On May 11, 8:30*pm, Art Unwin wrote:
When an array is
in equilibrium then Maxwell's equations are exact.

maxwell's equations are ALWAYS exact, it is digital models that are
inexact and have limitations due to the approximations made and the
numeric representations used.

On May 12, 12:10*pm, K1TTT wrote:
On May 11, 8:30*pm, Art Unwin wrote:

When an array is
in equilibrium then Maxwell's equations are exact.

maxwell's equations are ALWAYS exact, it is digital models that are
inexact and have limitations due to the approximations made and the
numeric representations used.

On this I have total agreement. The moment one strays from the concept
of equilibrium is when we expose ourselves to errors.
Regards
Art

On May 12, 3:29*pm, Art Unwin wrote:
On May 12, 12:10*pm, K1TTT wrote:

On May 11, 8:30*pm, Art Unwin wrote:

When an array is
in equilibrium then Maxwell's equations are exact.

maxwell's equations are ALWAYS exact, it is digital models that are
inexact and have limitations due to the approximations made and the
numeric representations used.

On this I have total agreement. The moment one strays from the concept of equilibrium is when we expose ourselves to errors.
Regards
Art

ok, so you DO agree that maxwell's equations that make no mention of
particles like neutrinos, gravity, coriolis forces, or levitation ARE
correct! And therefor you must agree that the representation of
gauss's law encapsulated in maxwell's equations, WITHOUT an explicit t
in it must be correct! You must also be admitting that your
optimization experiments are full of errors. wow, now its time to go
and rejoice, art has finally come around to the real world!

K1TTT wrote:
On May 11, 8:30 pm, Art Unwin wrote:
When an array is
in equilibrium then Maxwell's equations are exact.

maxwell's equations are ALWAYS exact, it is digital models that are
inexact and have limitations due to the approximations made and the
numeric representations used.

Inexactness of the solution isn't because the method is digital. The
field equations solved by the digital methods simply can't be solved by
other methods, except for a relatively few very simple cases. Many
non-digital methods were developed over the years before high speed
computers to arrive at various approximate solutions, but all have
shortcomings. For example, I have a thick file of papers devoted to the
apparently simple problem of finding the input impedance of a dipole of
arbitrary length and diameter. Even that can't be solved in closed form.
Solution by digital methods is vastly superior, and is capable of giving
much more accurate results, than solution by any known method.

Roy Lewallen, W7EL

On May 13, 8:56*am, Roy Lewallen wrote:
K1TTT wrote:
On May 11, 8:30 pm, Art Unwin wrote:
When an array is
in equilibrium then Maxwell's equations are exact.

maxwell's equations are ALWAYS exact, it is digital models that are
inexact and have limitations due to the approximations made and the
numeric representations used.

Inexactness of the solution isn't because the method is digital. The
field equations solved by the digital methods simply can't be solved by
other methods, except for a relatively few very simple cases. Many
non-digital methods were developed over the years before high speed
computers to arrive at various approximate solutions, but all have
shortcomings. For example, I have a thick file of papers devoted to the
apparently simple problem of finding the input impedance of a dipole of
arbitrary length and diameter. Even that can't be solved in closed form.
Solution by digital methods is vastly superior, and is capable of giving
much more accurate results, than solution by any known method.

Roy Lewallen, W7EL

quantization of every number in a numeric simulation is but one of the
contributions to inaccuracy. the limitations of the physical model is
another, every modeling program i know of breaks the physical thing
being modeled into small pieces, some with fixed sizes, some use
adaptive methods, but then they all calculate using those small pieces
as if they were a single homogonous piece with step changes at the
edges... that also adds to inaccuracies. the robustness of the
algorithm and the residual errors created are a bit part of getting
more accurate results. There is no doubt that numerical methods have
allowed 'solutions' of many problems that would be extremely difficult
to find closed form solutions for, but they must always be examined
for the acceptibility of the unavoidable errors in the method used.

other non-digital methods also have their limitations. unless you are
using the original differential or integral equations and satisfying
all the boundary conditions, your method will introduce errors.
weather that means you represent an odd shaped solid object by a
sphere, or make other geometic replacements that give you simpler
field configurations, you have introduced errors at some level. you
must of course judge these methods by the same way to determine of the
errors introduced by the simplyfied geometry or other methods used are
acceptible for the problem at hand.

K1TTT wrote:
On May 13, 8:56 am, Roy Lewallen wrote:
K1TTT wrote:
On May 11, 8:30 pm, Art Unwin wrote:
When an array is
in equilibrium then Maxwell's equations are exact.
maxwell's equations are ALWAYS exact, it is digital models that are
inexact and have limitations due to the approximations made and the
numeric representations used.
Inexactness of the solution isn't because the method is digital. The
field equations solved by the digital methods simply can't be solved by
other methods, except for a relatively few very simple cases. Many
non-digital methods were developed over the years before high speed
computers to arrive at various approximate solutions, but all have
shortcomings. For example, I have a thick file of papers devoted to the
apparently simple problem of finding the input impedance of a dipole of
arbitrary length and diameter. Even that can't be solved in closed form.
Solution by digital methods is vastly superior, and is capable of giving
much more accurate results, than solution by any known method.

Roy Lewallen, W7EL

quantization of every number in a numeric simulation is but one of the
contributions to inaccuracy. the limitations of the physical model is
another, every modeling program i know of breaks the physical thing
being modeled into small pieces, some with fixed sizes, some use
adaptive methods, but then they all calculate using those small pieces
as if they were a single homogonous piece with step changes at the
edges...

Not all modeling uses step changes. Some modeling approaches use a model
description that is continuous at element boundaries (at least for some
number of derivatives). For example, a cubic spline has smoothly
varying values, first and second derivatives.

The tradeoff in the code is whether you use fewer, better (higher order
modeling) chunks or more simpler chunks. For instance, NEC uses a basis
function that represents the current in a segment (the chunk) as the
combination of a value and two sinusoid sections. Other codes assume
the current is uniform over the segment, yet others assume a sinusoidal
distribution or a triangle.

This leads to a tradeoff in computational resources required: numerical
precision, computational complexity, etc. (lots of simple elements tends
to require bigger precision)

I think that for codes hams are likely to encounter, these are pretty
subtle differences and irrelevant. A lot of the "computational
efficiency" issues are getting smaller, as cheap processor horsepower is
easy to come by.


that also adds to inaccuracies. the robustness of the
algorithm and the residual errors created are a bit part of getting
more accurate results. There is no doubt that numerical methods have
allowed 'solutions' of many problems that would be extremely difficult
to find closed form solutions for, but they must always be examined
for the acceptibility of the unavoidable errors in the method used.

That's why there's all those "validation of modeling code X" papers out
there.

On 5/14/2010 6:19 AM, K1TTT wrote:

quantization of every number in a numeric simulation is but one of the
contributions to inaccuracy. the limitations of the physical model is
another, every modeling program i know of breaks the physical thing
being modeled into small pieces, some with fixed sizes, some use
adaptive methods, but then they all calculate using those small pieces
as if they were a single homogonous piece with step changes at the
edges... that also adds to inaccuracies. the robustness of the
algorithm and the residual errors created are a bit part of getting
more accurate results. There is no doubt that numerical methods have
allowed 'solutions' of many problems that would be extremely difficult
to find closed form solutions for, but they must always be examined
for the acceptibility of the unavoidable errors in the method used.

I will assume that most here are familiar with Simpson's Rule
Integration. This allows one to compute the "area under the curve" of a
function with a fairly simple algorithm. It's as little as 7 statements
using Fortran. And it is quite amazing how accurate the answer can be
with even just a few slices of the curve from start to finish. If used
properly.

Don't think that seemingly large chunks mean poor accuracy. When the
algorithm is good, and the program selects the chunk size well, the
results can be very close to the true answer.

tom
K0TAR

On Fri, 14 May 2010 21:07:32 -0500, tom wrote:

Don't think that seemingly large chunks mean poor accuracy. When the
algorithm is good, and the program selects the chunk size well, the
results can be very close to the true answer.

I recall Simpson's Rule from work about 23 years ago that lead me to
finding more accurate methods in a great compendium of
"Numerical Recipes
The Art of Scientific Computing."
Press, Flannery, Teukolsky, Vetterling,
Cambridge University Press, 1986

which has Simpon's 3/8th Rule, and a more extensive
"Bode's rule... This is exact for polynomials up to and
including degree 5.
"At this point the formulas stop being named
after famous personages, so we will not go
any further. Consult Abramowitz and Stegun
for aditional formulas in the sequence."
The book continues with FORTRAN (my first language) and Pascal (my 9th
or 11th language or dialect by that time) interpretations of a
spectrum of math systems for another 700 pages....

73's
Richard Clark, KB7QHC

On Fri, 14 May 2010 22:48:57 -0700, Richard Clark
wrote:

Cambridge University Press, 1986

Honest, no name dropping here. In fact this citation neatly
dove-tails with a film I just finished watching (god bless streaming
Netflix) prior to this post that was about some of Cambridge's (and
Oxford's, hence Oxbridge's) noted Dons: Cleese, Idle, Chapman, Palin,
and Jones (with some Yank called Gilliam)
"Before the Flying Circus"

Some of these remarkable academics acknowledged, with gratitude, the
groundbreaking work of Stanley Unwin - on par with the Goon Show.

Somehow all these loose ends tie together here - eventually. One has
only to wait....

73's
Richard Clark, KB7QHC

On 5/15/2010 1:02 AM, Richard Clark wrote:

Some of these remarkable academics acknowledged, with gratitude, the
groundbreaking work of Stanley Unwin - on par with the Goon Show.

Lost on quite a few here I'd think. Who would know who Spike was? Or
what would become of Peter?

tom
K0TAR