相关论文: Exploring Oversampling in RBF Least-Squares Colloc…
The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the…
We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature layer phenomena, and are ubiquitous in many areas of applied…
The Ronen method (RM) demands for successive resolutions of the diffusion equation where local diffusion constants are modified to reproduce more accurate estimates of the currents by a transport operator. The methodology is currently…
While burst Low-Resolution (LR) images are useful for improving their Super Resolution (SR) image compared to a single LR image, prior burst SR methods are trained in a deterministic manner, which produces a blurry SR image. Since such…
Spatially-resolved techniques of laser scanning microscopy (LSM) have been used to image simultaneously the spatial variations of (i) rf current flow, J$_RF$(x,y), of (ii) areas of resistive dissipation and (iii) the sources of microwave…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
In this paper, we study the development of efficient multiscale methods for flows in heterogeneous media. Our approach uses the Generalized Multiscale Finite Element (GMsFEM) framework. The main idea of GMsFEM is to approximate the solution…
We extend Regularised Diffusion-Shock (RDS) filtering from Euclidean space $\mathbb{R}^2$ to the space of positions and orientations $\mathbb{M}_2 := \mathbb{R}^2 \times S^1$. This has numerous advantages, e.g. making it possible to enhance…
Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…
The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…
We present a new computational method by extending the Immersed Boundary (IB) method with a spectrally-accurate geometric model based on Radial Basis Function (RBF) interpolation of the Lagrangian structures. Our specific motivation is the…
Using scanning tunneling microscopy-induced luminescence (STML), the optical properties of two-dimensional (2D) semiconductors may be investigated at the nanoscale. This is possible because the tunneling current under the tip is an…
In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as…
Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least…
Exciton diffusion length plays a vital role in the function of opto-electronic devices. Oftentimes, the domain occupied by an organic semiconductor is subject to surface measurement error. In many experiments, photoluminescence over the…
An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where…
We present two novel additions to the semi-analytic solution of Lyman $\alpha$ (Ly$\alpha$) radiative transfer in spherical geometry: (1) implementation of the correct boundary condition for a steady source, and (2) solution of the…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…
The present work provides a critical assessment of numerical solutions of the space-fractional diffusion-advection equation, which is of high significance for applications in various natural sciences. In view of the fact that, in contrast…
The Radiative Transfer Equation (RTE) is essential for solving the spatial distribution of light energy. It plays a crucial role in the link budget analysis of Underwater Wireless Optical Communication (UWOC). However, due to its complex…