相关论文: Improvements of the Discrete Dipole Approximation …
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
This article studies a direct numerical approach for fractional advection-diffusion equations (ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential quadrature (DQ) method is firstly proposed for the 1D and…
Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some…
Data Augmentation (DA), i.e., synthesizing faithful and diverse samples to expand the original training set, is a prevalent and effective strategy to improve the performance of various data-scarce tasks. With the powerful image generation…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
In this work, we study the approximation properties of multi-patch dG-IgA methods, that apply the multipatch Isogeometric Analysis (IgA) discretization concept and the discontinuous Galerkin (dG) technique on the interfaces between the…
The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…
A multi-linear variable separation approach is developed to solve a differential-difference Toda equation. The semi-discrete form of the continuous universal formula is found for a suitable potential of the differential-difference Toda…
We present an error analysis for the discontinuous Galerkin method applied to the discrete-ordinate discretization of the steady-state radiative transfer equation. Under some mild assumptions, we show that the DG method converges uniformly…
A novel hybrid method based on Mie theory and the Discrete Dipole Approximation (DDA) was developed to study the microscopic parameters governing the optical response of tunable photonic crystals (PC). The method is based on a two-step…
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep learning algorithms through…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
We adapt the Gradient Discretisation Method (GDM), originally designed for elliptic and parabolic partial differential equations, to the case of a linear scalar hyperbolic equations. This enables the simultaneous design and convergence…
The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…
We present a fast iterative solver for scattering problems in 2D, where a penetrable object with compact support is considered. By representing the scattered field as a volume potential in terms of the Green's function, we arrive at the…