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Most learning-based image compression methods lack efficiency for high image quality due to their non-invertible design. The decoding function of the frequently applied compressive autoencoder architecture is only an approximated inverse of…
The localized artificial diffusivity (LAD) method is widely regarded as the preferred multi-material regularization scheme for the compact finite difference method, because it is conservative, easy to implement, and generally robust for a…
Patch-based relaxation refers to a family of methods for solving linear systems which partitions the matrix into smaller pieces often corresponding to groups of adjacent degrees of freedom residing within patches of the computational…
We explore a new way to handle flux boundary conditions imposed on level sets. The proposed approach is a diffuse interface version of the shifted boundary method (SBM) for continuous Galerkin discretizations of conservation laws in…
This paper deals with the local recovery of conservative fluxes for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed weakly and the discretisation is achieved by using…
We consider the problem of 3D shape reconstruction from multi-modal data, given uncertain calibration parameters. Typically, 3D data modalities can be in diverse forms such as sparse point sets, volumetric slices, 2D photos and so on. To…
Image restoration requires a careful balance between noise suppression and structure preservation. While first-order total variation (TV) regularization effectively preserves edges, it often introduces staircase artifacts, whereas…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
We propose a strategy for large volume non-perturbative renormalization which alleviates the window problem by reducing cut-off effects. We perform a proof-of-concept study using position space renormalization scheme and the CLS $N_f=2+1$…
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the…
We present new level set methods for multiphase, anisotropic (weighted) motion by mean curvature of networks, focusing on wetting-dewetting problems where one out of three phases is stationary -- a good testbed for checking whether…
Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction…
In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with a primal-dual active set method and a linearization is used in the degradation function to enhance the…
Within the context of Eulerian approaches, we aim to develop a new interface-capturing solver to predict two-phase flow in 2D/3D Cartesian meshes. To achieve mass conservation and to capture interface topology accurately, a mass-preserving…
We introduce a level set based approach to Bayesian geometric inverse problems. In these problems the interface between different domains is the key unknown, and is realized as the level set of a function. This function itself becomes the…
A novel coupled level-set lattice Boltzmann method on adaptive Cartesian grids for simulating liquid-gas multiphase flows is presented. The approach addresses the inherent challenges of accurately modeling multiphase systems characterized…
This paper presents a solver using the Level-Set method for incompressible two phase flows with surface tension. A one fluid approach is adopted where both phases share the same velocity and pressure field. The Level Set method has been…
A new approach is developed for computational modelling of microstructure evolution problems. The approach combines the phase-field method with the recently-developed laminated element technique (LET) which is a simple and efficient method…
An inverse problem of identifying inhomogeneity or crack in the workpiece made of nonlinear magnetic material is investigated. To recover the shape from the local measurements, a piecewise constant level set algorithm is proposed. By means…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…