Commonly Used Simulation Method
Competitor programs to silux operate in a manner that the
user can define his model over a very convenient user interface
that corresponds to a modern CAD program. The user can program
with it without noticing or seeing the differential equations
that are being built up in the background. When the user is
finished with drawing and defining, he can start the simulation.
The differential equation or the set of differential equations
that were set up in the background represent in this sense
the whole model or the whole problem, respectively, that is
to be solved.
These differential equations contain then the whole problematic
of the model even before they have been solved. Nothing new
is added during the solution of these equations and nothing
new can be added because the differential equations have already
These equations form a system closed within itself. They
only have to be solved numerically, that is, integrated. In
principle, this is a batch job that runs in the background.
When the differential equations have been solved, the result
can be observed as a film. Characteristically for simulation
programs that operate according to these methods - and a characteristic
that allows one to recognize these programs - the user can
choose the method of integration and/or the integration step
size from several possible choices. This always indicates
that the corresponding program operates on the basis of differential
equations called Finite Elements Method (FEM) that are built
up in the background.
silux works in a totally different
silux numerically integrates the elementary Newtonian equations
of movement in very small time steps. All forces that act
on a given object produce a momentary acceleration and from
this there is a change of velocity in the given time step
and, as a final result, a change in position. The time steps,
for models on the laboratory scale, move in intervals of about
one microsecond. It follows that during this very short period
of time the forces can be seen as constant.
After all objects have taken new positions in this way, new
forces result for all objects. We have a new state of the
model. In this, further constituent physical equations of
course play a role. To mention just a few:
- exchange of force during collisions
- gravitational laws, etc.
This method is called: Finite Differences
The fundamentals of Finite Differences were established already
at the beginning of this century. They became significant
however only after WW II, with the arrival of the first computer.
Von-Neumann, the well-known computer pioneer, published the
fundamental theoretical principles of the use and solution
of finite differences method with the computer around 1948.
These fundamentals are incidentally still valid today. The
key phrases of this work state the following:
- A problem solved with the FDM converges to the exact solution
if the time step is subject to certain limitations or is smaller
than a certain maximal value, respectively.
- This time step must be newly determined by a program like
silux after each calculation cycle and results from various
influences such as: maximum velocity, maximum pressure, the
smallest object, the sound velocities of the materials, etc.
- The user cannot influence the time step. This is a characteristic
of this calculation method. If the time step is just the smallest
bit too large, no part of the program will work at all. The
corresponding model will explode because vibrations will build
up. It is comforting to know that a finite difference program
actually controls itself in this sense.
The Finite Differences Method (FDM) of calculation
has decisive advantages over the commonly used differential
equations method (Finite Elements Method FEM):
- Finite Differences allow for a modularization of a problem
into individual objects. silux consistently takes advantage
of these possibilities.
- Finite Differences therefore allow models to be infinitely
complex: this includes both the number and the complexity
of the individual parts.
- Finite Differences programs have increasing speed advantage
with increasingly complex models in regard to calculation
- Finite Differences programs do not have any problems with
singularities that cause other programs using Finite Elements
Method (FEM) a lot of trouble.
- The Finite Differences Method FDM can be used continually
to the point of structure analysis. The method is then sufficient
to the point of plastic deformation. The decisive speed advantage
already comes into play here today. It will become even more
important in the future as models become increasingly more
Structure analysis in silux is also based on the method of
finite differences FD and not on the classical method of finite
The classical finite elements method is not very well suited
for dynamic and highly dynamic tasks. It is extremely unsuitable
for continuous, interactive simulation.
Animations and Simulation software (comparison)