Methods for Scientific Computing
Numerical simulations are a powerful tool to solve complex physical problems, providing insights and solutions that are often unattainable through analytical methods. The strength of simulations lies in their ability to tackle problems that are too intricate for exact mathematical solutions. However, simulations also have their limitations, as they are inherently approximations and, due to constrained computational resources, may not account for all relevant aspects. This limitation is particularly pronounced in simulations of failure mechanisms, which are influenced by processes occurring across multiple length and time scales. Consequently, there is a crucial need for more efficient and accurate numerical methods to solve increasingly complex problems.
In our work, we develop and apply a wide range of computational techniques to improve current simulation capabilities. We focus on methods such as the Eulerian finite-element method for solid mechanics (see image), spectral methods (FFT) for homogenization, spectral boundary integral methods, and hybrid methods that optimally combine different approaches. Specifically, we target methods needed for modeling material and structural failure, striving to create tools that enable predictive simulations. Additionally, we release our developed software as freely available open-source code online. Ultimately, these efforts contribute to a broader foundation of scientific computing, fostering more advanced simulation tools and supporting research that uses simulations to study the failure behavior of materials and structures.