Coarse space (numerical analysis)

This article deals with a component of numerical methods. For coarse space in topology, see coarse structure.

In numerical analysis, coarse problem is an auxiliary system of equations used in an iterative method for the solution of a given larger system of equations. A coarse problem is basically a version of the same problem at a lower resolution, retaining its essential characteristics, but with fewer variables. The purpose of the coarse problem is to propagate information throughout the whole problem globally.

In

Coarse spaces (coarse model, surrogate model) are the backbone of algorithms and methodologies exploiting the space mapping concept for solving computationally intensive engineering modeling and design problems.^{[1][2][3][4][5][6][7][8]} In space mapping, a fine or high fidelity (high resolution, computationally intensive) model is used to calibrate or recalibrate—or update on the fly, as in aggressive space mapping—a suitable coarse model. An updated coarse model is often referred to as surrogate model or mapped coarse model. It permits fast, but more accurate, harnessing of the underlying coarse model in the exploration of designs or in design optimization.

In

• Jan Mandel and Bedrich Sousedik, "Coarse space over the ages", Nineteenth International Conference on Domain Decomposition, Springer-Verlag, submitted, 2009. arXiv:0911.5725
• doi:10.1007/978-3-642-02677-5_26
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• Multiscale modeling