EMMA - Efficient Methods for Mechanical Analysis

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Applications in classical engineering discplines or in modern domains such as medical engineering require accurate simulations of complex technological problems. In order to obtain the required precision, elaborate simulation models are necessary. In general, these models consider geometrical and/or material nonlinearities. Simulations of these problems involve high computational costs (CPU time, memory requirement). Further, they imply a high energy consumption.The aim of the Emmy Noether Junior Research Group EMMA (Efficient Methods for Mechanical Analysis) is the development of novel methods for computationally efficient simulations of nonlinear mechanical and multi-field problems. The computational efficiency is achieved by using reduced basis model order reduction (RB-MOR) techniques. In order to accelerate the general RB-MOR ansatz, the physical nature of the underlying fields is analyzed in detail. Then the reduced basis framework is designed such that mechanical considerations can help to significantly accelerate the solution of the reduced form of the transient, nonlinear problem. This is a noteworthy difference to other model reduction strategies such as classical Galerkin subspace projection methods. Another important difference to existing model reduction methods for differential equations is the application to nonlinear optimization problems.Although model reduction can already be effective and ready for application for few realistic problems, its field of application is rather limited today. The investigations of the EMMA group will enable a wide application of high performance model reduction techniques in academia, applied science and, possibly, in industrial applications. The development of a virtual laboratory synthesizing the research results in order to demonstrate the capabilities of modern model reduction strategies is a major objective of EMMA. The massive computational savings can render simulations feasible that are impossible today. Thereby, challenging studies, e.g. in mechanical or medical engineering and in computational materials science, can be realized in the future. Besides the pure reduction of the computing time, the reduced models lead to a major improvement of the energy efficiency. Therefore, ecological importance is attributed to these developments.The EMMA group pursues an interdisciplinary approach, which is exemplified by the integration of methods from computer science, e.g., via GPU acceleration or data mining methods. The special synthesis of mathematics, physics and model reduction allows for computational gains that are unparalleled by existing model reduction algorithms. The activities of EMMA allow for many subsequent scientific and industrial applications and deliver the potential for future research projects.