Time Domain Simulation of Thin Layers - ICERM

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


Inclusion in FDTD

Conformal FDTD

Introduction

Context: Unmanned Air Vehicles (UAVs)

Conclusions

Introduction


Introduction

Thin layers

Inclusion in FDTD

Conformal FDTD

Conclusions

Introduction


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


Inclusion in FDTD

Conformal FDTD


Conclusions

Introduction


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


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


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


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


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


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


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


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


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


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


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


Inclusion in FDTD

Inclusion in FDTD

Conformal FDTD

Conclusions

Introduction


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


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


Inclusion in FDTD

Conformal FDTD

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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conformal FDTD

Conclusions

Introduction


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


Inclusion in FDTD

Conformal FDTD

Conclusions


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


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


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


Inclusion in FDTD

Conformal FDTD

Conformal SGBC

Validation: Shielding Effectiveness of a Sphere

Conclusions

Introduction


Inclusion in FDTD

Conclusions

Conformal FDTD

Conclusions

Introduction


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


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


Inclusion in FDTD

Conformal FDTD

Conclusions

Thanks for your attention

Conclusions