Related papers: Image Extrapolation for the Time Discrete Metamorp…
Super-time-stepping (STS) methods provide an attractive approach for enabling explicit time integration of parabolic operators, particularly in large-scale, higher-dimensional kinetic simulations where fully implicit schemes are…
Grafakos and Sansing \cite{GS} have shown how to obtain directionally sensitive time-frequency decompositions in $L^2(\mr^n)$ based on Gabor systems in $\ltr;$ the key tool is the "ridge idea," which lifts a function of one variable to a…
For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods (MFEM) in space for simulating…
We propose a novel image sampling method for differentiable image transformation in deep neural networks. The sampling schemes currently used in deep learning, such as Spatial Transformer Networks, rely on bilinear interpolation, which…
In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…
We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many…
Finite difference method was extended to unstructured meshes to solve Euler equations. The spatial discretization is made of two steps. First, numerical fluxes are computed at the middle point of each edge with high order accuracy. In this…
In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…
Statistical processing of speckle data enables observation of speed of processes. In intensity-based pointwise dynamic speckle analysis, a map related to speed's spatial distribution is extracted from a sequence of speckle patterns formed…
This work presents a new procedure to extract features of grey-level texture images based on the discrete Schroedinger transform. This is a non-linear transform where the image is mapped as the initial probability distribution of a wave…
We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a…
We consider a differential method of maximum entropy that is based on the linearity of Fourier transform and involves reconstruction of images from the differences of the visibility function. The efficiency of the method is demonstrated…
Radiative transfer coupled with highly realistic simulations of the solar atmosphere is routinely used to infer the physical properties underlying solar observations. Due to its computational efficiency, the method of short-characteristics…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
We employ Maxwell's equations formulated in Space-Time Algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of…
The main objective of this paper is to develop a general method of geometric discretization for infinite-dimensional systems and apply this method to the EPDiff equation. The method described below extends one developed by Pavlov et al. for…
The ill-posed problem of phase retrieval in optics, using one or more intensity measurements, has a multitude of applications using electromagnetic or matter waves. Many phase retrieval algorithms are computed on pixel arrays using discrete…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…