Numerical approaches that distribute computational effort uniformly within the problem domain may use computer resources inefficiently in such cases. For example, high spatial and temporal mesh resolution may be needed only locally to resolve fine-scale local features. Different physical and numerical models with different computational costs may be suited to capturing behavior in different regions or at different scales. In structured AMR, the mesh is a hierarchy of nested levels of varying spatial and temporal resolution. SAMR concentrates computational effort near features of interest, such as shock fronts in this hydrodynamics simulation.
Colored boxes show patches containing higher mesh resolution.
Beyond providing a systematic framework in which to manage AMR computations, structured AMR also provides a useful paradigm for applying different physical or numerical models at different spatial scales to resolve local features accurately. Each blue cell on the finest level contains several hundred particles. The complexity of numerical algorithms in multi-physics AMR computations requires a significant investment in software infrastructure. It has demonstrated its flexibility and robustness by evolving with the needs of computational scientists as they gain improved understanding of their applications and associated numerical methods. More importantly, as software and solver technology is leveraged across different application codes, development time is reduced and the task of code building is simplified.