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A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…

Fairness is becoming an increasingly crucial issue for computer vision, especially in the human-related decision systems. However, achieving algorithmic fairness, which makes a model produce indiscriminative outcomes against protected…

Semantic scene reconstruction from point cloud is an essential and challenging task for 3D scene understanding. This task requires not only to recognize each instance in the scene, but also to recover their geometries based on the partial…

Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and…

We propose Differentiable Surface Splatting (DSS), a high-fidelity differentiable renderer for point clouds. Gradients for point locations and normals are carefully designed to handle discontinuities of the rendering function.…

The spatial discretization of convective terms in compressible flow equations is studied from an abstract viewpoint, for finite-difference methods and finite-volume type formulations with cell-centered numerical fluxes. General conditions…

In this paper, a novel dual-field structure-preserving mixed finite element discretization for incompressible Hall MHD equations is introduced. The discretization satisfies pointwise conservation of mass, magnetic Gauss's law, and…

Diffusion models have been popular for point cloud generation tasks. Existing works utilize the forward diffusion process to convert the original point distribution into a noise distribution and then learn the reverse diffusion process to…

A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product…

We present a divergence-free semi-implicit finite volume scheme for the simulation of the ideal magnetohydrodynamics (MHD) equations which is stable for large time steps controlled by the local transport speed at all Mach and Alfv\'en…

Traditional 3D garment creation requires extensive manual operations, resulting in time and labor costs. Recently, 3D Gaussian Splatting has achieved breakthrough progress in 3D scene reconstruction and rendering, attracting widespread…

We present a novel framework for mesh reconstruction from unstructured point clouds by taking advantage of the learned visibility of the 3D points in the virtual views and traditional graph-cut based mesh generation. Specifically, we first…

In this paper we analyze the error as well for the semi-discretization as the full discretization of a time-dependent convection-diffusion problem. We use for the discretization in space the local discontinuous Galerkin (LDG) method on a…

This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…

We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…

A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid…

An accelerated block coordinate descent (ABCD) method in Hilbert space is analyzed to solve the sparse optimal control problem via its dual. The finite element approximation of this method is investigated and convergence results are…

This work investigates the effects of the choice of momentum diffusion operator on the evolution of multiphase fluid systems resolved with Meshless Lagrangian Methods (MLM). Specifically, the effects of a non-zero viscosity gradient at…

The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning…

We present a fast feature-metric point cloud registration framework, which enforces the optimisation of registration by minimising a feature-metric projection error without correspondences. The advantage of the feature-metric projection…