def get_latlon_mesh(mesh):
"""Build 2D projected mesh of spherical mesh"""
crds_orig = mesh.coordinates
mesh_dg_fs = VectorFunctionSpace(mesh, "DG", 1)
crds_dg = Function(mesh_dg_fs)
crds_latlon = Function(mesh_dg_fs)
par_loop(
"""
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
dg[i][j] = cg[i][j];
}
}
""", dx, {
'dg': (crds_dg, WRITE),
'cg': (crds_orig, READ)
})
# lat-lon 'x' = atan2(y, x)
crds_latlon.dat.data[:, 0] = arctan2(crds_dg.dat.data[:, 1],
crds_dg.dat.data[:, 0])
# lat-lon 'y' = asin(z/sqrt(x^2 + y^2 + z^2))
crds_latlon.dat.data[:, 1] = (arcsin(
crds_dg.dat.data[:, 2] /
np_sqrt(crds_dg.dat.data[:, 0]**2 + crds_dg.dat.data[:, 1]**2 +
crds_dg.dat.data[:, 2]**2)))
crds_latlon.dat.data[:, 2] = 0.0
kernel = op2.Kernel(
"""
#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
void splat_coords(double **coords) {
double diff0 = (coords[0][0] - coords[1][0]);
double diff1 = (coords[0][0] - coords[2][0]);
double diff2 = (coords[1][0] - coords[2][0]);
if (fabs(diff0) > PI || fabs(diff1) > PI || fabs(diff2) > PI) {
const int sign0 = coords[0][0] < 0 ? -1 : 1;
const int sign1 = coords[1][0] < 0 ? -1 : 1;
const int sign2 = coords[2][0] < 0 ? -1 : 1;
if (sign0 < 0) {
coords[0][0] += TWO_PI;
}
if (sign1 < 0) {
coords[1][0] += TWO_PI;
}
if (sign2 < 0) {
coords[2][0] += TWO_PI;
}
}
}
""", "splat_coords")
op2.par_loop(kernel, crds_latlon.cell_set,
crds_latlon.dat(op2.RW, crds_latlon.cell_node_map()))
return Mesh(crds_latlon)
def min(f_in):
fmin = op2.Global(1, [np.finfo(float).max], dtype=float)
if len(f_in.ufl_shape) > 0:
mesh = f_in.function_space().mesh()
V = FunctionSpace(mesh, "DG", 1)
f = Function(V).project(sqrt(inner(f_in, f_in)))
else:
f = f_in
op2.par_loop(
op2.Kernel(
"""void minify(double *a, double *b)
{
a[0] = a[0] > fabs(b[0]) ? fabs(b[0]) : a[0];
}""", "minify"), f.dof_dset.set, fmin(op2.MIN), f.dat(op2.READ))
return fmin.data[0]
def get_latlon_mesh(mesh):
coords_orig = mesh.coordinates
mesh_dg_fs = VectorFunctionSpace(mesh, "DG", 1)
coords_dg = Function(mesh_dg_fs)
coords_latlon = Function(mesh_dg_fs)
par_loop("""
for (int i=0; i<3; i++) {
for (int j=0; j<3; j++) {
dg[i][j] = cg[i][j];
}
}
""", dx, {'dg': (coords_dg, WRITE),
'cg': (coords_orig, READ)})
# lat-lon 'x' = atan2(y, x)
coords_latlon.dat.data[:,0] = np.arctan2(coords_dg.dat.data[:,1], coords_dg.dat.data[:,0])
# lat-lon 'y' = asin(z/sqrt(x^2 + y^2 + z^2))
coords_latlon.dat.data[:,1] = np.arcsin(coords_dg.dat.data[:,2]/np.sqrt(coords_dg.dat.data[:,0]**2 + coords_dg.dat.data[:,1]**2 + coords_dg.dat.data[:,2]**2))
coords_latlon.dat.data[:,2] = 0.0
kernel = op2.Kernel("""
#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
void splat_coords(double **coords) {
double diff0 = (coords[0][0] - coords[1][0]);
double diff1 = (coords[0][0] - coords[2][0]);
double diff2 = (coords[1][0] - coords[2][0]);
if (fabs(diff0) > PI || fabs(diff1) > PI || fabs(diff2) > PI) {
const int sign0 = coords[0][0] < 0 ? -1 : 1;
const int sign1 = coords[1][0] < 0 ? -1 : 1;
const int sign2 = coords[2][0] < 0 ? -1 : 1;
if (sign0 < 0) {
coords[0][0] += TWO_PI;
}
if (sign1 < 0) {
coords[1][0] += TWO_PI;
}
if (sign2 < 0) {
coords[2][0] += TWO_PI;
}
}
}""", "splat_coords")
op2.par_loop(kernel, coords_latlon.cell_set,
coords_latlon.dat(op2.RW, coords_latlon.cell_node_map()))
return Mesh(coords_latlon)
def get_latlon_mesh(mesh):
coords_orig = mesh.coordinates
coords_fs = coords_orig.function_space()
if coords_fs.extruded:
cell = mesh._base_mesh.ufl_cell().cellname()
DG1_hori_elt = FiniteElement("DG", cell, 1, variant="equispaced")
DG1_vert_elt = FiniteElement("DG", interval, 1, variant="equispaced")
DG1_elt = TensorProductElement(DG1_hori_elt, DG1_vert_elt)
else:
cell = mesh.ufl_cell().cellname()
DG1_elt = FiniteElement("DG", cell, 1, variant="equispaced")
vec_DG1 = VectorFunctionSpace(mesh, DG1_elt)
coords_dg = Function(vec_DG1).interpolate(coords_orig)
coords_latlon = Function(vec_DG1)
shapes = {"nDOFs": vec_DG1.finat_element.space_dimension(), 'dim': 3}
radius = np.min(
np.sqrt(coords_dg.dat.data[:, 0]**2 + coords_dg.dat.data[:, 1]**2 +
coords_dg.dat.data[:, 2]**2))
# lat-lon 'x' = atan2(y, x)
coords_latlon.dat.data[:, 0] = np.arctan2(coords_dg.dat.data[:, 1],
coords_dg.dat.data[:, 0])
# lat-lon 'y' = asin(z/sqrt(x^2 + y^2 + z^2))
coords_latlon.dat.data[:, 1] = np.arcsin(
coords_dg.dat.data[:, 2] /
np.sqrt(coords_dg.dat.data[:, 0]**2 + coords_dg.dat.data[:, 1]**2 +
coords_dg.dat.data[:, 2]**2))
# our vertical coordinate is radius - the minimum radius
coords_latlon.dat.data[:,
2] = np.sqrt(coords_dg.dat.data[:, 0]**2 +
coords_dg.dat.data[:, 1]**2 +
coords_dg.dat.data[:, 2]**2) - radius
# We need to ensure that all points in a cell are on the same side of the branch cut in longitude coords
# This kernel amends the longitude coords so that all longitudes in one cell are close together
kernel = op2.Kernel(
"""
#define PI 3.141592653589793
#define TWO_PI 6.283185307179586
void splat_coords(double *coords) {{
double max_diff = 0.0;
double diff = 0.0;
for (int i=0; i<{nDOFs}; i++) {{
for (int j=0; j<{nDOFs}; j++) {{
diff = coords[i*{dim}] - coords[j*{dim}];
if (fabs(diff) > max_diff) {{
max_diff = diff;
}}
}}
}}
if (max_diff > PI) {{
for (int i=0; i<{nDOFs}; i++) {{
if (coords[i*{dim}] < 0) {{
coords[i*{dim}] += TWO_PI;
}}
}}
}}
}}
""".format(**shapes), "splat_coords")
op2.par_loop(kernel, coords_latlon.cell_set,
coords_latlon.dat(op2.RW, coords_latlon.cell_node_map()))
return Mesh(coords_latlon)
