Related papers: The Numerics of VMEC++
ESBMC implements many state-of-the-art techniques for model checking. We report on new and improved features that allow us to obtain verification results for previously unsupported programs and properties. ESBMC employs a new static…
In response to the growing demand for high-quality videos, Versatile Video Coding (VVC) was released in 2020, building on the hybrid coding architecture of its predecessor, HEVC, achieving about 50% bitrate reduction for the same visual…
The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming virtual element formulations for the numerical approximation…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
Hyperdimensional Computing (HDC), a technique inspired by cognitive models of computation, has been proposed as an efficient and robust alternative basis for machine learning. HDC programs are often manually written in low-level and target…
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
Within the framework of the displacement-based Virtual Element Method (VEM) for plane elasticity a significant problem is represented by an accurate evaluation of the stress field. In particular, in the classical VEM formulation, a suitable…
This paper summarizes the development of mVEM, a MATLAB software package containing efficient and easy-following codes for various virtual element methods (VEMs) published in the literature. We explain in detail the numerical implementation…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
We present MemEC, an erasure-coding-based in-memory key-value (KV) store that achieves high availability and fast recovery while keeping low data redundancy across storage servers. MemEC is specifically designed for workloads dominated by…
SPACE-Timers are a lightweight hierarchical profiling framework for C++ designed for modern high-performance computing (HPC) applications. It uses a stack-based timing model to capture deeply nested execution patterns with minimal overhead,…
The MFEM (Modular Finite Element Methods) library is a high-performance C++ library for finite element discretizations. MFEM supports numerous types of finite element methods and is the discretization engine powering many computational…
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal…
The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…
Large Language Models (LLMs) have demonstrated significant capability in code generation, but their potential in code efficiency optimization remains underexplored. Previous LLM-based code efficiency optimization approaches exclusively…
Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…
We present finite-element numerical algorithms for the identification of vortices in quantum fluids described by a macroscopic complex wave function. Their implementation using the free software FreeFem++ is distributed with this paper as a…
We present a set of computer codes designed to test methods for optimizing time-dependent control protocols in fluctuating nonequilibrium systems. Each problem consists of a stochastic model, an optimization objective, and C++ and Python…
We report on the use of the recently-developed Mathematica package \emph{VEST} (Vector Einstein Summation Tools) to automatically derive the guiding center transformation. Our Mathematica code employs a recursive procedure to derive the…
We present pySecDec, a new version of the program SecDec, which performs the factorisation of dimensionally regulated poles in parametric integrals, and the subsequent numerical evaluation of the finite coefficients. The algebraic part of…