Is there any complete dynamics solver for gravity and EM? e.g., the
Jefimenko equations + gravity(is there a relativistic equivalent similar to
Jefimenko's?).

I'm thinking about implementing these buts its quite daunting... not
necessarily difficult I suppose but I know a brute force method isn't going
to cut it and implementing any optimization is whats going to be hard.

Anyways, I have a few ideas but I suppose it would be nice to see the work
of others. (Also if there are any good optimization's to those equations for
faster computation such as sparse grids or just anything along those longs
I'd appreciate some info)

Thanks,
Jon

"Jon Slaughter" wrote in message
...
Is there any complete dynamics solver for gravity and EM? e.g., the
Jefimenko equations + gravity(is there a relativistic equivalent similar
to Jefimenko's?).

I'm thinking about implementing these buts its quite daunting... not
necessarily difficult I suppose but I know a brute force method isn't
going to cut it and implementing any optimization is whats going to be
hard.

Anyways, I have a few ideas but I suppose it would be nice to see the work
of others. (Also if there are any good optimization's to those equations
for faster computation such as sparse grids or just anything along those
longs I'd appreciate some info)

Thanks,
Jon
Actually, Jon, Jefimenko has taken the next step and developed a
comprehensive set of Gravitational Equations. A preliminary version is in
his "Causality..." book. A much-developed version is in "Gravitation and
Cogravitation."

I am not aware of any "solvers" that have been built using either set of
equations.

Bill Miller

On Jul 21, 10:34*am, "Bill Miller"
wrote:

Actually, Jon, Jefimenko has taken the next step and developed a
comprehensive set of Gravitational Equations. A preliminary version is in
his "Causality..." book. A much-developed version is in "Gravitation and
Cogravitation."

I am not aware of any "solvers" that have been built using either set of
equations.

Bill Miller

Actually there's been no work on "solvers" for even classical EM. For
example, if you take the arbitrary object in space and put a couple of
terminals on it in different places, we know that the resistance,
capacitance, and inductance observed are a function ONLY of the
geometry of the device (and a few material parameters). But while
with modern numerical methods it is possible to attack this problem
and crank out an answer, as far as I know next to no work has been
done in that regard. Inductance and capacitance calculations in
particular are usually restricted to just a few special cases where
the math is simple. Even in certain cases of inductance and
capacitance where exact solutions are known it is rarely done. Hence
the whole concept of a geometrical "solver" is basically yet to be
done. And needless to say including relativity and/or gravitation
takes that up a notch to an even higher level which means that even
less has been done there.

"Benj" wrote in message
...
On Jul 21, 10:34 am, "Bill Miller"
wrote:

Actually, Jon, Jefimenko has taken the next step and developed a
comprehensive set of Gravitational Equations. A preliminary version is in
his "Causality..." book. A much-developed version is in "Gravitation and
Cogravitation."

I am not aware of any "solvers" that have been built using either set of
equations.

Bill Miller

Actually there's been no work on "solvers" for even classical EM. For
example, if you take the arbitrary object in space and put a couple of
terminals on it in different places, we know that the resistance,
capacitance, and inductance observed are a function ONLY of the
geometry of the device (and a few material parameters). But while
with modern numerical methods it is possible to attack this problem
and crank out an answer, as far as I know next to no work has been
done in that regard. Inductance and capacitance calculations in
particular are usually restricted to just a few special cases where
the math is simple. Even in certain cases of inductance and
capacitance where exact solutions are known it is rarely done. Hence
the whole concept of a geometrical "solver" is basically yet to be
done. And needless to say including relativity and/or gravitation
takes that up a notch to an even higher level which means that even
less has been done there.

------

What I was thinking, and actually implemented, was to use the equation of
continuity:

div J = -p'

since J = p*v and v' = F/p we can evolve the system(hypothetically at least)

F = sum of forces(such as gravity and EM... call it EMG(electromagnetic
gravitation)_


in fact we have two such equations, one for charge and one for mass. Both
share the same velocity too.

so

p_m' = - div (p_m*v) = - grad p_m dot v - p_m*div v
p_e' = - div(p_e*v)

v' = F/p_m

----

Now I implemented this using a psuedo force function (2^(B^2 - r^2) - 1)/r^2
which approximates 1/r^2 very well but allows for some sorta of nuclear
repulsive force.

The problem is that my numerical approximations loose continuity and, of
course, the curse of dimensionality because its a brute force routine. (I
only implemented gravity to see if it would work but because of the
continuity issue I'm not sure(it sorta works but breaks down very quick)).

I imagine that one can use "regions" of fixed mass(set v to 0) or I was
thinking of maybe somehow evolving boundaries indead where the interior was
homogenous but couldn't find a way to do this without just a brute force.

----

Would be nice if it where possible to speed up the calculations but I'm not
sure what would be the best method. (in 2D its O((NxM)^2) and even for N =
100 it takes about 1-2 mins to compute one time step on my comp)

There seems to be a lot of potential for optimization though and I imagine
sparse grids would be the way to go and actually maybe some history
feature(since one really only needs to find the force over regions of large
mass and/or small distances).

Jon

"Bill Miller" wrote in message
...

"Jon Slaughter" wrote in message
...
Is there any complete dynamics solver for gravity and EM? e.g., the
Jefimenko equations + gravity(is there a relativistic equivalent similar
to Jefimenko's?).

I'm thinking about implementing these buts its quite daunting... not
necessarily difficult I suppose but I know a brute force method isn't
going to cut it and implementing any optimization is whats going to be
hard.

Anyways, I have a few ideas but I suppose it would be nice to see the
work of others. (Also if there are any good optimization's to those
equations for faster computation such as sparse grids or just anything
along those longs I'd appreciate some info)

Thanks,
Jon
Actually, Jon, Jefimenko has taken the next step and developed a
comprehensive set of Gravitational Equations. A preliminary version is in
his "Causality..." book. A much-developed version is in "Gravitation and
Cogravitation."


Seems very interesting but I don't have any clue what it is. Is it a
tensor/differential forms formulation of gravity(essentially GR)?

I am not aware of any "solvers" that have been built using either set of
equations.


Well, obviously any simulator of gravity using mass density would work too
as it can easily be modified to handle EM.

My plan of action was to use the continuity equations to evolve the mass and
charge density but ran into issues which seems to be due to numerical errors
causing loss of continuity(mass would apear in empty space after several
steps) and also because of the extreme time it takes to run any decent sim.

e.g., if you have such a simiulator for gravitation using mass density then
it can be easily converted to handle EM simply because the force only needs
to be modified and the mass density equations copied to the charge. (I only
did mine for gravity but it can easily be modified to handle charge with
little impact on speed)

If I could find, say, a numerical technique for computing volume integrals
very efficiently and with a high degree of accuracy then I might be able to
actually do something useful with my program... unfortunately I think I'll
always run into the issue of continuity loss and I have no idea how to solve
that(but maybe with a smaller step I can push it farther in the future).

Thanks,
Jon