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The multilevel basis method can be applied with the variational formulation to obtain the approximate solutions of nonlinear problem.
However, due to the global nature of the pressure unknowns, local multilevel basis functions for both matrix and fractures with flexible matrix-fracture coupling treatment are introduced for the pressure.
To extend to a more general class of multilevel basis for solving various types of boundary conditions, the anti-derivatives of Daubechies wavelets introduced by Xu and Shann [5] can be applied to solve many kinds of boundary conditions: Dirichlet and Neumann types.
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The underlying basis of multilevel coding is to partition a signal set into several levels and to encode separately each level through the respective layer of the encoder.
Therefore, de Lange et al. (2014) applied a multilevel analysis on the basis of data on young people from 29 countries who participated in the European Social Survey 2002, 2004, 2006 and 2008.
Such a framework can be the basis for multilevel modeling [ 17] and for causal analysis [ 18].
We used different types of kernel: linear, polynomial, radial basis function, and multilevel perceptron.
Furthermore, on the basis of the best multilevel models structured in the primary analyses, we will explore the moderating effects of some putative covariates at level 2 such as gender, age, coping styles, negative affectivity and social inhibition (Type D personality dimensions), perceived social support and writings ratings.
Furthermore, on the basis of the best multilevel model structured in the primary analyses, the moderating effects of some putative covariates such as gender, age, level of education, marital status, cardiovascular disease status, and diabetes, will be explored and no adjustment to alpha will be applied.
This method is extended from the multilevel augmentation method that uses polynomial wavelet basis.
In order to reduce the computational time, we apply the advantage of multilevel bases by connecting the information among basis levels.
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