def download_nodal_dg_if_not_present(path="nodal-dg"):
"""Download the nodal-DG source code.
:arg path: The destination path.
"""
import os
if os.path.exists(path):
return
import tempfile
with tempfile.TemporaryDirectory() as tmp:
filename = os.path.join(tmp, "master.zip")
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
url="https://github.com/tcew/nodal-dg/archive/master.zip",
local_name=filename)
import zipfile
with zipfile.ZipFile(filename, "r") as zp:
zp.extractall(tmp)
if not os.path.exists(path):
import shutil
shutil.move(os.path.join(tmp, "nodal-dg-master"), path)
def generate_festa_sommariva_quadrature_rules(outfile):
filename = f"set_amr_square.m"
download_from_web_if_not_present(
url=f"{_URL}",
local_name=filename)
with open(filename, "r") as fd:
mfile = fd.read()
# rules are hardcoded as part of a MATLAB file
# the are extracted by looking for the pattern
#
# xw=[
# <x> <y> <weight>
# ...
# ];
#
# The degree of each quadrature rule is written in a line above the
# nodes and weights in the pattern
#
# DEGREE: <degree>
_re_degree = re.compile(r"DEGREE:\s+(\d+)")
_re_xw = re.compile(r"xw\s?=\s?\[(.+?)\];", re.DOTALL)
# NOTE: some degrees have multiple quadrature rules with a repeated
# header, so we just take the unique ones here
degrees = np.unique(
np.fromiter(_re_degree.findall(mfile), dtype=np.int)
)
rules = {}
for imatch, match in enumerate(_re_xw.findall(mfile)):
d = degrees[imatch]
assert d == imatch + 1, (d, imatch + 1)
xw = np.fromstring(match.strip(), dtype=np.float64, sep=" ").reshape(-1, 3)
rules[d] = {
"quad_degree": d,
"points": xw[:, :-1].T.tolist(),
"weights": xw[:, -1].tolist(),
}
assert abs(np.sum(xw[:, -1]) - 4.0) < 1.0e-12
print("degree {} points {} / {}".format(
d, xw.shape[0], (d + 1) * (d + 2) // 2
))
from pprint import pformat
txt = (_PYTHON_TEMPLATE % pformat(rules, width=80)).replace('"', "")
if outfile:
with open(outfile, "w") as fd:
fd.write(txt)
else:
print(txt)
def generate_witherden_vincent_quadrature_rules(outfile):
filename = "witherden_vincent.zip"
download_from_web_if_not_present(
url="https://ars.els-cdn.com/content/image/1-s2.0-S0898122115001224-mmc1.zip", # noqa: E501
local_name=filename)
import zipfile
with zipfile.ZipFile(filename, "r") as zp:
zp.extractall(filename[:-4])
# files are named <strength>-<number-of-nodes>.txt
# contents of each row are <x> <y> [<z>] <weight>
quad_rules = {}
dirname = os.path.join(filename[:-4], "expanded", "quad")
for f in os.listdir(dirname):
degree = int(f.split("-")[0])
txt = np.loadtxt(os.path.join(dirname, f)).reshape(-1, 3)
quad_rules[degree] = {
"quad_degree": degree,
"points": txt[:, :-1].T.tolist(),
"weights": txt[:, -1].tolist()
}
assert abs(np.sum(txt[:, -1]) - 4.0) < 1.0e-12
hex_rules = {}
dirname = os.path.join(filename[:-4], "expanded", "hex")
for f in os.listdir(dirname):
degree = int(f.split("-")[0])
txt = np.loadtxt(os.path.join(dirname, f)).reshape(-1, 4)
hex_rules[degree] = {
"quad_degree": degree,
"points": txt[:, :-1].T.tolist(),
"weights": txt[:, -1].tolist()
}
assert abs(np.sum(txt[:, -1]) - 8.0) < 1.0e-12
from pprint import pformat
txt = (_PYTHON_TEMPLATE % (
pformat(quad_rules), pformat(hex_rules)
)).replace('"', "")
if outfile:
with open(outfile, "w") as fd:
fd.write(txt)
else:
print(txt)
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/master/"
"surface-3d/elliptiplane.brep")
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("elliptiplane.brep"), 2, order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
# now centered at origin and extends to -1,1
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/master/"
"surface-3d/elliptiplane.brep")
from meshmode.mesh.io import generate_gmsh, FileSource
mesh = generate_gmsh(
FileSource("elliptiplane.brep"), 2, order=2,
other_options=[
"-string",
"Mesh.CharacteristicLengthMax = %g;" % resolution])
# now centered at origin and extends to -1,1
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/a869fc3/"
"surface-3d/betterplane.brep")
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
mesh = generate_gmsh(
ScriptWithFilesSource("""
Merge "betterplane.brep";
Mesh.CharacteristicLengthMax = %(lcmax)f;
Mesh.ElementOrder = 2;
Mesh.CharacteristicLengthExtendFromBoundary = 0;
// 2D mesh optimization
// Mesh.Lloyd = 1;
l_superfine() = Unique(Abs(Boundary{ Surface{
27, 25, 17, 13, 18 }; }));
l_fine() = Unique(Abs(Boundary{ Surface{ 2, 6, 7}; }));
l_coarse() = Unique(Abs(Boundary{ Surface{ 14, 16 }; }));
// p() = Unique(Abs(Boundary{ Line{l_fine()}; }));
// Characteristic Length{p()} = 0.05;
Field[1] = Attractor;
Field[1].NNodesByEdge = 100;
Field[1].EdgesList = {l_superfine()};
Field[2] = Threshold;
Field[2].IField = 1;
Field[2].LcMin = 0.075;
Field[2].LcMax = %(lcmax)f;
Field[2].DistMin = 0.1;
Field[2].DistMax = 0.4;
Field[3] = Attractor;
Field[3].NNodesByEdge = 100;
Field[3].EdgesList = {l_fine()};
Field[4] = Threshold;
Field[4].IField = 3;
Field[4].LcMin = 0.1;
Field[4].LcMax = %(lcmax)f;
Field[4].DistMin = 0.15;
Field[4].DistMax = 0.4;
Field[5] = Attractor;
Field[5].NNodesByEdge = 100;
Field[5].EdgesList = {l_coarse()};
Field[6] = Threshold;
Field[6].IField = 5;
Field[6].LcMin = 0.15;
Field[6].LcMax = %(lcmax)f;
Field[6].DistMin = 0.2;
Field[6].DistMax = 0.4;
Field[7] = Min;
Field[7].FieldsList = {2, 4, 6};
Background Field = 7;
""" % {
"lcmax": resolution,
}, ["betterplane.brep"]), 2)
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
def get_mesh(self, resolution, target_order):
from pytools import download_from_web_if_not_present
download_from_web_if_not_present(
"https://raw.githubusercontent.com/inducer/geometries/a869fc3/"
"surface-3d/betterplane.brep")
from meshmode.mesh.io import generate_gmsh, ScriptWithFilesSource
mesh = generate_gmsh(
ScriptWithFilesSource(
"""
Merge "betterplane.brep";
Mesh.CharacteristicLengthMax = %(lcmax)f;
Mesh.ElementOrder = 2;
Mesh.CharacteristicLengthExtendFromBoundary = 0;
// 2D mesh optimization
// Mesh.Lloyd = 1;
l_superfine() = Unique(Abs(Boundary{ Surface{
27, 25, 17, 13, 18 }; }));
l_fine() = Unique(Abs(Boundary{ Surface{ 2, 6, 7}; }));
l_coarse() = Unique(Abs(Boundary{ Surface{ 14, 16 }; }));
// p() = Unique(Abs(Boundary{ Line{l_fine()}; }));
// Characteristic Length{p()} = 0.05;
Field[1] = Attractor;
Field[1].NNodesByEdge = 100;
Field[1].EdgesList = {l_superfine()};
Field[2] = Threshold;
Field[2].IField = 1;
Field[2].LcMin = 0.075;
Field[2].LcMax = %(lcmax)f;
Field[2].DistMin = 0.1;
Field[2].DistMax = 0.4;
Field[3] = Attractor;
Field[3].NNodesByEdge = 100;
Field[3].EdgesList = {l_fine()};
Field[4] = Threshold;
Field[4].IField = 3;
Field[4].LcMin = 0.1;
Field[4].LcMax = %(lcmax)f;
Field[4].DistMin = 0.15;
Field[4].DistMax = 0.4;
Field[5] = Attractor;
Field[5].NNodesByEdge = 100;
Field[5].EdgesList = {l_coarse()};
Field[6] = Threshold;
Field[6].IField = 5;
Field[6].LcMin = 0.15;
Field[6].LcMax = %(lcmax)f;
Field[6].DistMin = 0.2;
Field[6].DistMax = 0.4;
Field[7] = Min;
Field[7].FieldsList = {2, 4, 6};
Background Field = 7;
""" % {
"lcmax": resolution,
}, ["betterplane.brep"]), 2)
# Flip elements--gmsh generates inside-out geometry.
from meshmode.mesh.processing import perform_flips
return perform_flips(mesh, np.ones(mesh.nelements))
