Related papers: SfePy - Write Your Own FE Application
The $hp$-adaptive finite element method (FEM) - where one independently chooses the mesh size ($h$) and polynomial degree ($p$) to be used on each cell - has long been known to have better theoretical convergence properties than either $h$-…
QuaPy is an open-source framework for performing quantification (a.k.a. supervised prevalence estimation), written in Python. Quantification is the task of training quantifiers via supervised learning, where a quantifier is a predictor that…
This work consists in two parts. The first part is a review of the finite element method (FEM) for one and two-dimensional problems. The second part, concerns the application of the FEM to find numerical solutions of the Stokes equation and…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
An emerging theme across many domains of science and engineering is materials that change shape, often dramatically. Determining their structure involves solving a shape optimization problem where a given energy functional is minimized with…
Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic…
We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s-r of the variables where s is the degree of the monomial or,…
We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic…
A novel numerical formulation for solving fluid-structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element…
One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…
This study presents a finite element and virtual element (FE-VE) coupled method for thermomechanical analysis in electronic packaging structures. The approach partitions computational domains strategically, employing FEM for regular…
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory…
SPEEDY is an Eclipse-based IDE for exploring techniques that assist users in generating correct specifications, particularly including invariant inference algorithms and tools. It integrates with several back-end tools that propose…
A numerical scheme is presented for approximating fractional order Poisson problems in two and three dimensions. The scheme is based on reformulating the original problem posed over $\Omega$ on the extruded domain…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
Flaky tests obstruct software development, and studying and proposing mitigations against them has therefore become an important focus of software engineering research. To conduct sound investigations on test flakiness, it is crucial to…
We introduce Devito, a new domain-specific language for implementing high-performance finite difference partial differential equation solvers. The motivating application is exploration seismology where methods such as Full-Waveform…
The scaled boundary finite element method is known for its capability in reproducing highly-detailed solution fields. This, however, is only attainable in those cases where analytical solutions exist. Many others invoke the use of numerical…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…