[SI-LIST] Re: TLM: Laplace and discrete difference equations
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: <write2larsj@xxxxxxxxx>, <richardg@xxxxxxxxxxxxxxxx>
- Date: Tue, 15 May 2007 07:35:44 -0700
Lars,
The TLM method is slightly different subject, but I guess it might be
relevant to this list (it has been extensively used to simulate PDNs for
instance).
Good introductory books are:
1) W.J.R. Hoefer The Transmission Line Matrix (TLM) Method, in Numerical
techniques for microwave and millimeter-wave passive structures, Edited =
by
T. Itoh, John Wiley & sons, 1989, p.496
2) C. Christopoulos, The Transmission-Line Modeling Method (TLM), IEEE
Press, 1995.
Transmission Line Matrix method and Transmission Line Modeling method =
are
the same things in computational electromagnetics. If you prefer more
mathematical description of the method, it can be derived as Trefftz =
Finite
Elements (TFEs) or Ultra-Week Discontinuous Galerkin's Finite Elements =
(see
for instance Y. Shlepnev, Trefftz Finite Elements for Electromagnetics =
in
IEEE Trans. on MTT, v. 50, N 5, p. 1328-1339).=20
Best regards,
Yuriy Shlepnev
Simberian Inc.
http://simberian.com/=20
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =
On
Behalf Of Lars Juul
Sent: Tuesday, May 15, 2007 5:24 AM
To: shlepnev@xxxxxxxxxxxxx; richardg@xxxxxxxxxxxxxxxx
Cc: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: TLM: Laplace and discrete difference equations
Yuriy and Richard,
Which books on the TLM method would you recommend for =
application-oriented
people wanting to implement their own TLM code?
So far I identified:
"Electromagnetic Analysis Using Transmission Line Variables" By Maurice
Weiner (ISBN 981024438X)
"Die "Transmission Line Matrix" (TLM) Methode im Zeitbereich" By Ulf =
M=DDller
(ISBN 3817115164)
Thanks in advance,
Lars Juul
2007/5/14, Yuriy Shlepnev <shlepnev@xxxxxxxxxxxxx>:
>
> Richard,
>
> There are no universal recommendations on the step and area sizes. It=20
> depends on multiple details of the algorithm and implementation such=20
> as the boundary condition approximation, type of basis functions or=20
> order of the local approximation. You have to investigate the=20
> dependency of the characteristic impedance from the step size and from =
> the area size to get an idea on accuracy. It is called convergence=20
> study. Fix the area size for instance and solve the problem multiple=20
> times with different grids (keep the same high accuracy for the=20
> iterative solver or use a direct solver). Plot the impedance vs. step=20
> size - it will give you rough idea on the method convergence from the=20
> step size. Use a geometry with known answer to validate your solution=20
> and to estimate accuracy (an ideal 50-Ohm strip line for instance). =20
> Richardson's extrapolation can be used sometime to find the=20
> convergence limit and to estimate the accuracy for complex geometries=20
> without comparisons.
> In general, the convergence study and comparisons with results=20
> obtained analytically or with other methods are essential steps to=20
> validate a field solver algorithm and to find balance between accuracy =
and
performance.
>
> Best regards,
> Yuriy Shlepnev
> Simberian Inc.
> http://www.simberian.com/
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx=20
> [mailto:si-list-bounce@xxxxxxxxxxxxx]
> On
> Behalf Of Richard Georgerian
> Sent: Sunday, May 13, 2007 11:05 AM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] TLM: Laplace and discrete difference equations
>
> Greetings All,
> I have been reading some books on transmission line modeling and one=20
> of the things that interest me was the Laplace equation. The material=20
> explains Laplace using the discrete difference equations, creating the =
> boundary conditions and the incremental steps. The area that I don't=20
> fully understand is how to determine the size of the incremental step=20
> size and how large the area of interest should be when calculating an=20
> impedance for a stripline for example. Since this is an iterative=20
> process to calculate the voltages and charges, the larger the area and =
> smaller the step sizes will increase the time to convergence. So with=20
> difference step sizes or different boundary dimensions that gives=20
> different results (to within a tolerance), how do I determine those=20
> step sizes or boundary dimensions?
>
> Many thanks in advance.
>
> > Richard
> EMC2007 Arrangements
> > 2007 PSES Symposium Chair
> > 2007 PSES Web site: http://www.ewh.ieee.org/soc/pses/symposium/
> > 2007 PSES Symposium date: 22-23 October 2007 =3D=3D=3D=3D=3D Richard =
> > Georgerian Compliance Engineer NewsFlex Ltd.
> > "...turning the world one page at a time..."
> > Web site: http://newsflex.net
> > email: richardg@xxxxxxxx
> > =3D=3D=3D=3D=3D
> >
>
>
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