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The obtained basis functions can capture the small scale features of the solution within a coarse-grid block and give us an accurate coarse-scale solution.
The application of multiscale basis functions can capture the fine scale medium property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values.
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CM-Functions can capture the safety impact of factors through a continuous and quantitative approach, avoiding the problematic categorical analysis that is often used to capture CMF variability.
Our method is based on a mixed Galerkin type method with carefully designed basis functions that can capture various scales in the solution.
Several basis functions can jointly mask one or several other basis functions.
Generating functions for the Bernstein basis functions can be defined as follows.
Note that the number of basis functions can differ between random effects.
Then the network basis function can be formed.
Also, a Gaussian basis function can be used to sparsely represent environmental signals [37].
Particular solutions of anisotropic radial basis function can be found by the same procedure as that of regular radial basis functions under Laplace operator.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com