Structure and interpretation of computer programs
Structure and interpretation of computer programs
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Spectral methods on triangles and other domains
Journal of Scientific Computing
Matrix computations (3rd ed.)
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Nodal high-order methods on unstructured grids
Journal of Computational Physics
Optimizing FIAT with level 3 BLAS
ACM Transactions on Mathematical Software (TOMS)
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)
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)
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Construction of a high order fluid-structure interaction solver
Journal of Computational and Applied Mathematics
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
Optimized code generation for finite element local assembly using symbolic manipulation
ACM Transactions on Mathematical Software (TOMS)
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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Much of finite element computation is constrained by the difficulty of evaluating high-order nodal basis functions. While most codes rely on explicit formulae for these basis functions, we present a new approach that allows us to construct a general class of finite element basis functions from orthonormal polynomials and evaluate and differentiate them at any points. This approach relies on fundamental ideas from linear algebra and is implemented in Python using several object-oriented and functional programming techniques.