Related papers: Firedrake: automating the finite element method by…
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…
In general, there is a mismatch between a finite element model {(FEM)} of a structure and its real behaviour. In aeronautics, this mismatch must be small because {FEM}s are a fundamental part of the development of an aircraft and of…
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…
This paper presents the generalized formulations of fundamental schemes for efficient unconditionally stable implicit finite-difference time-domain (FDTD) methods. The fundamental schemes constitute a family of implicit schemes that feature…
In this paper we represent a new framework for integrated distributed and reliable systems. In the proposed framework we have used three parts to increase Satisfaction and Performance of this framework. At first we analyze previous…
We present an efficient and robust numerical algorithm for solving the two-dimensional linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve…
In an effort to increase the versatility of finite element codes, we explore the possibility of automatically creating the Jacobian matrix necessary for the gradient-based solution of nonlinear systems of equations. Particularly, we aim to…
Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial…
Hierarchical problem abstraction, when applicable, may offer exponential reductions in computational complexity. Previous work on coarse-to-fine dynamic programming (CFDP) has demonstrated this possibility using state abstraction to speed…
This paper presents a novel operational matrix method to accelerate the training of fractional Physics-Informed Neural Networks (fPINNs). Our approach involves a non-uniform discretization of the fractional Caputo operator, facilitating…
Imposing physical constraints on neural networks as a method of knowledge embedding has achieved great progress in solving physical problems described by governing equations. However, for many engineering problems, governing equations often…
In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
Exascale computing will feature novel and potentially disruptive hardware architectures. Exploiting these to their full potential is non-trivial. Numerical modelling frameworks involving finite difference methods are currently limited by…
FEniCS Mechanics is a Python package to facilitate computational mechanics simulations. The Python library dolfin, from the FEniCS Project, is used to formulate and numerically solve the problem in variational form. The general balance laws…
In this paper, a peridynamics-based finite element method (Peri-FEM) is proposed for the quasi-static fracture analysis, which is of the consistent computational framework with the classical finite element method (FEM). First, the integral…
This paper presents a new data-driven finite element framework that is applicable to a broad range of engineering simulation problems. In the data-driven approach, the conservation laws and boundary conditions are satisfied by means of the…
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…
We present a finite-element software library, IRENE, which allows to solve numerically the dynamics of a viscous fluid layer embedded in three-dimensional space. Unlike finite-element libraries present in the literature, IRENE can handle…
For the parallel computation of partial differential equations, one key is the grid partitioning. It requires that each process owns the same amount of computations, and also, the partitioning quality should be proper to reduce the…