Spatial multi-scale calculations

The alternative to the hierarchical modeling is known as concurrent modeling and consists of combining different numerical models that simultaneously describe different sub-domains. Each numerical model runs in its sub-domain and exchanges information with its parent/child sub-domain at defined boundaries. The critical issue here is to define the criteria and protocols in order to automate the application of more detailed numerical models in a simulation domain in time and realizing the so-called temporal multi-scale calculations or/ and space referred as spatial multi-scale ones. 

Spatial multi-scale methods are based on the paradigm that in many real situations the atomic description is only required within small parts of the simulation domain whereas for the majority the continuum model is still valid. This allows one to apply concurrent continuum and molecular simulations for the respective parts of the simulation domain using a coupling scheme that permits to connect between the two domains. The majority of the spatial domain is calculated by continuum solvers (computational fluid dynamics) which are very fast and only the active part is calculated using molecular simulation methods. In some cases several other coarser-grained (mesoscale) methods than the atomic simulations ones are used as interfaces between the molecular simulation and the continuum domains. Such approaches are called hybrid molecular-continuum methods and allow the simulation of problems that are not accessible either by continuum or by pure molecular simulation methods. 

Within the scientific world, computers are used for two main tasks performing numerically intensive calculations and analyzing large amounts of data. Such data can, for example, be pictures generated by astronomical telescopes or gene sequences in the bioinformatics area that need to be compared. The numerically intensive tasks are typically related to simulating the behaviour of the real world, by a more or less sophisticated computational model. The main problem in such simulations is the multi-scale nature of real-world problems, spanning from sub-nano to millimetres (10 ° - 10" ) in spatial dimensions, and from femto- to milliseconds (10 - 10 ) in the time domain. 

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