Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Local modification of meshes for adaptive and/or multigrid finite-element methods
Journal of Computational and Applied Mathematics
Automated scientific software scripting with SWIG
Future Generation Computer Systems - Tools for program development and analysis
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
ACM Transactions on Mathematical Software (TOMS)
An overview of the Trilinos project
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Optimizing the Evaluation of Finite Element Matrices
SIAM Journal on Scientific Computing
Topological Optimization of the Evaluation of Finite Element Matrices
SIAM Journal on Scientific Computing
A compiler for variational forms
ACM Transactions on Mathematical Software (TOMS)
Efficient compilation of a class of variational forms
ACM Transactions on Mathematical Software (TOMS)
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Mesh algorithms for PDE with Sieve I: Mesh distribution
Scientific Programming
On the efficiency of symbolic computations combined with code generation for finite element methods
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Efficient representation of computational meshes
International Journal of Computational Science and Engineering
Automated Code Generation for Discontinuous Galerkin Methods
SIAM Journal on Scientific Computing
GrAL-the grid algorithms library
Future Generation Computer Systems
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
ACM Transactions on Mathematical Software (TOMS)
Efficient representation of computational meshes
International Journal of Computational Science and Engineering
Applied Numerical Mathematics
Algorithms and data structures for massively parallel generic adaptive finite element codes
ACM Transactions on Mathematical Software (TOMS)
Adaptive simulation of turbulent flow past a full car model
State of the Practice Reports
Unified Embedded Parallel Finite Element Computations via Software-Based Fréchet Differentiation
SIAM Journal on Scientific Computing
Analysis of an Interface Stabilized Finite Element Method: The Advection-Diffusion-Reaction Equation
SIAM Journal on Numerical Analysis
Automatic energy-momentum conserving time integrators for hyperelastic waves
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific Computing
A Fast Solver for a Nonlocal Dielectric Continuum Model
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Approximation of sparse controls in semilinear elliptic equations
LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
PyDEC: Software and Algorithms for Discretization of Exterior Calculus
ACM Transactions on Mathematical Software (TOMS)
A measure space approach to optimal source placement
Computational Optimization and Applications
Benchmarking FEniCS for mantle convection simulations
Computers & Geosciences
Application-tailored linear algebra algorithms: A search-based approach
International Journal of High Performance Computing Applications
Vectorized OpenCL implementation of numerical integration for higher order finite elements
Computers & Mathematics with Applications
ACM Transactions on Mathematical Software (TOMS)
Playa: High-performance programmable linear algebra
Scientific Programming
Numerical integration on GPUs for higher order finite elements
Computers & Mathematics with Applications
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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 with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled, and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This article discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.