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ACM Transactions on Mathematical Software (TOMS), Volume 44 Issue 1, April 2017

SYM-ILDL: Incomplete LDLT Factorization of Symmetric Indefinite and Skew-Symmetric Matrices
Chen Greif, Shiwen He, Paul Liu
Article No.: 1
DOI: 10.1145/3054948

SYM-ILDL is a numerical software package that computes incomplete LDLT (ILDL) factorizations of symmetric indefinite and real skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally...

Complex Additive Geometric Multilevel Solvers for Helmholtz Equations on Spacetrees
Bram Reps, Tobias Weinzierl
Article No.: 2
DOI: 10.1145/3054946

We introduce a family of implementations of low-order, additive, geometric multilevel solvers for systems of Helmholtz equations arising from Schrödinger equations. Both grid spacing and arithmetics may comprise complex numbers, and we thus...

An Algorithm for the Optimization of Finite Element Integration Loops
Fabio Luporini, David A. Ham, Paul H. J. Kelly
Article No.: 3
DOI: 10.1145/3054944

We present an algorithm for the optimization of a class of finite-element integration loop nests. This algorithm, which exploits fundamental mathematical properties of finite-element operators, is proven to achieve a locally optimal operation...