THU OCT 19 2017



Scientific/mathematical explanations:

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 been established.

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 way
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
- friction
- gravitational laws, etc.

This method is called: Finite Differences Method (FDM)
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.

Major advantages
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 performance.
- 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 complex.

Structure Analysis
Structure analysis in silux is also based on the method of finite differences FD and not on the classical method of finite elements FE.
The classical finite elements method is not very well suited for dynamic and highly dynamic tasks. It is extremely unsuitable for continuous, interactive simulation.


Other Topics:
Animations and Simulation software (comparison)
Pop-Science Explanation