EMMA - Efficient Methods for Mechanical Analysis

在经典工程学科或现代领域(如医学工程)中的应用需要对复杂技术问题进行准确的模拟。为了获得所需的精度，必须建立复杂的仿真模型。一般来说，这些模型考虑了几何和/或材料的非线性。这些问题的模拟需要很高的计算成本(CPU时间、内存需求)。此外，它们还意味着高能量消耗。艾美诺特初级研究小组EMMA(高效力学分析方法)的目标是开发新的方法，用于计算高效地模拟非线性力学和多场问题。通过使用降维基模型降阶(RB-MOR)技术提高了计算效率。为了加速一般的RB-Mor ansatz，详细分析了下垫场的物理性质。然后，简化的基本框架被设计为使得机械考虑可以帮助显著地加速简化形式的瞬变、非线性问题的求解。这与经典的Galerkin子空间投影法等模型降阶策略有很大的不同。与已有的微分方程组模型降阶方法的另一个重要区别是将模型降阶应用于非线性优化问题，虽然模型降阶对于一些实际问题已经是有效的并且可以应用，但是它的应用范围是相当有限的。EMMA小组的研究将使高性能模型简化技术在学术界、应用科学以及可能在工业应用中得到广泛应用。开发一个综合研究结果的虚拟实验室，以演示现代模型降阶策略的能力，是EMMA的主要目标。大量的计算节省可以使模拟变得可行，而这在今天是不可能的。因此，未来可以实现具有挑战性的研究，例如在机械或医学工程和计算材料科学方面。简化后的模型在减少计算时间的同时，大大提高了系统的能效。因此，生态的重要性被归因于这些发展。Emma小组追求跨学科的方法，这是从计算机科学的方法集成的例子，例如，通过GPU加速或数据挖掘方法。数学、物理和模型降阶的特殊综合使得计算收益是现有模型降阶算法所无法比拟的。EMMA的活动允许许多后续的科学和工业应用，并为未来的研究项目提供潜力。

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.