## Final Report Summary - MODSIMCONMP (Modeling, Simulation and Control of Multi-Physics Systems)

Modeling, simulation and control of multi-physics systems is at the heart of future technology development in all areas of science and engineering. With modern computers it is e.g. already possible to virtually design complete cars or airplanes and it is on the horizon to design individual operation plans for patients.

In order to get good agreement between the dynamical behavior of the design object and the mathematical model one uses hierarchically constructed networks of submodels which are coupled by interfaces. This modeling also becomes more and more automatized using specially constructed modeling languages that lead to systems of partial differential equations, ordinary differential equations and algebraic equations which are often called partial-differential-algebraic equations (PDAEs), or differential-algebraic equations (DAEs) when only the dynamical behavior in time is essential or when the system has been discretized in space or modeled discretely via a finite element model.

The resulting models typically are in very good agreement with the underlying multi-physics problem, but they are difficult to treat with standard simulation, optimization and control methods.

The main reason is that due to the network based modeling there may be hidden constraints depending on derivatives of equations in the system that constrain the initial conditions and the dynamics and which are not easy to fulfill in a discretization framework.

The degree of differentiation that is needed to identify all these constraints is usually counted by an index, and almost all problems with an index higher than 1, so called high index problems, cause difficulties in the simulation and control procedures.

To deal with this problem was the main goal of the project, which has as essential aspects the appropriate mathematical modeling, the analysis and regularization of the model equations, e.g. replacing the equations by equations of lower index, the numerical simulation, i.e., the numerical solution of the regularized model equations, and the control of such systems.

For a large variety of application areas, like multibody systems or electrical circuits, there exist standardized automated modeling approaches which are widely used in industrial practice.

However, when it comes to combine different multi-physical models an appropriate modeling approach is still a challenge.

The work is complemented by the development of appropriate software and the testing of the software on the basis of real world applications to verify the theoretical analysis as well as the implemented software.

In order to get good agreement between the dynamical behavior of the design object and the mathematical model one uses hierarchically constructed networks of submodels which are coupled by interfaces. This modeling also becomes more and more automatized using specially constructed modeling languages that lead to systems of partial differential equations, ordinary differential equations and algebraic equations which are often called partial-differential-algebraic equations (PDAEs), or differential-algebraic equations (DAEs) when only the dynamical behavior in time is essential or when the system has been discretized in space or modeled discretely via a finite element model.

The resulting models typically are in very good agreement with the underlying multi-physics problem, but they are difficult to treat with standard simulation, optimization and control methods.

The main reason is that due to the network based modeling there may be hidden constraints depending on derivatives of equations in the system that constrain the initial conditions and the dynamics and which are not easy to fulfill in a discretization framework.

The degree of differentiation that is needed to identify all these constraints is usually counted by an index, and almost all problems with an index higher than 1, so called high index problems, cause difficulties in the simulation and control procedures.

To deal with this problem was the main goal of the project, which has as essential aspects the appropriate mathematical modeling, the analysis and regularization of the model equations, e.g. replacing the equations by equations of lower index, the numerical simulation, i.e., the numerical solution of the regularized model equations, and the control of such systems.

For a large variety of application areas, like multibody systems or electrical circuits, there exist standardized automated modeling approaches which are widely used in industrial practice.

However, when it comes to combine different multi-physical models an appropriate modeling approach is still a challenge.

The work is complemented by the development of appropriate software and the testing of the software on the basis of real world applications to verify the theoretical analysis as well as the implemented software.

## Contact

## Subjects

Scientific Research**Record Number**: 189349 /

**Last updated on**: 2016-09-16