# Main Page

**Welcome to the MOR Wiki**

The purpose of the Model Order Reduction (MOR) Wiki is to bring together experts in the area of model reduction, as well as researchers from application areas in an attempt to provide a platform for exchanging ideas and examples.

Modeling and numerical simulation are unavoidable in many application and research areas, e.g. reaction processes, micro-electro-mechanical systems (MEMS) design, and control design. The processes or devices can be modeled by partial differential equations (PDEs). To simulate such models, spatial discretization via e.g. finite element discretization is necessary, which results in a system of ordinary differential equations (ODEs), or differential algebraic equations (DAEs).

After spatial discretization, the number of degrees of freedom is usually very high. It is therefore very time consuming to simulate such large-scale systems of ODEs or DAEs. Developed from well-established mathematical theories and robust numerical algorithms, MOR (see Projection based MOR for the basic idea) has been recognized as very efficient for reducing the simulation time of large-scale systems. Through model order reduction, a small system with reduced number of equations (reduced model) is derived. The reduced model is simulated instead, and the solution of the original PDEs or ODEs can then be recovered from the solution of the reduced model. As a result, the simulation time of the original large-scale system can be shortened by several orders of magnitude. The reduced model as a whole can also replace the original system and be reused repeatedly during the design process, which can further save much time.

Parametric model order reduction (PMOR) methods are designed for model order reduction of parametrized systems, where the parameters of the system play an important role in practical applications such as Integrated Circuit (IC) design, MEMS design, and chemical engineering. The parameters could be the variables describing geometrical measurements, material properties, the damping of the system or the component flow-rate. The reduced models are constructed such that all the parameters can be preserved with acceptable accuracy.

MOR Wiki is divided in pages providing benchmarks of parametric or non-parametric models and pages explaining applicable (P)MOR methods.

Following the submission rules, one can also submit new benchmarks or method pages.

Consult the User's Guide for information on using the wiki software.