Iterative solver (again) [Was: Re: [ODE] Russ' plans for ODE?]

[Alen Ladavac]

> I'm not sure what you mean with iterating over a large step.

Something like:
"The term 'iterative method' refers to a wide range of techniques that use
successive
approximations to obtain more accurate solutions to a linear system at each
step."

So, an iterative algorithm goes joint by joint (just like stepfast), or body
by body, or dof by dof, or some other variation of that, over the problem,
and when it does one pass over it, it gets the first approximation. But this
first approximation is then re-entered in the algorithm and refined with one
more pass. You usually repeat until you do a fixed number of passes, or you
determine that the solution has converged (because the values don't change,
or change very slowly).

For some very simple explanations, see Jakobsen's paper at
http://www.ioi.dk/Homepages/thomasj/publications/gdc2001.htm . (Though this
one is particle-based so it cannot solve LCP problem in the form that ODE
has it, but it is simple to understand).

> Well, I know very little about solvers but I believe the StepFast solver
makes
> some assumptions about the world which are only true (or close the true)
when
> the steps are very small. It is so fast because it uses those assumptions
to
> optimize the stepping.

What StepFast does is to take this first approximation and call it the
solution. What is not very good, usually, because it is too far from the
real solution in most cases. It covers up that flaw by using smaller
timesteps, so the error is smaller. This is the assumption you mentioned -
the assumption is that the first approximation is good enough if time step
is very small. I'd say that this is not "the way to go". Primarily because
there is no way you can tell in advance how many steps you will need for
some particular system to be "exact enough".

Overall, it looks like StepFast is a bit upside-down version of an iterative
solver. Please do correct me if I am wrong.

Has anyone had any thoughts on this? I belive there were some talks about
this some year or so ago on the list, but the thread died quickly. Russ, did
you experiment with this?

Alen


----- Original Message -----
From: "Roel van Dijk" <roelvandijk at home.nl>
To: <ode at q12.org>
Sent: Friday, April 23, 2004 17:28
Subject: Re: Iterative solver (again) [Was: Re: [ODE] Russ' plans for ODE?]


> On Thursday 22 April 2004 18:03, Alen Ladavac wrote:
> > For a start, I was wondering... is there any particular reason why does
the
> > StepFast solver subdivide a step into smaller substeps of shorter
length?
> > Shouldn't it instead reiterate over the same large step, improving the
> > solution each time?
> Well, I know very little about solvers but I believe the StepFast solver
makes
> some assumptions about the world which are only true (or close the true)
when
> the steps are very small. It is so fast because it uses those assumptions
to
> optimize the stepping.
>
> I'm not sure what you mean with iterating over a large step.
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