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In this study, a new framework of constructing very high order discontinuity-capturing schemes is proposed for finite volume method. These schemes, so-called $\mathrm{P}_{n}\mathrm{T}_{m}-\mathrm{BVD}$ (polynomial of $n$-degree and THINC…
We consider a one--spatial dimensional tumour growth model [2, 3, 4] that consists of three dependent variables of space and time: volume fraction of tumour cells, velocity of tumour cells, and nutrient concentration. The model variables…
The vertical shear instability (VSI) is widely believed to be effective in driving turbulence in protoplanetary disks. Prior studies on VSI exclusively exploit the reflecting boundary conditions (BCs) at the disk surfaces. VSI depends…
Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave…
When fully conservative methods are used to simulate transcritical flow, spurious pressure oscillations and numerical instability are generated. The strength and speed of propagation of shock waves cannot be represented correctly using a…
We develop a fourth order accurate finite difference method for the three dimensional elastic wave equation in isotropic media with the piecewise smooth material property. In our model, the material property can be discontinuous at curved…
Over the last 30 years a plethora of variational regularisation models for image reconstruction has been proposed and thoroughly inspected by the applied mathematics community. Among them, the pioneering prototype often taught and learned…
Balancing spectral, spatial, and temporal resolutions is a key challenge in spectral imaging. The Dual-Camera Coded Aperture Snapshot Spectral Imaging (DC-CASSI) system alleviates this trade-off but suffers from severely ill-posed…
We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
We investigate a local incremental stationary scheme for the numerical solution of rate-independent systems. Such systems are characterized by a (possibly) non-convex energy and a dissipation potential, which is positively homogeneous of…
Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
We present for astrophysical use a multi-dimensional numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference method on an Eulerian grid, called the Total Variation Diminishing…
The use of machine-learning in neuroimaging offers new perspectives in early diagnosis and prognosis of brain diseases. Although such multivariate methods can capture complex relationships in the data, traditional approaches provide…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
The Variation Evolving Method (VEM) that originates from the continuous-time dynamics stability theory seeks the optimal solutions with variation evolution principle. After establishing the first and the second evolution equations within…
A novel numerical method for the estimation of large time-varying parameter (TVP) models is proposed. The updating and smoothing estimates of the TVP model are derived within the context of generalised linear least squares and through…
The aim of this paper is the derivation of structure preserving schemes for the solution of the EPDiff equation, with particular emphasis on the two dimensional case. We develop three different schemes based on the Discrete Variational…
In the present article we describe a few simple and efficient finite volume type schemes on moving grids in one spatial dimension combined with appropriate predictor-corrector method to achieve higher resolution. The underlying finite…