Difference between revisions of "Main Page"

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The purpose of morwiki is to bring together experts in the area of model order reduction, as well as researchers from application areas in an attempt to provide a platform for exchanging ideas.

Modeling and numerical simulation are unavoidable in many application research areas, e.g. reaction process, micro-electro-mechanical systems (MEMS) design, control design, etc.. 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 algebra equations (DAEs).

After spatial discretization, the number of degrees of freedom is usually very high. It is therefore very time consuming to simulate the large-scale systems of ODEs or DAEs. Developed from well-established mathematical theories and robust numerical algorithms, model order reduction (MOR) 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) are 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.

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	Modeling and numerical simulation are unavoidable in many application research areas, e.g. reaction process, micro-electro-mechanical systems (MEMS) design, control design, etc.. 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 algebra equations (DAEs).		Modeling and numerical simulation are unavoidable in many application research areas, e.g. reaction process, micro-electro-mechanical systems (MEMS) design, control design, etc.. 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 algebra equations (DAEs).

−	After spatial discretization, the number of degrees of freedom is usually very high. It is therefore very time consuming to simulate the large-scale systems of ODEs or DAEs. Developed from well-established mathematical theories and robust numerical algorithms, model order reduction (MOR) 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) are 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 ~~for many times~~ during the design process, which can further save much time.	+	After spatial discretization, the number of degrees of freedom is usually very high. It is therefore very time consuming to simulate the large-scale systems of ODEs or DAEs. Developed from well-established mathematical theories and robust numerical algorithms, model order reduction (MOR) 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) are 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.