Unified form language: A domain-specific language for weak formulations of partial differential equations
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 …
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 …
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
In this work, we introduce the ConvPDE-UQ framework for constructing light-weight
numerical solvers for partial differential equations (PDEs) using convolutional neural …
numerical solvers for partial differential equations (PDEs) using convolutional neural …
Robust topology optimization of negative Poisson's ratio metamaterials under material uncertainty
Metamaterials are synthetic materials designed to have unique properties like negative
Poisson ratio (NPR). NPR metamaterials, also known as auxetics, offer significant value in …
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
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 …
possible by automated code generation. Given a variational form in a syntax that resembles …
A traveling-wave solution for bacterial chemotaxis with growth
Bacterial cells navigate their environment by directing their movement along chemical
gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial …
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
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 …
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
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 …
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
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** …
partial differential equations on complex geometries based on nonmatching or overlap** …
PyOP2: A high-level framework for performance-portable simulations on unstructured meshes
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 …
manner whilst achieving high efficiency on a diverse range of architectures. We present …