Related papers: A compiler for variational forms
This work develops, for the first time, a face-centred finite volume (FCFV) solver for the simulation of laminar and turbulent viscous incompressible flows. The formulation relies on the Reynolds-averaged Navier-Stokes (RANS) equations…
A coarse-grained computational procedure based on the Finite Element Method is proposed to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by the elastic network model, proteins…
In this paper we use a Variational Quantum Algorithm to solve Initial Value Problems with the Implicit Crank-Nicolson and the Method of Lines (MoL) evolution schemes. The unknown functions use a spectral decomposition with the Fourier…
We present a novel approach to fast on-the-fly low order finite element assembly for scalar elliptic partial differential equations of Darcy type with variable coefficients optimized for matrix-free implementations. Our approach introduces…
We describe different optimization techniques to perform the assembly of finite element matrices in Matlab and Octave, from the standard approach to recent vectorized ones, without any low level language used. We finally obtain a simple and…
In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…
The Finite Element Method (FEM) is a widely used technique for simulating crash scenarios with high accuracy and reliability. To reduce the significant computational costs associated with FEM, the Finite Element Method Integrated Networks…
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 propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is ``exact'' in that given the approximation inherent in the…
For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always…
The variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…
Physical units are fundamental to scientific computing. However, many finite element frameworks lack built-in support for dimensional analysis. In this work, we present a systematic framework for integrating physical units into the Unified…
In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently,…
We develop a new methodology for extracting Compton form factors (CFFs) in from deeply virtual exclusive reactions such as the unpolarized DVCS cross section using a specialized inverse problem solver, a variational autoencoder inverse…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…
We address multiscale elliptic problems with random coefficients that are a perturbation of multiscale deterministic problems. Our approach consists in taking benefit of the perturbative context to suitably modify the classical Finite…