Finite Elements for Helmholtz equations with a nonlocal boundary condition

Published in SIAM Journal on Scientific Computing, 2021

A new nonlocal boundary condition for exterior Helmholtz problems along with the software infrastructure to express these boundary conditions in Unified Form Language

Recommended citation: Kirby, Robert C. and Klöckner, Andreas and Sepanski, Benjamin.(2021). "Finite Elements for Helmholtz Equations with a Nonlocal Boundary Condition." SIAM Journal on Scientific Computing, 43(3), A1671-A1691.

Augmented Hilbert series of numerical semigroups

Published in Integers, 2019

Several new explicit formulas for certain augmented Hilbert Series measuring maximal and minimal factorization lengths for all numerical semigroups.

Recommended citation: Glenn, Jeske and O'Neill Christopher and Ponomarenko, Vadim and Sepanski, Benjamin (June 3, 2019). "Augmented Hilbert series of numerical semigroups." Integers 19 #A32.