Related papers: MPM Lite: Linear Kernels and Integration without P…
We develop a new meshfree geometric multilevel (MGM) method for solving linear systems that arise from discretizing elliptic PDEs on surfaces represented by point clouds. The method uses a Poisson disk sampling-type technique for coarsening…
Post-training quantization (PTQ) is an effective technique for compressing large language models (LLMs). However, while uniform-precision quantization is computationally efficient, it often compromises model performance. To address this, we…
In this paper, we present a new framework for addressing the nonlinear Landau collision operator in terms of particle-in-cell methods. We employ the underlying metriplectic structure of the collision operator and, using a macro particle…
Particle collisions are the primary mechanism of inter-particle momentum and energy exchange for dense particle-laden flow. Accurate approximation of this collision operator in four-way coupled Euler-Lagrange approaches remains challenging…
The family of Multiscale Hybrid-Mixed (MHM) finite element methods has received considerable attention from the mathematics and engineering community in the last few years. The MHM methods allow solving highly heterogeneous problems on…
The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
Dense linear layers are a dominant source of computational and parametric cost in modern machine learning models, despite their quadratic complexity and often being misaligned with the compositional structure of learned representations. We…
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding…
MPS-VG, a Virtual Grating (VG) model for the Lagrangian mesh-free Moving Particle Semi-implicit (MPS) method is proposed for replacing conventional particle-based solid modeling of gratings with a set of thin inclined slats. Unlike most…
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…
The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is…
The multiscale hybrid-mixed (MHM) method consists of a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients. In this context, we propose a family of low-order finite elements for the…
Ductile fracture of metallic materials typically involves the elastoplastic deformation and associated damaging process. The nonlocal lattice particle method (LPM) can be extended to model this complex behavior. Recently, a distortional…
Fine-tuning a pre-trained language model (PLM) emerges as the predominant strategy in many natural language processing applications. However, this process is known to be expensive, especially on edge devices with low computing power. While…
We present a simple modification of the direct-forcing immersed boundary method (IBM) proposed by Uhlmann [J. Comput. Phys, 2005] in order to enable it to be applied to particulate flows with solid-to-fluid density ratios around unity. The…
In this paper we introduce a novel quantifier elimination method for conjunctions of linear real arithmetic constraints. Our algorithm is based on the Fourier-Motzkin variable elimination procedure, but by case splitting we are able to…
Aiming at a drastic speedup for point-data embeddings at test time, we propose a new framework that uses a pair of multi-layer perceptron (MLP) and look-up table (LUT) to transform point-coordinate inputs into high-dimensional features.…
Simulating nonlinear reaction-diffusion dynamics on complex, non-Euclidean manifolds remains a fundamental challenge in computational morphogenesis, constrained by high-fidelity mesh generation costs and symplectic drift in discrete…
In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to…