6. Parameter tests

The modeller emg3d has quite a few parameters which can influence the speed of a computation. It can be difficult to estimate which is the best setting. In the case that speed is of utmost importance, and a lot of similar models are going to be computed (e.g. for inversions), it might be worth to do some input parameter testing.

IMPORTANT: None of the conclusions you can draw from these figures are applicable to other models. What is faster depends on your input. Influence has particularly the degree of anisotropy and of grid stretching. These are simply examples that you can adjust for your problem at hand.

import emg3d
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
plt.style.use('bmh')
def plotit(infos, labels):
    """Simple plotting routine for the tests."""

    plt.figure()

    # Loop over infos.
    for i, info in enumerate(infos):
        plt.plot(info['runtime_at_cycle'],
                 info['error_at_cycle']/info1['ref_error'],
                 '.-', label=labels[i])

    plt.legend()
    plt.xlabel('Time (s)')
    plt.ylabel('Rel. Error $(-)$')
    plt.yscale('log')

    plt.show()
# Survey
zwater = 1000                  # Water depth.
src = [0, 0, 50-zwater, 0, 0]  # Source at origin, 50 m above seafloor.
freq = 1.0                     # Frequency (Hz).

# Mesh
grid = emg3d.construct_mesh(
    frequency=freq,
    min_width_limits=100,
    properties=[0.3, 1., 1., 0.3],
    center=(src[0], src[1], -1000),
    domain=([-1000, 5000], [-500, 500], [-2500, 0]),
)
print(grid)

# Source-field
sfield = emg3d.get_source_field(grid, source=src, frequency=freq)

# Create a simple marine model for the tests.

# Layered_background
res_x = 1e8*np.ones(grid.shape_cells)              # Air
res_x[:, :, grid.cell_centers_z <= 0] = 0.3     # Water
res_x[:, :, grid.cell_centers_z <= -1000] = 1.  # Background

# Target
xt = np.nonzero((grid.cell_centers_x >= -500) &
                (grid.cell_centers_x <= 5000))[0]
yt = np.nonzero((grid.cell_centers_y >= -1000) &
                (grid.cell_centers_y <= 1000))[0]
zt = np.nonzero((grid.cell_centers_z >= -2100) &
                (grid.cell_centers_z <= -1800))[0]
res_x[xt[0]:xt[-1]+1, yt[0]:yt[-1]+1, zt[0]:zt[-1]+1] = 100

# Create a model instance
model_iso = emg3d.Model(grid, property_x=res_x, mapping='Resistivity')

# Plot it for QC
grid.plot_3d_slicer(model_iso.property_x.ravel('F'),
                    pcolor_opts={'norm': LogNorm()})
parameter tests

Out:

TensorMesh: 76,800 cells

                    MESH EXTENT             CELL WIDTH      FACTOR
dir    nC        min           max         min       max      max
---   ---  ---------------------------  ------------------  ------
 x     80     -4,244.80      8,244.80    100.00    656.64    1.21
 y     24     -3,703.39      3,703.39    100.00    996.95    1.39
 z     40     -5,714.95      2,357.76    100.00    857.19    1.31

Test 1: F, W, and V MG cycles

inp = {'model': model_iso, 'sfield': sfield, 'return_info': True,
       'sslsolver': False, 'semicoarsening': False, 'linerelaxation': False}

_, info1 = emg3d.solve(cycle='F', **inp)
_, info2 = emg3d.solve(cycle='W', **inp)
_, info3 = emg3d.solve(cycle='V', **inp)

plotit([info1, info2, info3], ['F-cycle', 'W-cycle', 'V-cycle'])
parameter tests

Test 2: semicoarsening, line-relaxation

inp = {'model': model_iso, 'sfield': sfield, 'return_info': True,
       'sslsolver': False}

_, info1 = emg3d.solve(semicoarsening=False, linerelaxation=False, **inp)
_, info2 = emg3d.solve(semicoarsening=True, linerelaxation=False, **inp)
_, info3 = emg3d.solve(semicoarsening=False, linerelaxation=True, **inp)
_, info4 = emg3d.solve(semicoarsening=True, linerelaxation=True, **inp)

plotit([info1, info2, info3, info4], ['MG', 'MG+SC', 'MG+LR', 'MG+SC+LR'])
parameter tests

Test 3: MG and BiCGstab

inp = {'model': model_iso, 'sfield': sfield, 'return_info': True, 'maxit': 500,
       'semicoarsening': True, 'linerelaxation': False}

_, info1 = emg3d.solve(cycle='F', sslsolver=False, **inp)
_, info2 = emg3d.solve(cycle='F', sslsolver=True, **inp)
_, info3 = emg3d.solve(cycle=None, sslsolver=True, **inp)

plotit([info1, info2, info3], ['MG', 'MG+BiCGStab', 'BiCGStab'])
parameter tests

Out:

* WARNING :: Error in bicgstab (-10)

Test 4: nu_init, nu_pre, nu_coarse, nu_post

inp = {'model': model_iso, 'sfield': sfield, 'return_info': True,
       'sslsolver': False, 'semicoarsening': True, 'linerelaxation': False}

_, info1 = emg3d.solve(**inp)
_, info2 = emg3d.solve(nu_pre=0, **inp)
_, info3 = emg3d.solve(nu_post=0, **inp)
_, info4 = emg3d.solve(nu_init=2, **inp)

plotit([info1, info2, info3, info4],
       ['{0,2,1,2} (default)', '{0,0,1,2}', '{0,2,1,0}', '{2,1,2,1}'])
parameter tests
Sat Jul 17 18:00:52 2021 CEST
OS Linux CPU(s) 4 Machine x86_64
Architecture 64bit RAM 15.5 GiB Environment Python
Python 3.9.4 | packaged by conda-forge | (default, May 10 2021, 22:13:33) [GCC 9.3.0]
numpy 1.21.0 scipy 1.7.0 numba 0.53.1
emg3d 1.1.0 empymod 2.1.2 xarray 0.18.2
discretize 0.7.0 h5py 3.3.0 matplotlib 3.4.2
tqdm 4.61.2
Intel(R) oneAPI Math Kernel Library Version 2021.2-Product Build 20210312 for Intel(R) 64 architecture applications


Total running time of the script: ( 2 minutes 45.699 seconds)

Estimated memory usage: 39 MB

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