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)
Benchmarking Domain-Specific Compiler Optimizations for Variational Forms
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)
DOLFIN: Automated finite element computing
ACM Transactions on Mathematical Software (TOMS)
Increased efficiency in finite element computations through template metaprogramming
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
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
Finite Element Integration on GPUs
ACM Transactions on Mathematical Software (TOMS)
Numerical integration on GPUs for higher order finite elements
Computers & Mathematics with Applications
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Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier--Stokes operators. For the Laplace operator in two space dimensions, we have developed a heuristic graph algorithm that searches for such redundancies and generates code for computing the local stiffness matrices. Up to cubics, we are able to build the stiffness matrix on any triangle in less than one multiply-add pair per entry. Up to sixth degree, we can do it in less than about two pairs. Preliminary low-degree results for Poisson and Navier-Stokes operators in three dimensions are also promising.