Related papers: T-IFISS: a toolbox for adaptive FEM computation
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…
A general adaptive refinement strategy for solving linear elliptic partial differential equation with random data is proposed and analysed herein. The adaptive strategy extends the a posteriori error estimation framework introduced by…
Data-adaptive (machine learning-based) effect estimators are increasingly popular to reduce bias in high-dimensional bioinformatic and clinical studies (e.g. real-world data, target trials, -omic discovery). Their relative statistical…
Identifying anomalies has become one of the primary strategies towards security and protection procedures in computer networks. In this context, machine learning-based methods emerge as an elegant solution to identify such scenarios and…
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…
A multilevel adaptive refinement strategy for solving linear elliptic partial differential equations with random data is recalled in this work. The strategy extends the a posteriori error estimation framework introduced by Guignard and…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
A precise domain triangulation is recognized as indispensable for the accurate numerical approximation of differential operators within collocation methods, leading to a substantial reduction in discretization errors. An efficient finite…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
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…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…
Mesh sensitivity of finite element solution for linear elliptic partial differential equations is analyzed. A bound for the change in the finite element solution is obtained in terms of the mesh deformation and its gradient. The bound shows…
Because the choice and tuning of the optimizer affects the speed, and ultimately the performance of deep learning, there is significant past and recent research in this area. Yet, perhaps surprisingly, there is no generally agreed-upon…
We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…
We present the Maple package TDDS (Thomas Decomposition of Differential Systems). Given a polynomially nonlinear differential system, which in addition to equations may contain inequations, this package computes a decomposition of it into a…
This article presents new immersed finite element (IFE) methods for solving the popular second order elliptic interface problems on structured Cartesian meshes even if the involved interfaces have nontrivial geometries. These IFE methods…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allowing us to work directly on the strong form of a linear PDE.…
Path sampling approaches have become invaluable tools to explore the mechanisms and dynamics of so-called rare events that are characterized by transitions between metastable states separated by sizeable free energy barriers. Their…