Solutions exhibiting discontinuities and singularities, such as those arising at cracks and interfaces, occur in a wide range of engineering and materials science problems, and emerge in solids, fluids, and multi-field mechanics at all scales, ranging from the macro to the atomistic. The degree of complexity of these problems requires advanced analytical, numerical and computational tools. The current state-of-the-art computational methods include Meshless and Partition of Unity Finite Element Methods, Fictitious Domain Methods, Mimetic Finite Difference Methods, Polygonal Finite Element, and Virtual Element Method. Broadly, most efforts have focused either on computational efficiency or on theoretical results, often with less emphasis on ensuring mechanical consistency. Therefore, much remains to be done to unify and harmonize mechanical, numerical, and computational aspects.
We solicit contributions from researchers with multidisciplinary backgrounds from the computational and analytical mechanics communities. The minisymposium aims to:
- propose innovative formulations suited to advanced discretization methods;
- point out open issues of existing approaches and suggest improvements;
- shed light on the similarities among different methods.
While contributions in all aspects related to these topics are invited, some of the featured topics in this MS will include:
- novel aspects and applications of Partition of Unity Finite Element and Meshless Methods, Fictitious Domain Method, Mimetic Finite Difference Method, Polygonal Finite Element Method, and Virtual Element Method;
- advanced quadrature and implementation algorithms;
- new developments concerning the mechanical and variational consistency of computational formulations;
- definition of case-studies, for which analytical and experimental results exist, that can serve as benchmarks for different computational models.