[SI-LIST] Re: TLM: Laplace and discrete difference equations
- From: "Yuriy Shlepnev" <shlepnev@xxxxxxxxxxxxx>
- To: <richardg@xxxxxxxxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
- Date: Mon, 14 May 2007 12:52:38 -0700
Richard,
There are no universal recommendations on the step and area sizes. It
depends on multiple details of the algorithm and implementation such as the
boundary condition approximation, type of basis functions or order of the
local approximation. You have to investigate the dependency of the
characteristic impedance from the step size and from the area size to get an
idea on accuracy. It is called convergence study. Fix the area size for
instance and solve the problem multiple times with different grids (keep the
same high accuracy for the iterative solver or use a direct solver). Plot
the impedance vs. step size - it will give you rough idea on the method
convergence from the step size. Use a geometry with known answer to validate
your solution and to estimate accuracy (an ideal 50-Ohm strip line for
instance). Richardson's extrapolation can be used sometime to find the
convergence limit and to estimate the accuracy for complex geometries
without comparisons.
In general, the convergence study and comparisons with results obtained
analytically or with other methods are essential steps to 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 [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 of the
things that interest me was the Laplace equation. The material explains
Laplace using the discrete difference equations, creating the boundary
conditions and the incremental steps. The area that I don't fully understand
is how to determine the size of the incremental step size and how large the
area of interest should be when calculating an impedance for a stripline for
example. Since this is an iterative process to calculate the voltages and
charges, the larger the area and smaller the step sizes will increase the
time to convergence. So with difference step sizes or different boundary
dimensions that gives different results (to within a tolerance), how do I
determine those 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 ===== Richard Georgerian
> Compliance Engineer NewsFlex Ltd.
> "...turning the world one page at a time..."
> Web site: http://newsflex.net
> email: richardg@xxxxxxxx
> =====
>
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