Related papers: An efficient way to assemble finite element matric…
This paper presents an algorithm for computing Sine-Cosine pairs to modest accuracy, but in a manner which contains no conditional tests or branching, making it highly amenable to vectorization. An exemplary implementation for PowerPC…
To obtain the highest confidence on the correction of numerical simulation programs for the resolution of Partial Differential Equations (PDEs), one has to formalize the mathematical notions and results that allow to establish the soundness…
Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
Large Vision-Language Models (LVLMs) have achieved remarkable success, yet their significant computational demands hinder practical deployment. While efforts to improve LVLM efficiency are growing, existing methods lack comprehensive…
Lattice rules and polynomial lattice rules are quadrature rules for approximating integrals over the $s$-dimensional unit cube. Since no explicit constructions of such quadrature methods are known for dimensions $s > 2$, one usually has to…
Although, many scientists and engineers use Octave or MATLAB as their preferred programming language, dynamic nature of these languages can lead to slower running-time of programs written in these languages compared to programs written in…
Vision-Language Models (VLMs) are integral to tasks such as image captioning and visual question answering, but their high computational cost, driven by large memory footprints and processing time, limits their scalability and real-time…
In this paper, we present FPT-algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems' formulations are near square. The…
We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The mixed finite element VEF…
Modular arithmetic is widely used in crytography and symbolic computation. This paper presents a vectorized Montgomery algorithm for modular multiplication, the key to fast modular arithmetic, that fully utilizes the SIMD instructions. We…
Code generation based software platforms, such as Firedrake, have become popular tools for developing complicated finite element discretisations of partial differential equations. We extended the code generation infrastructure in Firedrake…
We examine the effect of using complexity-reducing relations to generate optimized code for the evaluation of finite element variational forms. The optimizations are implemented in a prototype code named FErari, which has been integrated as…
Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…
A lattice of integers is the collection of all linear combinations of a set of vectors for which all entries of the vectors are integers and all coefficients in the linear combinations are also integers. Lattice reduction refers to the…
Vector-based word representations help countless Natural Language Processing (NLP) tasks capture the language's semantic and syntactic regularities. In this paper, we present the characteristics of existing word embedding approaches and…
Finite element (FE) analysis guides the design and verification of nearly all manufactured objects. It is at the core of computational engineering, enabling simulation of complex physical systems, from fluids and solids to multiphysics…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…
Matrices with hierarchical low-rank structure, including HODLR and HSS matrices, constitute a versatile tool to develop fast algorithms for addressing large-scale problems. While existing software packages for such matrices often focus on…
We present a novel parallelization strategy for evaluating Finite Element Method (FEM) variational forms on GPUs, focusing on those that are expressible through the Unified Form Language (UFL) on simplex meshes. We base our approach on code…