Related papers: LRBF meshless methods for predicting soil moisture…
The Richards' equation is a model for flow of water in unsaturated soils. The coefficients of this (nonlinear) partial differential equation describe the permeability of the medium. Insufficient or uncertain measurements are commonly…
This contribution presents a new analysis of properties of the interpolation using Radial Bases Functions (RBF) related to large data sets interpolation. The RBF application is convenient method for scattered d-dimensional interpolation.…
A novel method to enable application of the Multiscale Restricted Smoothed Basis (MsRSB) method to non M-matrices is presented. The original MsRSB method is enhanced with a filtering strategy enforcing M-matrix properties to enable the…
Local Fr'echet Regression (LFR) is a nonparametric regression method for settings in which the explanatory variable lies in a Euclidean space and the response variable lies in a metric space. It is used to estimate smooth trajectories in…
In this paper, we present a meshless hybrid method combining the Generalized Finite Difference (GFD) and Finite Difference based Radial Basis Function (RBF-FD) approaches to solve non-homogeneous partial differential equations (PDEs)…
Meshfree radial basis function (RBF) methods are popular tools used to numerically solve partial differential equations (PDEs). They take advantage of being flexible with respect to geometry, easy to implement in higher dimensions, and can…
Characterizing soil moisture (SM) around drip irrigation pipes is crucial for precise and optimized farming. Machine learning (ML) approaches are particularly suitable for this task as they can reduce uncertainties caused by soil conditions…
This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…
We present a numerical framework for solving neural field equations on surfaces using Radial Basis Function (RBF) interpolation and quadrature. Neural field models describe the evolution of macroscopic brain activity, but modeling studies…
This paper investigates the numerical behavior of the radial basis functions least-squares collocation (RBF-LSC) method of lines (MoL) for solving surface diffusion problems, building upon the theoretical analysis presented in [SIAM J.…
The microwave imaging system(MIS) stands out among prominent imaging tools for capturing images of concealed obstacles. Leveraging its capability to penetrate through heterogeneous environments MIS has been widely used for subsurface…
We introduce a new local meshfree method for the approximation of the Laplace-Beltrami operator on a smooth surface of co-dimension one embedded in $\R^3$. A key element of this method is that it does not need an explicit expression of the…
Gaussian Random Fields (GRFs) with Mat\'ern covariance functions have emerged as a powerful framework for modeling spatial processes due to their flexibility in capturing different features of the spatial field. However, the smoothness…
Flow and multicomponent reactive transport in saturated/unsaturated porous media are modeled by ensembles of computational particles moving on regular lattices according to specific random walk rules. The occupation number of the lattice…
A model is presented for the gravity-driven flow of rainwater descending through the soil layer of a green roof, treated as a porous medium on a flat permeable surface representing an efficient drainage layer. A fully saturated zone is…
We develop a new coarse-scale approximation strategy for the nonlinear single-continuum Richards equation as an unsaturated flow over heterogeneous non-periodic media, using the online generalized multiscale finite element method (online…
In the context of stochastic two-phase flow in porous media, we introduce a novel and efficient method to estimate the probability distribution of the wetting saturation field under uncertain rock properties in highly heterogeneous porous…
Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…
We present a three-dimensional model, based on cohesive spherical particles, of rain-induced landslides. The rainwater infiltration into the soil follow the either the fractional or the fractal diffusion equations. We solve analytically the…
We provide novel random surface density functional theory (RSDFT) formulation in the case of geometric heterogeneous surface of solid media which is essential for description of thermodynamic properties of confined fluids. The major…