525 citations · 1.3k across the 23 of their papers we have counts for
6 papers · 1 filter
Absorbing boundary conditions for the Helmholtz equation using Gauss-Legendre quadrature reduced integrations
Koki Sagiyama
We introduce a new class of absorbing boundary conditions (ABCs) for the Helmholtz equation. The proposed ABCs are obtained by using discrete layers and the Lagrange fini…
Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
Justin Crum, Cyrus Cheng, David A. Ham +4
We present an implementation of the trimmed serendipity finite element family, using the open source finite element package Firedrake. The new elements can be used seamlessly withi…
Automated shape differentiation in the Unified Form Language
David A. Ham, Lawrence Mitchell, Alberto Paganini +1
We discuss automating the calculation of weak shape derivatives in the Unified Form Language (Alnæs et al., ACM Trans. Math. Softw., 2014) by introducing an appropriate additional…
Automated generation and symbolic manipulation of tensor product finite elements
Andrew T. T. McRae, Gheorghe-Teodor Bercea, Lawrence Mitchell +2
We describe and implement a symbolic algebra for scalar and vector-valued finite elements, enabling the computer generation of elements with tensor product structure on quadrilater…
On the shallow atmosphere approximation in finite element dynamical cores
C. J. Cotter, D. A. Ham, A. T. T. McRae +2
We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the f…
Numerical wave propagation for the triangular - finite element pair
C. J. Cotter
Inertia-gravity mode and Rossby mode dispersion properties are examined for discretisations of the linearized rotating shallow-water equations using the - finite eleme…