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To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D magnetic textures, the Hopf index serves as a key topological descriptor for 3D magnetic structures. In this work, we present and compare various methods for numerically calculating the Hopf index, provide implementations, and offer a detailed analysis of their accuracy and computational efficiency. Additionally, we identify and address common pitfalls and challenges associated with the numerical computation of the Hopf index, offering insights for improving the robustness of these techniques.

Typing mathematics is sometimes difficult with text editor functions for students with motor impairment and other associated impairments (visual, cognitive). Based on the HandiMathKey software keyboard, a user-centred design method involving the ecosytem of disabled students was applied to design the HMK-D physical keyboard for mathematical input. We opted for the Stream Deck device because of its multimedia features and its appeal to young students to the HMK-D. Preliminary tests with 8 students (5 in secondary school and 3 in high school) shows that HMK-D is highly accepted, accessible and fun for mathematical input by students with impairments. A longitudinal study of the usability and acceptability of HMK-D is planned for the 2023-2024 school year., Comment: Universal Access in Human-Computer Interaction. HCII 2023, Jul 2023, Copenhagen (Virtual), Denmark

We present a sequence of optimizations to the performance-critical compute kernels of the high-order discontinuous Galerkin solver of the hyperbolic PDE engine ExaHyPE -- successively tackling bottlenecks due to SIMD operations, cache hierarchies and restrictions in the software design. Starting from a generic scalar implementation of the numerical scheme, our first optimized variant applies state-of-the-art optimization techniques by vectorizing loops, improving the data layout and using Loop-over-GEMM to perform tensor contractions via highly optimized matrix multiplication functions provided by the LIBXSMM library. We show that memory stalls due to a memory footprint exceeding our L2 cache size hindered the vectorization gains. We therefore introduce a new kernel that applies a sum factorization approach to reduce the kernel's memory footprint and improve its cache locality. With the L2 cache bottleneck removed, we were able to exploit additional vectorization opportunities, by introducing a hybrid Array-of-Structure-of-Array data layout that solves the data layout conflict between matrix multiplications kernels and the point-wise functions to implement PDE-specific terms. With this last kernel, evaluated in a benchmark simulation at high polynomial order, only 2\% of the floating point operations are still performed using scalar instructions and 22.5\% of the available performance is achieved., Comment: PDSEC 2020

The development of a high performance PDE solver requires the combined expertise of interdisciplinary teams with respect to application domain, numerical scheme and low-level optimization. In this paper, we present how the ExaHyPE engine facilitates the collaboration of such teams by isolating three roles: application, algorithms, and optimization expert. We thus support team members in letting them focus on their own area of expertise while integrating their contributions into an HPC production code. Inspired by web application development practices, ExaHyPE relies on two custom code generation modules, the Toolkit and the Kernel Generator, which follow a Model-View-Controller architectural pattern on top of the Jinja2 template engine library. Using Jinja2's templates to abstract the critical components of the engine and generated glue code, we isolate the application development from the engine. The template language also allows us to define and use custom template macros that isolate low-level optimizations from the numerical scheme described in the templates. We present three use cases, each focusing on one of our user roles, showcasing how the design of the code generation modules allows to easily expand the solver schemes to support novel demands from applications, to add optimized algorithmic schemes (with reduced memory footprint, e.g.), or provide improved low-level SIMD vectorization support., Comment: SC19 SE-HER

ExaHyPE ("An Exascale Hyperbolic PDE Engine") is a software engine for solving systems of first-order hyperbolic partial differential equations (PDEs). Hyperbolic PDEs are typically derived from the conservation laws of physics and are useful in a wide range of application areas. Applications powered by ExaHyPE can be run on a student's laptop, but are also able to exploit thousands of processor cores on state-of-the-art supercomputers. The engine is able to dynamically increase the accuracy of the simulation using adaptive mesh refinement where required. Due to the robustness and shock capturing abilities of ExaHyPE's numerical methods, users of the engine can simulate linear and non-linear hyperbolic PDEs with very high accuracy. Users can tailor the engine to their particular PDE by specifying evolved quantities, fluxes, and source terms. A complete simulation code for a new hyperbolic PDE can often be realised within a few hours - a task that, traditionally, can take weeks, months, often years for researchers starting from scratch. In this paper, we showcase ExaHyPE's workflow and capabilities through real-world scenarios from our two main application areas: seismology and astrophysics.

Soft error rates are increasing as modern architectures require increasingly small features at low voltages. Due to the large number of components used in HPC architectures, these are particularly vulnerable to soft errors. Hence, when designing applications that run for long time periods on large machines, algorithmic resilience must be taken into account. In this paper we analyse the inherent resiliency of a-posteriori limiting procedures in the context of the explicit ADER DG hyperbolic PDE solver ExaHyPE. The a-posteriori limiter checks element-local high-order DG solutions for physical admissibility, and can thus be expected to also detect hardware-induced errors. Algorithmically, it can be interpreted as element-local checkpointing and restarting of the solver with a more robust finite volume scheme on a fine subgrid. We show that the limiter indeed increases the resilience of the DG algorithm, detecting and correcting particularly those faults which would otherwise lead to a fatal failure., Comment: 2018 IEEE/ACM 8th Workshop on Fault Tolerance for HPC at eXtreme Scale (FTXS)

Can we assume that because someone is intellectually aware about gender-inclusive pedagogy they will actualize this awareness in their classes? No, for that reason, the aim of the current study is to explore and widen an understanding whether an individual can walk the walk as well as talk the talk. This is a qualitative study in nature, conducted in the summer of 2005, of a Professor of Science Education's attempts to make his classes gender-inclusive. Methods used to gather data for this study were a combination of action research and case study techniques. Accordingly, classroom observations, field notes, interviews, and journals were the primary sources of data. Preliminary findings indicate that the professor's teaching efforts are more gender-neutral then gender-inclusive. The inclusion of multiple reflections and truths in a higher education class could help students understand other people's values in society and improve the quality and accessibility of science education.