Unified form language: A domain-specific language for weak formulations of partial differential equations

MS Alnæs, A Logg, KB Ølgaard, ME Rognes… - ACM Transactions on …, 2014 - dl.acm.org
We present the Unified Form Language (UFL), which is a domain-specific language for
representing weak formulations of partial differential equations with a view to numerical …

[BOOK][B] Lecture notes in computational science and engineering

TJ Barth, M Griebel, DE Keyes, RM Nieminen, D Roose… - 2005 - Springer
The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains

N Winovich, K Ramani, G Lin - Journal of Computational Physics, 2019 - Elsevier
In this work, we introduce the ConvPDE-UQ framework for constructing light-weight
numerical solvers for partial differential equations (PDEs) using convolutional neural …

Robust topology optimization of negative Poisson's ratio metamaterials under material uncertainty

G Agrawal, A Gupta, R Chowdhury… - Finite Elements in …, 2022 - Elsevier
Metamaterials are synthetic materials designed to have unique properties like negative
Poisson ratio (NPR). NPR metamaterials, also known as auxetics, offer significant value in …

Optimizations for quadrature representations of finite element tensors through automated code generation

KB Ølgaard, GN Wells - ACM Transactions on Mathematical Software …, 2010 - dl.acm.org
We examine aspects of the computation of finite element matrices and vectors that are made
possible by automated code generation. Given a variational form in a syntax that resembles …

A traveling-wave solution for bacterial chemotaxis with growth

AV Narla, J Cremer, T Hwa - Proceedings of the National …, 2021 - National Acad Sciences
Bacterial cells navigate their environment by directing their movement along chemical
gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial …

A length scale insensitive phase field model for brittle fracture of hyperelastic solids

TK Mandal, A Gupta, VP Nguyen, R Chowdhury… - Engineering Fracture …, 2020 - Elsevier
Fracture of hyperelastic materials such as synthetic rubber, hydrogels, textile fabrics is an
essential problem in many engineering fields. The computational simulation of such a …

Adaptive phase-field modeling of brittle fracture using a robust combination of error-estimator and markers

UM Krishnan, A Gupta, R Chowdhury - Engineering Fracture Mechanics, 2022 - Elsevier
An error estimator is proposed to carry out adaptive mesh refinement (AMR) for phase-field
fracture (PFF) simulation. The proposed error estimator works with the mesh-induced crack …

Efficient implementation of finite element methods on nonmatching and overlap** meshes in three dimensions

A Massing, MG Larson, A Logg - SIAM Journal on Scientific Computing, 2013 - SIAM
In recent years, a number of finite element methods have been formulated for the solution of
partial differential equations on complex geometries based on nonmatching or overlap** …

PyOP2: A high-level framework for performance-portable simulations on unstructured meshes

F Rathgeber, GR Markall, L Mitchell… - 2012 SC Companion …, 2012 - ieeexplore.ieee.org
Emerging many-core platforms are very difficult to program in a performance portable
manner whilst achieving high efficiency on a diverse range of architectures. We present …