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Showing posts from September, 2019

A revisit of spatial discretization

Discretization by definition from Wikipedia: In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Now we add “spatial” to the term. The first intuitive definition is the discretization of functions in the spatial domain. There are two elements in this description: functions and spatial domain. For functions, we often refer to integral or ODEs/PDEs in numerical simulations. If these functions involve with gradient information, then they depend on spatial domain, which is how gradient is calculated. For spatial domain, we often refer to mesh or grid. And mesh can generally be classified into structured and unstructured grid. In practice, we have spent great effects on both aspects of the spatial discretization: mesh and corresponding function s…