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A Primer on Radial Basis Functions with Applications to the Geosciences (Paperback)
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A Primer on Radial Basis Functions with Applications to the Geosciences (Paperback)
Series: CBMS-NSF Regional Conference Series, 87
Expected to ship within 10 - 15 working days
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Adapted from a series of lectures given by the authors, this
monograph focuses on radial basis functions (RBFs), a powerful
numerical methodology for solving PDEs to high accuracy in any
number of dimensions. This method applies to problems across a wide
range of PDEs arising in fluid mechanics, wave motions, astro- and
geosciences, mathematical biology, and other areas and has lately
been shown to compete successfully against the very best previous
approaches on some large benchmark problems. Using examples and
heuristic explanations to create a practical and intuitive
perspective, the authors address how, when, and why RBF-based
methods work. The authors trace the algorithmic evolution of RBFs,
starting with brief introductions to finite difference (FD) and
pseudospectral (PS) methods and following a logical progression to
global RBFs and then to RBF-generated FD (RBF-FD) methods. The
RBF-FD method, conceived in 2000, has proven to be a leading
candidate for numerical simulations in an increasingly wide range
of applications, including seismic exploration for oil and gas,
weather and climate modeling, and electromagnetics, among others.
This is the first survey in book format of the RBF-FD methodology
and is suitable as the text for a one-semester first-year graduate
class.
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