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- resistive panel
- 09-24-2020
Re: resistive panel
Well, mathematically, it's an application of conformal mapping; the
key algorithms use a Schwartz-Christoffel transformation for the corners.
So, Morse and Feshbach, _Methods_of_Theoretical_Physics_ has the
method, around page 445 of volume I. Then with the plate shape
tamed, you just solve Laplace's equation, with the boundary conditions,
and reverse the transformation.
Re: resistive panel
"then a miracle occurs" <-- I think Whit could be more explicit here. ;)
Analytical conformal mapping is generally hard unless the transformation
is simple, such as mapping the upper half plane onto a circular disc.
Every corner in the domain gives rise to a fractional power term in the
integrand, which is a bear.
A simple 2D Laplace solver that you can code up very quickly is the
relaxation method, where you divide the domain up into a square grid,
and on each iteration replace the voltage at each point with the average
of its four nearest neighbours.
There are lots of faster methods, but that one works fine and is sure easy.
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
Dr Philip C D Hobbs
Principal Consultant
We've slightly trimmed the long signature. Click to see the full one.
Re: resistive panel
Phil - I was thinking along the same lines you mentioned but a bit
more so. The simplicty of a flat panel does make methods for 3 dimensional
surfaces seem excessive.
I'm hoping to find something similar to calculating position
from a knowledge of 2 distances. The hooker being that distances
on the panel would be curved, so some code is required for
corrections.
If you or anyone else have any suggestions along these
lines, please mention them.
Hul
more so. The simplicty of a flat panel does make methods for 3 dimensional
surfaces seem excessive.
I'm hoping to find something similar to calculating position
from a knowledge of 2 distances. The hooker being that distances
on the panel would be curved, so some code is required for
corrections.
If you or anyone else have any suggestions along these
lines, please mention them.
Hul
Re: resistive panel
On 2020-09-24 18:56, Hul Tytus wrote:
Conformal mapping is inherently a 2D method because it relies on
complex-variable calculus--it maps one region of the complex plane into
another. If the geometry is sufficiently simple, it can do magic on
Laplace's equation problems. It's also useful numerically.
It would be easier to help if you could give more details about the
panel--all you've said about it is that it's resistive and is connected
at multiple points on its edges.
One fairly general approach would be to use the relaxation method to
calculate the response for various source positions, fit a 2-D
polynomial or a 2-D spline, and use that. (Numerical Recipes has a
pretty good discussion of surface fitting.)
Cheers
Phil Hobbs
Conformal mapping is inherently a 2D method because it relies on
complex-variable calculus--it maps one region of the complex plane into
another. If the geometry is sufficiently simple, it can do magic on
Laplace's equation problems. It's also useful numerically.
It would be easier to help if you could give more details about the
panel--all you've said about it is that it's resistive and is connected
at multiple points on its edges.
One fairly general approach would be to use the relaxation method to
calculate the response for various source positions, fit a 2-D
polynomial or a 2-D spline, and use that. (Numerical Recipes has a
pretty good discussion of surface fitting.)
Cheers
Phil Hobbs
--
Dr Philip C D Hobbs
Principal Consultant
Dr Philip C D Hobbs
Principal Consultant
We've slightly trimmed the long signature. Click to see the full one.
Re: resistive panel
That's a tad ugly, but do-able. Even uglier would be an 'exact' conformal
solution with an equation-solve element that does least-entropy fitting to X,Y, and source value.
The desired solution is a single-point current source, or voltage source, I hope?
Before I did the relaxation method, I'd wonder if ultrasound time-of-flight is easier.
Heck, I'd wonder if attack-the-prototype with probes, on a grid, is easier.
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