Benchmarking Domain-Specific Compiler Optimizations for Variational Forms
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
Optimized code generation for finite element local assembly using symbolic manipulation
ACM Transactions on Mathematical Software (TOMS)
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This paper continues earlier work on mathematical techniques for generating optimized algorithms for computing finite element stiffness matrices. These techniques start from representing the stiffness matrix for an affine element as a collection of contractions between reference tensors and an element-dependent geometry tensor. We go beyond the complexity-reducing binary relations explored in [R. C. Kirby, A. Logg, L. R. Scott, and A. R. Terrel, SIAM J. Sci. Comput., 28 (2006), pp. 224-240] to consider geometric relationships between three or more objects. Algorithms based on these relationships often have even fewer operations than those based on complexity-reducing relations.