Design patterns: elements of reusable object-oriented software
Design patterns: elements of reusable object-oriented software
Evaluating derivatives: principles and techniques of algorithmic differentiation
Evaluating derivatives: principles and techniques of algorithmic differentiation
FLAME: Formal Linear Algebra Methods Environment
ACM Transactions on Mathematical Software (TOMS)
Decomposing monomial representations of solvable groups
Journal of Symbolic Computation
Algorithm 839: FIAT, a new paradigm for computing finite element basis functions
ACM Transactions on Mathematical Software (TOMS)
Representing linear algebra algorithms in code: the FLAME application program interfaces
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
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)
Geometric Optimization of the Evaluation of Finite Element Matrices
SIAM Journal on Scientific Computing
Scientific Programming - Parallel/High-Performance Object-Oriented Scientific Computing (POOSC '05), Glasgow, UK, 25 July 2005
Benchmarking Domain-Specific Compiler Optimizations for Variational Forms
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)
The Theory of Critical Phenomena: An Introduction to the Renormalization Group
The Theory of Critical Phenomena: An Introduction to the Renormalization Group
Automatic generation of fast discrete signal transforms
IEEE Transactions on Signal Processing
Algebraic Signal Processing Theory: Foundation and 1-D Time
IEEE Transactions on Signal Processing - Part I
ACM Transactions on Mathematical Software (TOMS)
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
ACM Transactions on Mathematical Software (TOMS)
Playa: High-performance programmable linear algebra
Scientific Programming
Sundance: High-level software for PDE-constrained optimization
Scientific Programming
Scientific Programming - A New Overview of the Trilinos Project --Part 1
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Computational analysis of systems governed by partial differential equations (PDEs) requires not only the calculation of a solution but the extraction of additional information such as the sensitivity of that solution with respect to input parameters or the inversion of the system in an optimization or design loop. Moving beyond the automation of discretization of PDEs by finite element methods, we present a mathematical framework that unifies the discretization of PDEs with these additional analysis requirements. In particular, Fréchet differentiation on a class of functionals together with a high-performance finite element framework has led to a code, called Sundance, that provides high-level programming abstractions for the automatic, efficient evaluation of finite variational forms together with the derived operators required by engineering analysis.