Related papers: Bound preserving Point-Average-Moment PolynomiAl-i…
In this paper, we develop a novel well-balanced Point-Average-Moment PolynomiAl-interpreted (PAMPA) numerical method for solving the two-dimensional shallow water equations with temperature gradients on unstructured triangular meshes. The…
The PAMPA (Point-Average-Moment PolynomiAl-interpreted) method, proposed in [R. Abgrall, Commun. Appl. Math. Comput., 5: 370-402, 2023], combines conservative and non-conservative formulations of hyperbolic conservation laws to evolve cell…
We present a novel hydrostatic and non-hydrostatic equilibria preserving Point-Average-Moment PolynomiAl-interpreted (PAMPA) method for solving the one-dimensional hyperbolic balance laws, with applications to the shallow water models…
We present a novel discretisation strategy, strongly inspired from Roe's Active Flux scheme. It can use polygonal meshes and is provably bound preserving for scalar problems and the Euler equations. Several cases demonstrates the quality of…
We propose an improved version of the PAMPA algorithm where the solution is sought as globally continuous. The scheme is locally conservative, and there is no mass matrix to invert. This method had been developed in a series of papers, see…
In this paper, we provide a few new properties of Active Flux (AF)/Point-Average-Moment PolynomiAl-interpreted (\pampa) schemes. First, we show, in full generality, that the AF/pampa schemes can be interpreted in such a way that the…
We develop a positivity-preserving (PP) PAMPA (Point-Average-Moment PolynomiAl-interpreted) scheme that enforces a discrete divergence-free (DDF) magnetic field for ideal MHD on Cartesian grids. Extending our 1D invariant-domain-preserving…
Applying pre-trained models to assist point cloud understanding has recently become a mainstream paradigm in 3D perception. However, existing application strategies are straightforward, utilizing only the final output of the pre-trained…
In this paper, we explore the use of the Virtual Element Method concepts to solve scalar and system hyperbolic problems on general polygonal grids. The new schemes stem from the active flux approach \cite{AF1}, which combines the usage of…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…
This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…
The proximal point algorithm (PPA) has been developed to solve the monotone variational inequality problem. It provides a theoretical foundation for some methods, such as the augmented Lagrangian method (ALM) and the alternating direction…
Mamba, based on state space model (SSM) with its linear complexity and great success in classification provide its superiority in 3D point cloud analysis. Prior to that, Transformer has emerged as one of the most prominent and successful…
Multidimensional population balance models (PBMs) describe chemical and biological processes having a distribution over two or more intrinsic properties (such as size and age, or two independent spatial variables). The incorporation of…
Motivation: Generative models for protein backbone design have to simultaneously ensure geometric validity, sampling efficiency, and scalability to long sequences. However, most existing approaches rely on iterative refinement, quadratic…
Point cloud analysis has seen substantial advancements due to deep learning, although previous Transformer-based methods excel at modeling long-range dependencies on this task, their computational demands are substantial. Conversely, the…
We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…
In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of…
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…