Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Computational Differential Equations
Computational Differential Equations
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
ACM Transactions on Mathematical Software (TOMS)
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
Optimizing FIAT with level 3 BLAS
ACM Transactions on Mathematical Software (TOMS)
A compiler for variational forms
ACM Transactions on Mathematical Software (TOMS)
Benchmarking Domain-Specific Compiler Optimizations for Variational Forms
ACM Transactions on Mathematical Software (TOMS)
Algorithms and Data Structures for Multi-Adaptive Time-Stepping
ACM Transactions on Mathematical Software (TOMS)
Singularity-free evaluation of collapsed-coordinate orthogonal polynomials
ACM Transactions on Mathematical Software (TOMS)
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)
Unified framework for finite element assembly
International Journal of Computational Science and Engineering
DOLFIN: Automated finite element computing
ACM Transactions on Mathematical Software (TOMS)
Efficient Assembly of $H(\mathrm{div})$ and $H(\mathrm{curl})$ Conforming Finite Elements
SIAM Journal on Scientific Computing
Unified Embedded Parallel Finite Element Computations via Software-Based Fréchet Differentiation
SIAM Journal on Scientific Computing
Benchmarking FEniCS for mantle convection simulations
Computers & Geosciences
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We investigate the compilation of general multilinear variational forms over affines simplices and prove a representation theorem for the representation of the element tensor (element stiffness matrix) as the contraction of a constant reference tensor and a geometry tensor that accounts for geometry and variable coefficients. Based on this representation theorem, we design an algorithm for efficient pretabulation of the reference tensor. The new algorithm has been implemented in the FEniCS Form Compiler (FFC) and improves on a previous loop-based implementation by several orders of magnitude, thus shortening compile-times and development cycles for users of FFC.