GPU-accelerated discontinuous Galerkin methods on hybrid meshes

We present a time-explicit discontinuous Galerkin (DG) solver for the time-domain acoustic wave equation on hybrid meshes containing vertex-mapped hexahedral, wedge, pyramidal and tetrahedral elements. Discretely energy-stable formulations are presented for both Gauss-Legendre and Gauss-Legendre-Lobatto (Spectral Element) nodal bases for the hexahedron. Stable timestep restrictions for hybrid meshes are derived by bounding the spectral radius of the DG operator using order-dependent constants in trace and Markov inequalities. Computational efficiency is achieved under a combination of element-specific kernels (including new quadrature-free operators for the pyramid), multi-rate timestepping, and acceleration using Graphics Processing Units.Comment: Submitted to CMAM

Exploring Fijian high school students’ conceptions of averages

This paper focuses on part of a much larger study that explored form five (14 to 16 year-old) students’ ideas in statistics. A range of ideas was explored, including the students’ ideas about measures of centre and graphical representations. Students’ ideas about measures of centre were analysed and categories of responses identified. While students could compute mean and median, they were less competent with tasks that involved constructing meanings for averages. This could be due to an emphasis in the classroom on developing procedural knowledge or to linguistic and contextual problems. Some students used strategies based on prior school and everyday experiences. The paper concludes by suggesting some implications for mathematics education