Jun 26, 2018 - Workshop on Computational Aspects of Time Domain. Electromagnetic Wave Problems in Complex Materials. ICERM, Providence, USA ...
Time Domain Simulation of Thin Layers L. D. Angulo (UGR), M. R. Cabello (UGR), D. Escot (INTA), A. R. Bretones (UGR), S. G. Garcia (UGR)
June 26th, 2018 Workshop on Computational Aspects of Time Domain Electromagnetic Wave Problems in Complex Materials ICERM, Providence, USA
Introduction
Modeling and validation
Inclusion in FDTD
1
Thin layer modeling and validation Theoretical models Validation
2
Inclusion in FDTD Matrix Impedance Boundary Condition Sub-Gridding Boundary Condition
3
Conformal FDTD Conformal SGBC
4
Conclusions
Conformal FDTD
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Introduction
Context: Unmanned Air Vehicles (UAVs)
Conclusions
Introduction
Modeling and validation
Introduction
Thin layers
Inclusion in FDTD
Conformal FDTD
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Introduction
Workflow Manufacturer's data
Geometry and material data Thin layer modeling or Simulations
Vector Fitting
- ABCD Matrices - S Parameters - SE (TE, TM, av)
Experimental measures
Analytical transformations
Single layer effective parameters
CCPR Pairs
NIBC
Samples
FDTD Solver
SGBC
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Modeling and validation
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Theoretical models
Theoretical models Typical assumptions Normal propagation within the panel. Transmission matrices for different layers are independent. 1
2
ε0 , µ 0
m−1
m
ε0 , µ 0
...
~ d ,H ~d E
~ 0 ,H ~0 E ...
~ E
~ H
~k
d1
d2
dm−1
dm
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Theoretical models
Close-to-normal refraction In the thin layer approximation we assume that the refracted wave travels perpendicular to the surface, sin θi sin θt = p 1 − j/Q with Q = 2πf τ and τ = ε/σ. The higher the frequency and the conductivity, the better the approximation. For grazing incidence θi → π/2 (worst-case) we have |θt | < 10−2 if f [GHz] < 1.8σ[kS/m].
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Theoretical models
Models evaluated Holloway model Slices layers in subsequent regions, and computes an effective media on each. The model fails at high frequencies for loose wire structures because of the dominance of the proximity effect between wires. C.L. Holloway, M.S. Sarto, and M. Johansson. Analyzing carbon-fiber composite materials with equivalent-layer models. Electromagnetic Compatibility, IEEE Transactions on, 47(4):833–844, Nov 2005
McFarlane-Wait-Sarto model Uses sheet impedance Zs to derive ABCD matrices using an infinitely periodic thin-wire hypothesis (a P ) to account for the reactance of the layer. Fails at high frequencies for dense wire structures because of the neglection of the proximity effect. M. S. Sarto, S. Greco, and A. Tamburrano. Shielding effectiveness of protective metallic wire meshes: EM modeling and validation. IEEE Transactions on Electromagnetic Compatibility, 56(3):615–621, June 2014
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Validation
Loose Wire Bronze Mesh M. S. Sarto, S. Greco, and A. Tamburrano. Shielding effectiveness of protective metallic wire meshes: EM modeling and validation. IEEE Transactions on Electromagnetic Compatibility, 56(3):615–621, June 2014
Bronze mesh average SE computed from provided data.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Validation
100 Wait Av Wait TE Wait TM Simulated Av Simulated TE Simulated TM
90 80 70
a2
SE [dB]
60
P2
50 40
P1
30 20 10 0 8 10
9
10
10
10
11
10
a1
Frequency [Hz]
SE results for the loose wire mesh configuration. This was modeled with two layers of wires having a1 = a2 = 50 µm, σ = 58 MS/m, and P1 = P2 = 558 µm. In this case, wires are widely separated (P/a ≈ 11). Inductive effects to dominate. Holloway’s model results are not shown for falling out of the scale.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Validation
Expanded Aluminum Foil
Expanded aluminum foil average SE computed from provided data.
M. S. Sarto, S. Greco, and A. Tamburrano. Shielding effectiveness of protective metallic wire meshes: EM modeling and validation. IEEE Transactions on Electromagnetic Compatibility, 56(3):615–621, June 2014
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Validation
100 Wait Av Wait TE Wait TM Simulated Av Simulated TE Simulated TM
90 80 70
SE [dB]
60 50 40
W
30 20 10 0 8 10
9
10
10
10
11
H
10
Frequency [Hz]
SE results for the expanded foil. The rectangular cross sections of the expanded foil were substituted by area-equivalent round wires with a = 90 µm and σ = 38 MS/m. Unit cell has periodicities of W = 2129 µm and H = 1259 µm.
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Validation
Dense Steel Mesh 100 90 80 70
SE [dB]
60
Wait Av Wait TE Wait TM Holloway Av Holloway TE Holloway TM Simulated Av Simulated TE Simulated TM
50 40 30 20
a1
10 0 8 10
9
10
10
10 Frequency [Hz]
11
10
P1
a2 , P2
SE results for the dense steel mesh configuration. M. S. Sarto, S. Greco, and A. Tamburrano. Shielding effectiveness of protective metallic wire meshes: EM modeling and validation. IEEE Transactions on Electromagnetic Compatibility, 56(3):615–621, June 2014
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Validation
Carbon fiber composite
(a) 5x zoom
(b) 50x zoom
Microscopic images of multilayered CFCs (courtesy of INTA).
P
a
P A single layer of CFC has been modeled
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Validation L. D. Angulo, M. R. Cabello, J. Alvarez, A. R. Bretones, and S. G. Garcia. From microscopic to macroscopic description of composite thin panels: A roadmap for their simulation in time domain. IEEE Transactions on Microwave Theory and Techniques, 66(2), 2018 100 90 80 70
SE [dB]
60 50 40 30 20 10 0 8 10
Wait TM Holloway TM Anisotropic effective layer TM Simulated TM 9
10
10
10
11
10
Frequency [Hz]
SE results for a layer of 24 stacked carbon fiber threads. Proximity effects dominate and Holloway’s model reproduces adequately the results.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Validation
Summary on modeling and validation
Table summarizing the validity of models. A model is considered to be valid if it matches other existing data or model.
Loose mesh Loose expanded foil Dense mesh CFC
Wait Yes Yes LF only LF only
Holloway LF only LF only LF only Yes
FEM-FD Yes Yes LF only Yes
Experimental Yes Yes Unavailable Unavailable
Introduction
Modeling and validation
Inclusion in FDTD
Inclusion in FDTD
Conformal FDTD
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Matrix Impedance Boundary Condition
Matrix Impedance Boundary Condition (MIBC) ~ and H ~ at front A standard approach is to make use of the fact E and at the back of a thin layer are related by the matrix, " # " # ~ front (ω) ~ back (ω) E E ˜ ~ front (ω) = Φ(ω) H ~ back (ω) H or, equivalently, by the matrix impedances, " # # " ~ front (ω) ~ front (ω) Z˜front (ω) Z˜fr-bk (ω) H E ~ back (ω) = Z˜bk-fr (ω) Z˜back (ω) H ~ back (ω) E then converted into TD with a convolutional or ADE procedure. M.S. Sarto. Sub-cell model of multilayer composite materials for full FDTD and hybrid mfie/FDTD analyses. 2:737– 742 vol.2, Aug 2002 D.A. Frickey. Conversions between S, Z, Y, H, ABCD, and T parameters which are valid for complex source and load impedances. IEEE Transactions on Microwave Theory and Techniques, 42(2):205–211, 1994
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Matrix Impedance Boundary Condition
Weak late-time stability These conditions arise to weak late-time stability often requiring a very small time step to be used. Possible causes: Extrapolation of H-field half cell and half time-step away (zeroth-order approximation). Failure to meet stability conditions of the new system of discretized equations when coupled with the standard Yee’s algorithm. Existence of high frequency oscillations that fall out of the stability region of the leap-frog time integration used in FDTD.
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Sub-Gridding Boundary Condition
Sub-Gridding Boundary Condition
An 1D fine mesh is embedded the usual 3D coarse space. Eqs. are evolved with an unconditionally stable Crank-Nicolson scheme.
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Sub-Gridding Boundary Condition
The materials forming the slabs in the fine mesh are bulk anisotropic materials with ε(ω) and µ(ω) chosen to mimic the Z˜ matrices of the original thin layer. These are later converted into an ADE system of equations. M. R. Cabello, L. D. Angulo, J. Alvarez, I. Flintoft, S. Bourke, J. Dawson, R. G. Martin, and S. G. Garcia. A hybrid Crank-Nicolson FDTD subgridding boundary condition for lossy thin-layer modeling. IEEE Transactions on Microwave Theory and Techniques, 2017. Accepted.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Sub-Gridding Boundary Condition
SGBC Resolution (PPW)
-120
22.4·PPWfine
10.0·PPWfine
3.2·PPWfine
1.0·PPWfine
106
107
-130
S12 (dB)
-140 -150 -160 -170 -180 -190 -200 4 10
Slab Setup Thickness σ [S/m] ε 0.3 mm 3.456 107 ε0
Analytical Maloney DigFilt Order 12th NIBC SGBC 10 Layers PPWfine=5.7 SGBC 40 Layers PPWfine=22.7
105
Frequency (Hz)
S12 = SE−1 for an aluminum planar slab with σ = 3.456 · 107 S/m and th = 0.3 mm. ∆coarse = 2.5 mm.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Sub-Gridding Boundary Condition
1500.0
90
PPWcoarse
150.0
15.0
7.5
80 70 60 SE (dB)
50 40 30 Analytical
20
FDTD, face centered, DigFilt order 6th NIBC FDTD, edge centered, SGBC 4 Layers FDTD, edge centered, SGBC 1 Layers
10 0
106
107
108 Frequency (Hz)
109
SE for a sphere of radius 1 m, 200 S/m conductivity and 5 mm thickness.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Sub-Gridding Boundary Condition
SIVA UAV: DCI setup
DCI test-setup of SIVA in INTA OATS. The cover is modeled as an homogeneous material with σ = 104 S/m, th = 0.92 mm, ∆coarse = 6 mm. M. R. Cabello, S. Fern´ andez, M. Pous, E. Pascual-Gil, L. D. Angulo, P. L´ opez, P. J. Riu, G. G. Gutierrez, D. Mateos, D. Poyatos, M. Fernandez, J. Alvarez, M. F. Pantoja, M. A˜ n´ on, F. Silva, A. R. Bretones, R. Trallero, L. Nu˜ no, D. Escot, R. G. Martin, and S. G. Garcia. Siva UAV: A case study for the EMC analysis of composite air vehicles. IEEE Transactions on Electromagnetic Compatibility, PP(99):1103–1113, 2017.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Sub-Gridding Boundary Condition
SIVA Results
Results for measurements and simulation at four different points. MIBC required a time step ten times smaller than SGBC to be stable.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conformal FDTD
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Extension to Conformal FDTD
Why Conformal FDTD? Staircasing error reduces error convergence of FDTD from O(h2 ) to O(h) in practice.
Dey Mittra method. Location of the electric fields Ek,ν on the closed contour. The magnetic field is assumed to be constant inside the contour.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Extension to Conformal FDTD
Efficient implementation, CRDM Relaxation factor Choose the factor, Frlx = lf /∆ which restricts, p ∆t = 3Frlx /2∆tCFL For instance: Frlx = 0.5, slanted FDTD. Frlx = 0, perfect fit, small time-step. M. R. Cabello, L. D. Angulo, J. Alvarez, A. R. Bretones, G. G. Gutierrez, and S. G. Garcia. A new efficient and stable 3D conformal FDTD. IEEE Microwave and Wireless Components Letters, 26(8):553–555, Aug 2016.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Extension to Conformal FDTD
Detail of the mesh generated by a conformal mesher DMesheR (purple) from an input geometric mesh (transparent blue). In the surface boundaries, the mesh is treated in a structured way.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Extension to Conformal FDTD
140
70
PPW
28
20
14
7
20
RCS [dBsm]
15
10
5
0
Theoretical (Mie) Staircase CRDM Frlx = 0.3 Yu-Mittra
107
Frequency [Hz]
108
Comparison of the RCS for a sphere of radius 3 m with meshes for CRDM and structured with space resolution of ∆ = 3/14 m and CFLN = 0.9.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Extension to Conformal FDTD
100
Error
O(∆) 10−1 Staircase DM CRDM Frlx = 0.1 CRDM Frlx = 0.48
10−2 30
40
O(∆2)
50
60
PPW
70
80
90
102
Error convergence is improved with the CRDM method. This is the RMS error for the monostatic RCS of a NASA Almond.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Extension to Conformal FDTD
Method CRDM Frlx CRDM Frlx CRDM Frlx CRDM Frlx Yu-Mittra Staircase
= 0.05 = 0.1 = 0.3 = 0.48
CFLN 0.273 0.39 0.67 0.85 0.9 0.9
Error RMS [dBsm] 0.198 0.201 0.225 0.278 0.595 1.201
CPU Time 3.32 2.44 1.40 1.10 1.05 1.0
RMS error in the interval [10, 100] MHz for different Frlx values of the conformal method. The CPU time is shown as the number of times employed by the structured case.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Conformal SGBC
SGBC in Conformal FDTD
C-FDTD cell with a NIBC boundary.
C-FDTD cell with a SGBC boundary.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Conformal SGBC
Validation: Slanted surface
Staircasing has an even larger impact if we model line-shaped geometries. There is no convergence, no matter how much the mesh is refined. This is critical when solving wires.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conformal SGBC
Validation: Shielding Effectiveness of a Sphere
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conclusions
Conformal FDTD
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Thin layer modeling No universal model exists, validity depends on distance between conducting elements. CFCs behave mostly as a conductive layer of material.
Conclusions
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Conclusions
Numerical simulation of thin layers MIBC presents stability problems. SGBC is a robust alternative to MIBC. No stability problems have been found. No reduction of time-step is necessary. Accurate reproduces the used model. Extension of SGBC to Conformal Conformal FDTD has better accuracy than classic FDTD using less computational resources. The models have been extended to SGBC. Preliminar results are satisfactory.
Introduction
Modeling and validation
Inclusion in FDTD
Conformal FDTD
Conclusions
Thanks for your attention
Conclusions