretch='normal', size='scalable')) = 11.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/P052-Bold.otf', name='P052', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/StandardSymbolsPS.otf', name='Standard Symbols PS', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeMonoBoldOblique.otf', name='FreeMono', style='oblique', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-LightIt.otf', name='Source Code Pro', style='italic', variant='normal', weight=300, stretch='normal', size='scalable')) = 11.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-Medium.otf', name='Source Code Pro', style='normal', variant='normal', weight=500, stretch='normal', size='scalable')) = 10.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSerifItalic.otf', name='FreeSerif', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSans-BoldItalic.otf', name='Nimbus Sans', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWGothic-Book.otf', name='URW Gothic', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeSerifBoldItalic.otf', name='FreeSerif', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusRoman-BoldItalic.otf', name='Nimbus Roman', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-SemiboldIt.otf', name='Source Code Pro', style='italic', variant='normal', weight=600, stretch='normal', size='scalable')) = 11.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-Black.otf', name='Source Code Pro', style='normal', variant='normal', weight=900, stretch='normal', size='scalable')) = 10.525

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-Regular.otf', name='Source Code Pro', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeMono.otf', name='FreeMono', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSans-Italic.otf', name='Nimbus Sans', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/C059-Bold.otf', name='C059', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-BoldIt.otf', name='Source Code Pro', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gnu-free/FreeMonoBold.otf', name='FreeMono', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusRoman-Bold.otf', name='Nimbus Roman', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSansNarrow-Regular.otf', name='Nimbus Sans Narrow', style='normal', variant='normal', weight=400, stretch='condensed', size='scalable')) = 10.25

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusRoman-Italic.otf', name='Nimbus Roman', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWGothic-DemiOblique.otf', name='URW Gothic', style='oblique', variant='normal', weight=600, stretch='normal', size='scalable')) = 11.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-Bold.otf', name='Source Code Pro', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSansNarrow-BoldOblique.otf', name='Nimbus Sans Narrow', style='oblique', variant='normal', weight=700, stretch='condensed', size='scalable')) = 11.535

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWGothic-BookOblique.otf', name='URW Gothic', style='oblique', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSans-Bold.otf', name='Nimbus Sans', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusRoman-Regular.otf', name='Nimbus Roman', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-It.otf', name='Source Code Pro', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusMonoPS-Bold.otf', name='Nimbus Mono PS', style='normal', variant='normal', weight=700, stretch='normal', size='scalable')) = 10.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/P052-BoldItalic.otf', name='P052', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/C059-Roman.otf', name='C059', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/URWBookman-DemiItalic.otf', name='URW Bookman', style='italic', variant='normal', weight=600, stretch='normal', size='scalable')) = 11.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-Light.otf', name='Source Code Pro', style='normal', variant='normal', weight=300, stretch='normal', size='scalable')) = 10.145

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSans-Regular.otf', name='Nimbus Sans', style='normal', variant='normal', weight=400, stretch='normal', size='scalable')) = 10.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusMonoPS-BoldItalic.otf', name='Nimbus Mono PS', style='italic', variant='normal', weight=700, stretch='normal', size='scalable')) = 11.335

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-ExtraLight.otf', name='Source Code Pro', style='normal', variant='normal', weight=200, stretch='normal', size='scalable')) = 10.24

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusMonoPS-Italic.otf', name='Nimbus Mono PS', style='italic', variant='normal', weight=400, stretch='normal', size='scalable')) = 11.05

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/adobe-source-code-pro/SourceCodePro-BlackIt.otf', name='Source Code Pro', style='italic', variant='normal', weight=900, stretch='normal', size='scalable')) = 11.525

DEBUG:matplotlib.font_manager:findfont: score(FontEntry(fname='/usr/share/fonts/gsfonts/NimbusSansNarrow-Bold.otf', name='Nimbus Sans Narrow', style='normal', variant='normal', weight=700, stretch='condensed', size='scalable')) = 10.535

DEBUG:matplotlib.font_manager:findfont: Matching sans\-serif:style=normal:variant=normal:weight=normal:stretch=normal:size=10.0 to DejaVu Sans ('/var/lib/gitlab-runner/builds/e3EQ9HiK/0/ogs/build/release-petsc/.venv/lib/python3.12/site-packages/matplotlib/mpl-data/fonts/ttf/DejaVuSans.ttf') with score of 0.050000.

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

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DEBUG:matplotlib.dviread:lh=18, bc=0, ec=127, nw=52, nh=16, nd=11

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DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

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DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

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DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

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DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

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DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/58/d9/58d9a487f5fba1c1e4c3f6b2207013e3.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/2d/84/2d84808fb62fe6c38d400d3ac2dda4e0.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.dviread:lh=18, bc=0, ec=127, nw=54, nh=16, nd=11

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/5d/40/5d403f1c901577df0497afdfd5548983.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.dviread:opening tfm file /usr/share/texmf-dist/fonts/tfm/public/cm/cmmi12.tfm

DEBUG:matplotlib.dviread:lh=18, bc=0, ec=127, nw=97, nh=15, nd=9

DEBUG:matplotlib.dviread:opening tfm file /usr/share/texmf-dist/fonts/tfm/public/cm/cmmi9.tfm

DEBUG:matplotlib.dviread:lh=18, bc=0, ec=127, nw=97, nh=15, nd=9

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/92/b3/92b338f03fab20e237bf5e0ab1fa8f30.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/4a/79/4a79ff4e5f88243230d708bdca530646.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/85/17/8517ecfac9639c60aa1ba33f71a6ba0b.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.dviread:lh=18, bc=0, ec=127, nw=44, nh=15, nd=16

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/af/14/af14988e6d5123cc71723954c0f475cb.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/a6/53/a6530b5f5cca32cfe935c0837b2c7c48.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/fc/61/fc61794ee5902c9054afa73be96ae0a7.dvi

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

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DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

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DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

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DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

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DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

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DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

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DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

DEBUG:matplotlib.texmanager:family: cursive, package: \usepackage{chancery}, font: Zapf Chancery, skipped: Apple Chancery, Textile

DEBUG:matplotlib.texmanager:family: monospace, package: \usepackage{type1ec}, font: Computer Modern Typewriter, skipped: DejaVu Sans Mono, Bitstream Vera Sans Mono

DEBUG:matplotlib.dviread:Dvi: /var/lib/gitlab-runner/.cache/matplotlib/tex.cache/84/4f/844f707e0917555faafa721cd5105dbd.dvi

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: header=l3backend-dvips.pro

DEBUG:matplotlib.dviread:Dvi._xxx: encountered special: papersize=5203.43999pt,5203.43999pt

DEBUG:matplotlib.texmanager:family: serif, package: \usepackage{type1ec}, font: Computer Modern Roman, skipped: DejaVu Serif, Bitstream Vera Serif

DEBUG:matplotlib.texmanager:family: sans-serif, package: \usepackage{type1ec}, font: Computer Modern Sans Serif, skipped: DejaVu Sans, Bitstream Vera Sans

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png

To decrease computing time, we perform the simulation with an one coarse mesh; Mesh sensitivity can be investigated in order to assess the convergence of the opening profile for various mesh discretizations. Following are the mesh sensivity results for for Models $\texttt{AT}_1$ and $\texttt{AT}_2$ ($h=0.01,~0.005,~\text{and} ~0.0025$ m.)

Crack opening profiles of VPF ($\texttt{AT}_1$) with different mesh sizes compared against the Sneddon solution.

Crack opening profiles of VPF ($\texttt{AT}_2$) with different mesh sizes compared against the Sneddon solution.

Our mesh size sensitivity study shows even with coarse mesh. The results away from crack tips agree well with the Sneddon solution. Using finer mesh demonstrates that the opening along the whole crack length is accurate compared with the closed-form solution.

It’s worth noting that we estimate width as part of post-processing (using the line integral and a given crack normal vector). However, near crack tips the crack normal vector is different to the given normal vector, so the width values are inaccurate near crack tips. For the sake of simplicity, we neglect determining the normal crack vector here; for more information on the line integral approach, see Yoshioka et al., 2020.

References

[1] Yoshioka, Keita, Francesco Parisio, Dmitri Naumov, Renchao Lu, Olaf Kolditz, and Thomas Nagel. Comparative verification of discrete and smeared numerical approaches for the simulation of hydraulic fracturing. GEM-International Journal on Geomathematics 10, no. 1 (2019): 1-35.

[2] Yoshioka, Keita, Dmitri Naumov, and Olaf Kolditz. On crack opening computation in variational phase-field models for fracture. Computer Methods in Applied Mechanics and Engineering 369 (2020): 113210.

[3] Sneddon, Ian Naismith, and Morton Lowengrub. Crack problems in the classical theory of elasticity. 1969, 221 P (1969).

Static fracture opening under a constant pressure – Sneddon solution