Related papers: Multiscale finite element calculations in Python u…
SfePy (Simple Finite Elements in Python) is a framework for solving various kinds of problems (mechanics, physics, biology, ...) described by partial differential equations in two or three space dimensions by the finite element method. The…
In the paper a recent enhancement to the open source package SfePy (Simple Finite Elements in Python, http://sfepy.org) is introduced, namely the addition of another numerical discretization scheme, the isogeometric analysis, to the…
Manapy is a parallel, unstructured, finite-volume based solver for the solution of partial differential equations (PDE). The framework is written using Python, it is object-oriented, and is organized in such a way that it is easy to…
This document summarizes the main concepts of the finite element (FE) theory and constitutive relations as implemented in the open-source code phase-field multiphysics materials simulator PHIMATS https://github.com/ahcomat/PHIMATS. PHIMATS…
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness…
In resent years, the software ecosystem for numerical simulation still remains fragmented, with different algorithms and discretization methods often implemented in isolation, each with distinct data structures and programming conventions.…
Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only…
FlowPy is a numerical toolbox for the solution of partial differential equations encountered in Functional Renormalization Group equations. This toolbox compiles flow equations to fast machine code and is able to handle coupled systems of…
PySPH is an open-source, Python-based, framework for particle methods in general and Smoothed Particle Hydrodynamics (SPH) in particular. PySPH allows a user to define a complete SPH simulation using pure Python. High-performance code is…
Pyrit is a field simulation software based on the finite element method written in Python to solve coupled systems of partial differential equations. It is designed as a modular software that is easily modifiable and extendable. The…
The solutions of a system of polynomials in several variables are often needed, e.g.: in the design of mechanical systems, and in phase-space analyses of nonlinear biological dynamics. Reliable, accurate, and comprehensive numerical…
BayesPy is an open-source Python software package for performing variational Bayesian inference. It is based on the variational message passing framework and supports conjugate exponential family models. By removing the tedious task of…
We introduce FDApy, an open-source Python package for the analysis of functional data. The package provides tools for the representation of (multivariate) functional data defined on different dimensional domains and for functional data that…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an open-source…
In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the past two decades, a growing interest has been devoted to stochastic finite element method (SFEM) for the propagation of…
Applying proper orthogonal decomposition to a usual finite element (FE) formulation for space fractional partial differential equation, we get a reduced FE model, which greatly reduces the complexity of computation. Then, the stability…
Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable…