Related papers: A study of vectorization for matrix-free finite el…
In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
The matrix element method utilizes ab initio calculations of probability densities as powerful discriminants for processes of interest in experimental particle physics. The method has already been used successfully at previous and current…
Vector quantization (VQ) is a key component in discrete tokenizers for image generation, but its training is often unstable due to straight-through estimation bias, one-step-behind updates, and sparse codebook gradients, which lead to…
Improvements in computer systems have historically relied on two well-known observations: Moore's law and Dennard's scaling. Today, both these observations are ending, forcing computer users, researchers, and practitioners to abandon the…
Image tracing is a foundational component of the workflow in graphic design, engineering, and computer animation, linking hand-drawn concept images to collections of smooth curves needed for geometry processing and editing. Even for clean…
In high-order finite element analysis for elasticity, matrix-free (PA) methods are a key technology for overcoming the memory bottleneck of traditional Full Assembly (FA). However, existing implementations fail to fully exploit the special…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
Casting nonlocal problems in variational form and discretizing them with the finite element (FE) method facilitates the use of nonlocal vector calculus to prove well-posedeness, convergence, and stability of such schemes. Employing an FE…
Vectorizing hand-drawn sketches is a challenging task, which is of paramount importance for creating CAD vectorized versions for the fashion and creative workflows. This paper proposes a complete framework that automatically transforms…
Vectors of data are at the heart of machine learning and data mining. Recently, vector quantization methods have shown great promise in reducing both the time and space costs of operating on vectors. We introduce a vector quantization…
MFEM is an open-source, lightweight, flexible and scalable C++ library for modular finite element methods that features arbitrary high-order finite element meshes and spaces, support for a wide variety of discretization approaches and…
We introduce a high-performance virtual machine (VM) written in a numerically fast language like Fortran or C to evaluate very large expressions. We discuss the general concept of how to perform computations in terms of a VM and present…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2 containment as a climate change mitigation strategy. These simulations involve solving numerous…
Most modern processors contain vector units that simultaneously perform the same arithmetic operation over multiple sets of operands. The ability of compilers to automatically vectorize code is critical to effectively using these units.…
The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…
We study the properties of ultrametric matrices aiming to design methods for fast ultrametric matrix-vector multiplication. We show how to encode such a matrix as a tree structure in quadratic time and demonstrate how to use the resulting…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…