Upload
ioannis-georgakis
View
227
Download
0
Embed Size (px)
Citation preview
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
1/16
Challenges of SensitivityAnalysis with Time DomainEM Solvers
Guoqiang Shen, Helen Tam and Natalia Georgieva
Computational Electromagnetics Laboratory
Department of Electrical and Computer EngineeringMcMaster UniversityCanada
Outline
n Background
n Reviewed existing results
n Our current resultsn Challenges
n Conclusions
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
2/16
Outline
n Backgroundn Reviewed existing results
n Our current results
n Challenges
n Conclusions
Backgroundn Design Sensitivity Analysis (DSA)
DSA concerns the relationship between the objectivefunction and design variables that describe the shapeof geometry or the material properties to be
optimized.
( ) ( )0
, ,
T
z y x
F G dtdxdydz= p pe eObjective function:
T: fixed final time
G: arbitrary differentiable function
e: field variable vector, p: design variable vector
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
3/16
Purpose of DSA: to evaluate the derivative of thesystems response with respect to variations in thedesign parameters
0
1, 2, ... ,
T e
p
i i iz y x
F G Gdtdxdydz i n
p p p
= + =
e
e
Design sensitivity:
np: the total number of the design variable pi
/ :eG p the explicit dependence of G on pi
n Adjoint Variable Method (AVM)AVM is an efficient design approach to complex linearand nonlinear problems and it has been proposed inmany areas, such as structural design, circuit theoryand control theory, etc.
Comparing with direct difference method (DDM), AVMoffers significant reduction in CPU time by producingthe response and its gradient through a single full-wave analysis.n DDM: requires solving the system equation for each design
variable.
n AVM: only need to solve the adjoint variable equation in theintroduced adjoint system and it requires only a moderateamount of computation.
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
4/16
Implementation of AVM: by introducing adjoint systemand solving the adjoint variable equation as well asthe original system.
Vector wave equation:2
02 2
1 r
r c t t
+ =
E E J
Original system:
( )
( )
2
2,
0 0,
00
t
t
+ =
=
=
M K Qe
e
e
e
2M /r c=
1K r
=
0Q / t= J
( )
( )
2
2
0
0
TG
t
T
Tt
+ = =
=
M Ke
( )
( )
2
2
0 0
0 0
TG
+ =
=
=
M Ke
T t=
Adjoint system:
Terminal condition for t Initial condition for
Backward time scheme
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
5/16
Design sensitivity evaluated by AVM:
T
0
eT
i i iz y x
F Gdtdxdydz
p p p
= +
R
2
2t
=
R Q M K
%%e e
%e is independent of the design variable ip
.
Outline
n Background
n Reviewed existing results
n Our current resultsn Challenges
n Conclusions
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
6/16
Published achievements
n Results by FETD(Y.S. Chung et al. 2001)Design microwave passive devices with small return
loss by FETD technique
AVM is used to evaluate design sensitivity
Unstructured triangular elements used
n Results by FDTD(Y.S. Chung et al. 2000, 2001)
Using uniqueness theorem, adjoint variable equationsfrom FETD are derived as coupled Maxwells curlequations and can be solved by the FDTD method.
AVM is used to evaluate design sensitivity.
Unstructured quadrilateral grids and DSI techniqueare used to model the design space, and PML isemployed as ABC.
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
7/16
Outline
n Backgroundn Reviewed existing results
n Our current results
n Challenges
n Conclusions
Our current results
n Methodology
To evaluate the design sensitivity of the design variablesby employing AVM in the FDTD method.
execute the
original system
execute the
adjoint system
execute the
design
sensitivity
algorithmi
F
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
8/16
Original system
Inside the original
system
Compute and
record the adjoint
current
Compute the
objective function
for convergence
check
Record the electric
field in the
perturbation
domain
Adjoint system
Inside the adjointsystem
Reverse the signof Maxwellsequations
Record the adjointfield in the
perturbationdomain
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
9/16
Design sensitivity algorithm
Inside the design
sensitivity algorithm
Retrieve the data files of
the original field and the
adjoint field; save the
data into arrays
Update the adjoint
variable equation with
the corresponding fields
at each time step
n Numerical results and comparisonStep waveguide junction structure
The flow of the width variation in the step waveguide junction structure(symmetric about y-axis)
10
10y
300z
z
yPort 1
Port 2
Mid-section
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
10/16
Objective function:
2
0
2
0 1
2
2
T
x y
ymaxT
y
F zdxdydt
F z xdydt=
=
=
x
x
e
e
Design variable: the width of the mid section y.
Port 2Mid-section
Port 1
LengthWidthHeight
1 x
1 x
1 x
10 y
10 y
5 13y y
147 z
10 z
147 z
Comparison of the design sensitivity between the adjointvariable method and the central finite difference
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
11/16
Waveguide H-plane filter
y
z
the middle septum
28 y
600 z
The layout of the waveguide H-plane filter(symmetric about y-axis)
Objective function:
2
0
2
0 1
2
2
T
x y
ymaxT
y
F zdxdydt
F z xdydt=
=
=
x
x
e
e
Design variable: the width of the mid section y.
4th
3rd and 5th
2nd and 6th
1st and 7thLengthWidthHeightSepta
1
1
1
1
7 y
10 y
6 15 y
9 y
1 z
1 z
1 z
1 z
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
12/16
The design sensitivity of the septum waveguide
Single-section transformer
The layout of the single-section transformer(symmetric about y-axis)
10z
12y
600z
20y
Mid-section
Port 2
Port 1
z
y
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
13/16
The design sensitivity of the single-section transformer
Outline
n Background
n Reviewed existing results
n Our current resultsn Challenges
n Conclusions
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
14/16
Challenges
n Advantages of AVMComputationally efficient as it only requires two
simulations regardless of the number of design
variables.
AVM with FDTD can provide broad-band sensitivityestimation.
n Limitations of current algorithmExcitation cannot have a DC component.
The design variables can not be freely chosen.
The two ports are expected to have same width inorder to reduce the reflection.
For those with few field points, the results will be less
accurate.Absorbing boundary conditions affect the accuracy.
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
15/16
n Ways to improve the algorithm Increase the number of observation field points, i.e.,
increase the observation domain.
Use more efficient absorbing boundary conditions,such as PML (Perfectly Matched Layer) as ABC. Theaccuracy of the excitation of the adjoint systemdepends much on the efficiency of ABC.
Outline
n Background
n Reviewed existing results
n Our current resultsn Challenges
n Conclusions
8/10/2019 Challenges of Sensitivity Analysis with Time Domain EM Solvers
16/16
Conclusions
n Overview of DSA and AVM techniques.n Implementation with FETD and FDTD methods.
n Advantages and limitations.
n Challenges and improvements.
References
n Y.S. Chung, J. Ryu, C. Cheon, I.H. Park and S.Y. Hahn, Optimaldesign method for microwave device using time domain method anddesign sensitivity analysis Part I: FETD case, pp. 3289-3293,IEEE Trans. Magnetics, vol. 37, No. 5, Sep. 2001.
n Y.S. Chung, C. Cheon, I.H. Park and S.Y. Hahn, Optimal designmethod for microwave device using time domain method and designsensitivity analysis Part I: FDTD case, pp. 3255-3259, IEEE Trans.Magnetics, vol. 37, No. 5, Sep. 2001.
n Y.S. Chung, C. Cheon, I.H. Park and S.Y. Hahn, Optimal shapedesign of microwave device using FDTD and design sensitivityanalysis, pp. 2289-2296, IEEE Trans. Microwave Theory andTechniques, vol. 48, No. 12, Dec. 2000.