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Closest point method
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Closest point method : ウィキペディア英語版
Closest point method
The closest point method (CPM) is an embedding method for solving partial differential equations on surfaces. The closest point method uses standard numerical approaches such as finite differences, finite element or spectral methods in order to solve the embedding partial differential equation (PDE) which is equal to the original PDE on the surface. The solution is computed in a band surrounding the surface in order to be computationally efficient. In order to extend the data off the surface, the closest point method uses a closest point representation. This representation extends function values to be constant along directions normal to the surface.
==Definitions==
Closest Point function: Given a surface \mathcal S, cp(\bold x) refers to a (possibly non-unique) point belonging to \mathcal S , which is closest to \bold x ().
Closest point extension: Let \mathcal S , be a smooth surface in \mathbb R^d . The closest point extension of a function u : \mathcal S \rightarrow \mathbb R , to a neighborhood \Omega of \mathcal S , is the function v: \Omega \rightarrow \mathbb R , defined by v(\bold x) = u(cp(\bold x)).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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