Seminars

2023

• Committee chair of the SIAM International Meshing Roundtable Workshop

  SIAM IMR 2023, Committee chair, Amsterdam, Netherlands, March 2023. BibTeX Abstract

  @booklet{imr31-2023,
    title = {Committee chair of the SIAM International Meshing Roundtable Workshop},
    year = {2023},
    month = mar,
    series = {SIAM IMR 2023, \textbf{Committee chair}},
    location = {Amsterdam, Netherlands},
    url = {https://internationalmeshingroundtable.com/imr31/committee/}
  }
  

  The SIAM IMR workshop continues to focus on bringing together researchers and developers from academia, national labs and industry in a stimulating, open environment to share technical information related to mesh generation and general pre-processing techniques.

2022

• Paper chair of the SIAM International Meshing Roundtable Workshop

  SIAM IMR 2022, Paper chair, Virtual event, February 2022. BibTeX Abstract

  @booklet{imr30-2022,
    title = {Paper chair of the SIAM International Meshing Roundtable Workshop},
    year = {2022},
    month = feb,
    series = {SIAM IMR 2022, \textbf{Paper chair}},
    location = {Virtual event},
    url = {https://internationalmeshingroundtable.com/imr30/committee/}
  }
  

  The SIAM IMR workshop continues to focus on bringing together researchers and developers from academia, national labs and industry in a stimulating, open environment to share technical information related to mesh generation and general pre-processing techniques.
• Numerical and computational performance of spectral element methods for prototype fusion problems

  SIAM Conference on Parallel Processing for Scientific Computing, Virtual event, February 2022. BibTeX Abstract

  @booklet{siam-pp-2022,
    title = {Numerical and computational performance of spectral element methods for prototype fusion problems},
    year = {2022},
    month = feb,
    series = {SIAM Conference on Parallel Processing for Scientific Computing},
    location = {Virtual event}
  }
  

  High-order methods are increasingly being viewed as an enabling technology for bespoke high-fidelity modelling of challenging physical systems. The use of high-order polynomials within elements, when compared to classical linear and second-order methods, offers advantages from both a numerical analysis and implementation perspective. The ‘resolution power’ of high-order discretisations is far greater than at lower orders, with favourable dispersion and diffusion characteristics meaning that complex spatial structures and phenomena spanning multiple length scales can be accurately resolved and tracked across long timescales. This accuracy is critical in highly sensitive and complex systems, such as fluid dynamics, where high-order methods are amongst the most promising methods for next generation numerical simulations of high-fidelity problems at the exascale. This talk will outline the developments currently being made in the algorithmic and software improvements required to enable high-order simulations to be performed for the problems of interest to the NEPTUNE community. In particular, we will present current developments in curvilinear mesh generation for fusion-related geometries, and on the computationally-efficient high-order implementation of prototype systems related to heat transport in highly anisotropic systems.
• Tackling real-world problems with modern software

  Interdisciplinary Research Computing Seminar, Imperial College London, London, UK, January 2022. BibTeX

  @booklet{iclrse-2022,
    title = {Tackling real-world problems with modern software},
    year = {2022},
    month = jan,
    series = {Interdisciplinary Research Computing Seminar},
    location = {Imperial College London, London, UK},
    url = {https://davidmoxey.uk/assets/talks/2022-01-icl-rse.pdf}
  }
  

2021

• New and improved development practices in Nektar++

  Nektar++ Workshop 2021, Virtual event, December 2021. BibTeX

  @booklet{nektarpp-2021,
    title = {New and improved development practices in Nektar++},
    year = {2021},
    month = dec,
    series = {Nektar++ Workshop 2021},
    location = {Virtual event},
    url = {https://davidmoxey.uk/assets/talks/2021-12-13-nektarpp-workshop.pdf}
  }
  

• Recent advances in high-order mesh generation

  ICOSAHOM 2021, Minisymposium organiser, Virtual event, July 2021. BibTeX Abstract

  @booklet{icosahom-ms-2021,
    title = {Recent advances in high-order mesh generation},
    year = {2021},
    month = jul,
    series = {ICOSAHOM 2021, \textbf{Minisymposium organiser}},
    location = {Virtual event},
    url = {https://davidmoxey.uk/assets/talks/2021-07-icosahom-ms.pdf}
  }
  

  The use of high-order methods within the scientific community continues to expand, owing to their attractive numerical properties and potential to efficiently utilise modern hardware when compared against lower-order methods. However, the starting point for any high-order solver is a valid, high-quality mesh of the desired geometry, in order to provide good quality solutions to the problem at hand. At present, the generation of such meshes for complex configuations poses a significant challenge, imposing a barrier on the more widespread uptake of these methods. To provide a forum for discussion on this topic, we propose a two-session minisymposium of 8 speakers, in which we will bring together experts from academia and industry to discuss progress on the latest techniques in high-order mesh generation. The proposed talks include topics of significant interest in challenging problem areas, including boundary layer mesh generation, parallel distributed mesh curving and techniques that can be used to enable adaptive simulations in terms of mesh size (h-adaptation), element location (r-adaptation) and polynomial order (p-adaptation).
• Towards high-fidelity industrial fluid dynamics simulations at high order

  Platform for Advanced Scientific Computing, Invited speaker, Virtual event, July 2021. BibTeX Abstract

  @booklet{pasc-2021,
    title = {Towards high-fidelity industrial fluid dynamics simulations at high order},
    year = {2021},
    month = jul,
    series = {Platform for Advanced Scientific Computing, \textbf{Invited speaker}},
    location = {Virtual event},
    url = {https://davidmoxey.uk/assets/talks/2021-07-pasc.pdf}
  }
  

  As engineers look to increase the fidelity of their simulations, there is a keen interest in moving away from present industry-standard techniques such as RANS, which is implemented at the heart of most commerical software, towards transient large eddy simulations (LES), which offer increased fidelity with an associated increase in computational cost. To enable LES in reasonable timescales requires an increase in solver speed that, to date, commercial software has not been able to provide, despite dramatic increases in the calculation power of modern computational hardware. A promising route towards the goal of routine high-fidelity simulations is the use of higher-order methods, with an increased arithmetic intensity allowing them to address memory bandwidth bottlenecks present in modern hardware. The use of matrix-free methods, which avoid the generation of memory-expensive elemental matrices, alongside sum-factorisation evaluation techniques, is a central focus of the high-order community. This talk will discuss the challenges of this strategy within the setting of LES and industrial CFD problems. In particular, the complex geometries that regularly arise in industrial CFD problems typically require the use of hybrid meshes of different element types, which to date have not been well-studied from a matrix-free perspective. We present the results of a performance analysis on modern CPU and GPU architectures that demonstrates the efficacy of this scheme when applied to complex geometries.
• Tackling real-world problems with modern software

  Interdisciplinary Research Computing Seminar, Imperial College London, London, UK, January 2021. BibTeX

  @booklet{iclrse-2021,
    title = {Tackling real-world problems with modern software},
    year = {2021},
    month = jan,
    series = {Interdisciplinary Research Computing Seminar},
    location = {Imperial College London, London, UK},
    url = {https://davidmoxey.uk/assets/talks/2021-01-icl-rse.pdf}
  }
  

2020

• What is turbulence and why is it important?

  Virtual Summer School, Exeter, United Kingdom, June 2020. BibTeX

  @booklet{summerschool-2020,
    title = {What is turbulence and why is it important?},
    year = {2020},
    month = jun,
    series = {Virtual Summer School},
    location = {Exeter, United Kingdom}
  }
  

2019

• High-fidelity CFD with the Nektar++ spectral/hp element framework

  International Symposium on High-Fidelity Computational Methods and Applications, Keynote speaker, Shanghai, China, December 2019. BibTeX

  @booklet{shanghai-2019,
    title = {High-fidelity CFD with the Nektar++ spectral/\emph{hp} element framework},
    year = {2019},
    month = dec,
    series = {International Symposium on High-Fidelity Computational Methods and Applications, \textbf{Keynote speaker}},
    location = {Shanghai, China},
    url = {https://davidmoxey.uk/assets/talks/2019-12-ishfcma.pdf}
  }
  

• High-fidelity CFD with the Nektar++ spectral/hp element framework

  Coventry University, Invited speaker, Coventry, UK, October 2019. BibTeX Abstract

  @booklet{coventry-2019,
    title = {High-fidelity CFD with the Nektar++ spectral/\emph{hp} element framework},
    year = {2019},
    month = oct,
    series = {Coventry University, \textbf{Invited speaker}},
    location = {Coventry, UK},
    url = {https://davidmoxey.uk/assets/talks/2019-10-coventry.pdf}
  }
  

  Computational modelling is now firmly established as part of modern engineering design. This is especially true in fields such as aviation and turbomachinery, where the strive for increased aeronautical efficiency means that engineers are increasingly in need of high-fidelity simulations to understand the influence of even small design changes on overall aerodynamic performance. A step towards this is to consider moving away from present industry-standard techniques such as RANS, which is implemented at the heart of most commerical software, towards transient large eddy simulations (LES), which offer increased fidelity with an associated increase in computational cost. To enable LES simulations in reasonable timescales therefore requires an increase in solver speed that, to date, commercial software has not been able to provide, despite dramatic increases in the calculation power of modern computational hardware. In this talk, I will discuss how high-order methods, having been originally developed in academia some 30 years ago, can be used to overcome these issues and deliver high-fidelity LES simulations at reasonable computational cost for high-end engineering problems. I will broadly outline the formulation and capabilities of high-order methods and the spectral/hp element method in particular, as well as highlighting some of the many challenges that need to be overcome in this setting, such as stabilisation and mesh generation. One of the key issues in the use of high-order methods is their complexity in terms of their implementation, both in CFD and more generally for problems outside of fluids. I will therefore discuss their implementation in Nektar++ (www.nektar.info), an open-source framework for the spectral/hp element method, and show how this has been leveraged to perform simulations of complex, industrial geometries.
• Towards high-fidelity industrial fluid dynamics simulations at high order

  Software for Exascale Computing, Invited speaker, Dresden, Germany, October 2019. BibTeX Abstract

  @booklet{dresden-2019,
    title = {Towards high-fidelity industrial fluid dynamics simulations at high order},
    year = {2019},
    month = oct,
    series = {Software for Exascale Computing, \textbf{Invited speaker}},
    location = {Dresden, Germany},
    url = {https://davidmoxey.uk/assets/talks/2019-10-exadg.pdf}
  }
  

  Computational fluid dynamics (CFD) simulations are now a key part of the engineering design process. In fields related to aerodynamic performance such as aviation, motorsport and renewable energy, even small changes in geometry can yield large advantages. As such, engineers now require increasingly higher accuracy in their simulations. A step towards this is to consider moving away from present industry-standard techniques such as RANS, which is implemented at the heart of most commerical software, towards transient large eddy simulations (LES), which offer increased fidelity with an associated increase in computational cost. To enable LES simulations in reasonable timescales therefore requires an increase in solver speed that, to date, commercial software has not been able to provide, despite dramatic increases in the calculation power of modern computational hardware. A promising route towards the goal of routine high-fidelity simulations is the use of higher-order methods. The increased arithmetic intensity of such discretisations allows them to overcome the memory bandwidth bottlenecks present in modern many-core hardware. In particular, the use of matrix-free methods, which avoid the generation of dense local matrices, alongside efficient sum-factorisation evaluation techniques, is now a central focus of the high-order community. This talk will discuss the challenges of using such a strategy within the setting of LES and industrial CFD problems. In particular, the complex geometries that regularly arise in industrial CFD problems typically require the use of hybrid meshes of different element types, which to date have not been well-studied from a matrix-free perspective. Further to this, one of the key issues in the more widespread use of high-order methods is their implementation complexity, both in CFD and more generally for problems outside of fluids. I will therefore discuss their implementation in Nektar++ (www.nektar.info), an open-source framework for the spectral/hp element method.
• High-fidelity CFD with the Nektar++ spectral/hp element framework

  University of British Columbia, Invited speaker, Vancouver, Canada, March 2019. BibTeX Abstract

  @booklet{ubc-2019,
    title = {High-fidelity CFD with the Nektar++ spectral/\emph{hp} element framework},
    year = {2019},
    month = mar,
    series = {University of British Columbia, \textbf{Invited speaker}},
    location = {Vancouver, Canada},
    url = {https://davidmoxey.uk/assets/talks/2019-04-ubc.pdf}
  }
  

  Computational modelling is now firmly established as part of modern engineering design. This is especially true in fields such as aviation and turbomachinery, where the strive for increased aeronautical efficiency means that engineers are increasingly in need of high-fidelity simulations to understand the influence of even small design changes on overall aerodynamic performance. A step towards this is to consider moving away from present industry-standard techniques such as RANS, which is implemented at the heart of most commerical software, towards transient large eddy simulations (LES), which offer increased fidelity with an associated increase in computational cost. To enable LES simulations in reasonable timescales therefore requires an increase in solver speed that, to date, commercial software has not been able to provide, despite dramatic increases in the calculation power of modern computational hardware. In this talk, I will discuss how high-order methods, having been originally developed in academia some 30 years ago, can be used to overcome these issues and deliver high-fidelity LES simulations at reasonable computational cost for high-end engineering problems. I will broadly outline the formulation and capabilities of high-order methods and the spectral/hp element method in particular, as well as highlighting some of the many challenges that need to be overcome in this setting, such as stabilisation and mesh generation. One of the key issues in the use of high-order methods is their complexity in terms of their implementation, both in CFD and more generally for problems outside of fluids. I will therefore discuss their implementation in Nektar++ (www.nektar.info), an open-source framework for the spectral/hp element method, and show how this has been leveraged to perform simulations of complex, industrial geometries.
• High-order PDE Methods on CPU architectures with wide SIMD units

  SIAM CSE 2019, Minisymposium organiser, Spokane, Washington, USA, February 2019. BibTeX Abstract

  @booklet{siam-cse-ms-2019,
    title = {High-order PDE Methods on CPU architectures with wide SIMD units},
    year = {2019},
    month = feb,
    series = {SIAM CSE 2019, \textbf{Minisymposium organiser}},
    location = {Spokane, Washington, USA}
  }
  

  In Summer 2016 the 2nd generation Intel Xeon Phi Processor was released and since 2017 the Intel Scalable processor is available. Both are the computational heart of many current and future supercomputing installations. Examples are the DoE-machines Trinity-II, Cori-II and Theta, the NSF-machine Stampede-2, Oakforest-PACS in Japan, or Europe’s SuperMUC-NG. These processors combine the computational power of accelerator-based machines with the traditional approach of homogeneous high performance computing. From an application viewpoint, many research articles in the last years proved that high-order methods are able to the computational power of modern supercomputers. However, it is a challenging engineering problem to enable complex software packages on manycore architectures. This minisymposium brings together researchers working on efficient implementations of scalable high-order solvers. Of particular interest are applications which are known to require exascale computing resources in future, such as computational fluid dynamics, electro-magnetics and seismic simulations, as well as weather forecasting. Due to the broad spectrum of applications, this MS aims at identifying common algorithmic patterns of efficient high-order methods. Additionally, the comparison of different numerical approaches (e.g. CG vs. DG) will allow to identify best practices when leveraging Intel Xeon Phi and Intel Xeon Scalable systems at scale.
• Vectorisation for high-order simplicial elements

  SIAM CSE 2019, Spokane, Washington, USA, February 2019. BibTeX Abstract

  @booklet{siam-cse-2019,
    title = {Vectorisation for high-order simplicial elements},
    year = {2019},
    month = feb,
    series = {SIAM CSE 2019},
    location = {Spokane, Washington, USA},
    url = {https://davidmoxey.uk/assets/talks/2019-02-siamcse.pdf}
  }
  

  The use of SIMD vectorisation in combination with high-order methods is now well-established, with many development efforts now focusing on matrix-free formulations of key finite element operators, which avoid the memory bandwidth constraints of per-element matrices. In particular, attention has been drawn to how tensor products of one dimensional shape functions, when combined with the operator-reduction technique of sum-factorisation, can utilise wide SIMD units to attain near-peak performance on modern CPU architectures. So far however, only quadrilateral and hexahedral elements have been considered under this regime. Although these elements offer exceptional performance, from a practical perspective, it is difficult at best to construct all-hexahedral meshes for complex geometries. Unstructured meshes of triangles, tetrahedra and prisms therefore offer an alternative route to avoid this issue, but in the classical spectral element formulation using Lagrange interpolants, this leads to a non-tensorial expansion in shape functions, thereby losing the performance gains found by using sum-factorisation. In this talk, we demonstrate how an alternative choice of basis can be combined with vectorisation to construct an efficient matrix-free discretisation of elliptic operators for mixed element types. We present the results of a performance analysis on modern CPU architectures that demonstrates the efficacy of this scheme when applied to complex geometries.

2018

• Organiser of the International Conference on Spectral and High-Order Methods (ICOSAHOM)

  ICOSAHOM 2018, Conference organiser, London, UK, July 2018. BibTeX Abstract

  @booklet{icosahom-2018,
    title = {Organiser of the International Conference on Spectral and High-Order Methods (ICOSAHOM)},
    year = {2018},
    month = jul,
    series = {ICOSAHOM 2018, \textbf{Conference organiser}},
    location = {London, UK},
    url = {https://www.icosahom2018.org/}
  }
  

  The purpose of this conference series is to bring together researchers and practitioners with an interest in the theoretical, computational and applied aspects of high-order and spectral methods for the solution of differential equations. This conference is the leading international conference in this area. This is the 12th conference in the series and has been the most successful to date, with roughly 380 attendees and 350 presentations across 8 parallel sessions.
• Towards automatic high-order mesh generation for industrial geometries

  ICOSAHOM 2018, Minisymposium organiser, London, UK, July 2018. BibTeX Abstract

  @booklet{icosahom-talk-2018,
    title = {Towards automatic high-order mesh generation for industrial geometries},
    url = {https://davidmoxey.uk/assets/talks/2018-07-pasc.pdf},
    year = {2018},
    month = jul,
    series = {ICOSAHOM 2018, \textbf{Minisymposium organiser}},
    location = {London, UK}
  }
  

  Although high-order methods are continuing to make inroads into simulation practice, their use in industrial applications is predicated on the ability to generate valid high-order meshes. Commonly, such problems involve complex geometries, which pose several challenges for high-order mesh generation: the ability to generate sufficiently coarse and high quality linear meshes; converting these meshes to valid high-order meshes in an a posteriori manner; and the generation of boundary layers for applications involving fluid dynamics flows. In this presentation, we will outline the latest efforts in solving these problems in the high-order generator NekMesh, including GPU implementations for the efficient optimisation and correction of invalid meshes.
• Advances in high-order mesh generation

  ICOSAHOM 2018, London, UK, July 2018. BibTeX Abstract

  @booklet{icosahom-ms-2018,
    title = {Advances in high-order mesh generation},
    year = {2018},
    month = jul,
    series = {ICOSAHOM 2018},
    location = {London, UK}
  }
  

  Despite the increasing popularity of high-order methods in recent years, a significant barrier in the adoption of these methods is overcoming the challenge of generating curvilinear meshes that align with the underlying geometry. This is an important problem to overcome, since a valid mesh that accurately represents the underlying geometry is a prerequisite to running simulations and exploiting the potential of high-order methods for challenging industrial and academic problems. The generation of curved meshes is typically done in an a posteriori fashion, by first generating a coarse linear mesh and then deforming elements connected to the boundary in order to align elements to the geometry. Invariably, however, this combination results in the generation of elements that self-intersect and are therefore unsuitable for simulations. Additionally, the projection used to impose the curvature on the element may yield inaccuracies in representing the ’true’ CAD surface that defines the geometry. Recent work to solve these issues has focused on developing techniques based on solid body analogies or energy minimisations to deform the interior of the grid to accommodate boundary curvature and improve the accuracy of the surface representation. However, many challenges remain in, e.g. increasing robustness, generation of boundary layer grids and improving computational efficiency, amongst other issues. The purpose of this minisymposium is to provide a platform for researchers in the field of high-order to present the latest developments in this area and progress in addressing these issues. It will offer the opportunity discuss the latest methods related to the generation of curvilinear meshes, techniques assessing the quality and validity of generated grids, assess the application of these mesh generation techniques to real-world problems in computational engineering and fluid dynamics, and provide a means through which researchers can collaborate on new developments in the field.
• Developing methods for exascale CFD simulations at high orders

  Platform for Advanced Scientific Computing Conference, Basel, Switzerland, July 2018. BibTeX Abstract

  @booklet{pasc18-2018,
    title = {Developing methods for exascale CFD simulations at high orders},
    year = {2018},
    month = jul,
    series = {Platform for Advanced Scientific Computing Conference},
    location = {Basel, Switzerland},
    url = {https://davidmoxey.uk/assets/talks/2018-07-siamcse.pdf}
  }
  

  The established use of many-core computing hardware in current hardware, as well as its outlook to exascale computing platforms, poses a significant challenge for existing codes and numerical methods in achieving high levels of performance and scalability. In this presentation, we outline the approaches being taken in the Nektar++ spectral/hp element framework: a high-order framework that is used in a variety of fields, including the simulation of high-fidelity flow simulations for industry applications. We will present developments that aim to help improve on-node performance through modification of the underlying methods to improve data locality, as well as techniques that can be used to improve parallel scalability at high core counts.
• Recent developments in high-order mesh generation

  European Conference on Computational Fluid Dynamics, Minisymposium organiser, Glasgow, UK, June 2018. BibTeX Abstract

  @booklet{ecfd-2018,
    title = {Recent developments in high-order mesh generation},
    year = {2018},
    month = jun,
    series = {European Conference on Computational Fluid Dynamics, \textbf{Minisymposium organiser}},
    location = {Glasgow, UK},
    url = {https://davidmoxey.uk/assets/talks/2018-06-ecfd-ms.pdf}
  }
  

  The purpose of this minisymposium is to provide a platform for researchers in the field of high-order mesh generation to present their latest research. It will offer the opportunity discuss the latest methods related to the generation of curvilinear meshes, techniques assessing the quality and validity of generated grids, assess the application of these mesh generation techniques to real-world problems in computational engineering and fluid dynamics, and provide a means through which researchers can collaborate on new developments in the field.
• Spectral/hp element modelling for high fidelity simulation

  Culham Centre for Fusion Energy, Invited speaker, Culham, United Kingdom, June 2018. BibTeX

  @booklet{culham-2018,
    title = {Spectral/hp element modelling for high fidelity simulation},
    year = {2018},
    month = jun,
    series = {Culham Centre for Fusion Energy, \textbf{Invited speaker}},
    location = {Culham, United Kingdom},
    url = {https://davidmoxey.uk/assets/talks/2018-06-culham.pdf}
  }
  

2017

• Targeting the spectral/hp element method for exascale platforms

  Platform for Advanced Scientific Computing Conference, Lugano, Switzerland, June 2017. BibTeX Abstract

  @booklet{pasc17-2017,
    title = {Targeting the spectral/hp element method for exascale platforms},
    year = {2017},
    month = jun,
    series = {Platform for Advanced Scientific Computing Conference},
    location = {Lugano, Switzerland},
    url = {https://davidmoxey.uk/assets/talks/2017-06-pasc.pdf}
  }
  

  As the HPC community looks towards the use of many-core technology to enable the next generation of supercomputers and bring an exascale facility towards becoming reality, there is a need to understand how this new paradigm maps to existing codes and algorithms that can already effectively utilize current generation HPC facilities. In this presentation, we present the approaches currently being undertaken inside the Nektar++ spectral/hp element framework to tackle this challenging issue. In particular, we will examine some of the key mathematical operations in the spectral/hp formulation, which form the basis of many scientific and engineering problems, and examine how these can be grouped collectively to make more efficient use of modern hardware. We will show how this collective nature provides a route through which we can tackle the challenge of many-core hardware in our existing codebase.
• h-to-p efficiently: the use of collections with accelerators within Nektar++

  SIAM Computational Science & Engineering, Atlanta, GA, USA, February 2017. BibTeX Abstract

  @booklet{siam-2017,
    title = {{$h$-to-$p$ efficiently: the use of collections with accelerators within Nektar++}},
    year = {2017},
    month = feb,
    series = {SIAM Computational Science \& Engineering},
    location = {Atlanta, GA, USA},
    url = {https://davidmoxey.uk/assets/talks/2017-02-siamcse.pdf}
  }
  

  As the HPC community looks towards the use of many-core technology to enable the next generation of supercomputers, there is a need to understand how this new paradigm maps to existing codes and algorithms that can already effectively utilise current generation HPC facilities. In this presentation, we present the approaches currently being undertaken inside the Nektar++ spectral/hp element framework to tackle this challenging issue. Nektar++ provides solver developers with a toolbox of techniques that can be used to employ the use of high-order spectral elements for various solvers, with application areas including incompressible and compressible fluid dynamics, cardiac electrophysiology and advection-diffusion-reaction problems. Spectral elements provide increased compactness and memory efficiency over the more traditionally-used lower-order methods, meaning they have far greater potential to exploit many-core processors. The presentation will demonstrate our existing techniques for decreasing runtimes across a range of polynomial orders, by exploiting the mathematical framework of the method to admit a number of different collective operators that are key to the method. We will show how this collective nature provides a route through which we can tackle the challenge of many-core hardware in our existing codebase.

2016

• NekMesh: an open-source high-order mesh generator

  DiPaRT 2016, CFMS, Bristol and Bath Science Park, UK, November 2016. BibTeX Abstract

  @booklet{dipart-2016,
    title = {{NekMesh: an open-source high-order mesh generator}},
    year = {2016},
    month = nov,
    series = {DiPaRT 2016},
    location = {CFMS, Bristol and Bath Science Park, UK},
    url = {https://davidmoxey.uk/assets/talks/2016-11-dipart.pdf}
  }
  

  The generation of sufficiently high quality unstructured high-order meshes still remains a significant obstacle in the adoption of high-order methods. We will present an overview of the latest algorithmic developments for the generation of high-order meshes and their implementation in the open-source mesh generator NekMesh which is part of the suite of high-order solvers Nektar++. The focal point will be the presentation of an efficient variational framework for the generation of curvilinear meshes which encompasses a number of existing strategies. We will describe the underlying theoretical bases and discuss an efficient multi-threading parallel implementation. Using complex aerodynamical configurations, we will demonstrate how the proposed framework can be used for both mesh quality optimisation and untangling of invalid meshes.
• Optimising the performance of the spectral/hp element method with collective linear algebra operations

  PRISM Workshop on Embracing Accelerators, Imperial College London, London, UK, April 2016. BibTeX

  @booklet{prism-2016,
    title = {{Optimising the performance of the spectral/hp element method with collective linear algebra operations}},
    year = {2016},
    month = apr,
    series = {PRISM Workshop on Embracing Accelerators},
    location = {Imperial College London, London, UK},
    url = {https://davidmoxey.uk/assets/talks/2016-04-prism.pdf}
  }
  

2015

• High-order mesh generation for CFD solvers

  DiPaRT 2015, CFMS, Bristol and Bath Science Park, UK, November 2015. BibTeX

  @booklet{dipart-2015,
    title = {{High-order mesh generation for CFD solvers}},
    year = {2015},
    month = nov,
    series = {DiPaRT 2015},
    location = {CFMS, Bristol and Bath Science Park, UK},
    url = {https://davidmoxey.uk/assets/talks/2015-11-dipart.pdf}
  }
  

• Pre- and post-processing in Nektar++

  Nektar++ Workshop 2015, Imperial College London, London, UK, July 2015. BibTeX

  @booklet{nektarpp-2015,
    title = {{Pre- and post-processing in Nektar++}},
    year = {2015},
    month = jul,
    series = {Nektar++ Workshop 2015},
    location = {Imperial College London, London, UK},
    url = {https://davidmoxey.uk/assets/talks/2015-07-nekppworkshop.pdf}
  }
  

• High- and low-order finite element software for the future

  SIAM Computational Science & Engineering, Minisymposium organiser, Salt Lake City, Utah, March 2015. BibTeX Abstract

  @booklet{cse-2015a,
    title = {{High- and low-order finite element software for the future}},
    year = {2015},
    month = mar,
    series = {SIAM Computational Science \& Engineering, \textbf{Minisymposium organiser}},
    location = {Salt Lake City, Utah},
    url = {https://davidmoxey.uk/assets/talks/2015-03-siam-ms.pdf}
  }
  

  As scientific problems become larger, computational platforms become more diverse and the complexity of finite element software increases, it is essential to develop software in a sustainable way. The role of software design and the need to effectively manage the development process is therefore more important than ever before. This minisymposium will discuss experiences of how high- and low-order FEM software can be designed, developed and maintained to achieve maximum performance while remaining robust, rigorously tested and able to grow and adapt with the changing needs of the research environment, improvements in the methods and the evolving hardware landscape.
• Applications of the spectral/hp element method to complex flow geometries

  SIAM Computational Science & Engineering, Salt Lake City, Utah, March 2015. BibTeX Abstract

  @booklet{cse-2015b,
    title = {Applications of the spectral/hp element method to complex flow geometries},
    year = {2015},
    month = mar,
    series = {SIAM Computational Science \& Engineering},
    location = {Salt Lake City, Utah},
    url = {https://davidmoxey.uk/assets/talks/2015-03-siam-les.pdf}
  }
  

  As industrial requirements evolve to require both transient and scale-resolving capabilities, the use of under-resolved DNS and implicit LES methods is needed to capture the essential flow features. In this talk, we give some examples of industrially-relevant simulations, and highlight some of the challenges that arise when performing simulations in complex three-dimensional geometries. Furthermore we demonstrate how the spectral/hp element method combined with appropriate stabilisation and discretisations can resolve flow features in these complex domains.
• Spectral/hp element modelling in Nektar++

  SIAM Computational Science & Engineering, Salt Lake City, Utah, March 2015. BibTeX Abstract

  @booklet{cse-2015c,
    title = {Spectral/hp element modelling in Nektar++},
    year = {2015},
    month = mar,
    series = {SIAM Computational Science \& Engineering},
    location = {Salt Lake City, Utah},
    url = {https://davidmoxey.uk/assets/talks/2015-03-siam-highlevel.pdf}
  }
  

  In this talk we will highlight the high-level aspects of the Nektar++ high order finite element framework, which enables rapid development of high-performance parallel solvers. Using a straightforward linear PDE as an illustrative example, we will demonstrate how the library can be utilised at a variety of levels to fit the requirements of the end-user, and how simulation parameters such as the time-stepping scheme can be changed without detailed technical knowledge of the underlying methods.
• h-to-p efficiently: a Nektar++ update on comparisons of CG and HDG

  SIAM Computational Science & Engineering, Salt Lake City, Utah, March 2015. BibTeX Abstract

  @booklet{cse-2015d,
    title = {h-to-p efficiently: a Nektar++ update on comparisons of CG and HDG},
    year = {2015},
    month = mar,
    series = {SIAM Computational Science \& Engineering},
    location = {Salt Lake City, Utah},
    url = {https://davidmoxey.uk/assets/talks/2015-03-siam-hdg.pdf}
  }
  

  Since the inception of discontinuous Galerkin (DG) methods for elliptic problems, there has existed a question of whether DG methods can be made more computationally efficient than continuous Galerkin (CG) methods. Fewer degrees of freedom, approximation properties for elliptic problems together with the number of optimization techniques, such as static condensation, available within the CG framework made it challenging for DG methods to be competitive until recently. However, with the introduction of a static-condensation-amenable DG method, the hybridizable discontinuous Galerkin (HDG) method, it has become possible to perform a realistic comparison of CG and HDG methods when applied to elliptic problems. In this talk, we focus on embedded manifolds, which are considered a valid approximation for many scientific problems ranging from the shallow water equations to geophysics. We describe a comparison between a CG and an HDG numerical discretiztion in 2D, 3D and of an embedded two-dimensional manifold using high-order spectral/hp elements.

2014

• A thermo-elastic analogy for high-order curvilinear meshing with control of mesh validity and quality

  21st International Meshing Roundtable, London, October 2014. BibTeX Abstract

  @booklet{imr-2014,
    title = {{A thermo-elastic analogy for high-order curvilinear meshing with control of mesh validity and quality}},
    year = {2014},
    month = oct,
    series = {21st International Meshing Roundtable},
    location = {London},
    url = {https://davidmoxey.uk/assets/talks/2014-10-imr.pdf}
  }
  

  In recent years, techniques for the generation of high-order curvilinear mesh have frequently adopted mesh deformation procedures to project the curvature of the surface onto the mesh, thereby introducing curvature into the interior of the domain and lessening the occurrence of self-intersecting elements. In this article, we propose an extension of this approach whereby thermal stress terms are incorporated into the state equation to provide control on the validity and quality of the mesh, thereby adding an extra degree of robustness which is lacking in current approaches.
• Utilising high-order direct numerical simulation for transient aeronautics problems

  11th World Congress on Computational Mechanics, Barcelona, July 2014. BibTeX Abstract

  @booklet{wccm-2014,
    title = {Utilising high-order direct numerical simulation for transient aeronautics problems},
    year = {2014},
    month = jul,
    series = {11th World Congress on Computational Mechanics},
    location = {Barcelona},
    url = {https://davidmoxey.uk/assets/talks/2014-07-wccm.pdf}
  }
  

  https://davidmoxey.uk/assets/talks/2014-07-wccm-abs.pdf
• Curvilinear mesh generation and adaption

  ICOSAHOM 2014, Minisymposium organiser, Salt Lake City, June 2014. BibTeX Abstract

  @booklet{icosahom-2014a,
    title = {Curvilinear mesh generation and adaption},
    year = {2014},
    month = jun,
    series = {ICOSAHOM 2014, \textbf{Minisymposium organiser}},
    location = {Salt Lake City},
    url = {https://davidmoxey.uk/assets/talks/2014-06-icosahom-ms.pdf}
  }
  

  https://davidmoxey.uk/assets/talks/2014-06-icosahom-ms.pdf
• An isoparametric approach to high-order curvilinear boundary-layer meshing

  ICOSAHOM 2014, Salt Lake City, June 2014. BibTeX Abstract

  @booklet{icosahom-2014b,
    title = {An isoparametric approach to high-order curvilinear boundary-layer meshing},
    year = {2014},
    month = jun,
    series = {ICOSAHOM 2014},
    location = {Salt Lake City},
    url = {https://davidmoxey.uk/assets/talks/2014-06-icosahom-talk.pdf}
  }
  

  https://davidmoxey.uk/assets/talks/2014-06-icosahom-talk-abs.pdf
• Nektar++: a high-order finite element framework

  Invited talk under R. Moser, Institute for Computational Engineering and Sciences, University of Texas at Austin, June 2014. BibTeX Abstract

  @booklet{ices-2014,
    title = {Nektar++: a high-order finite element framework},
    year = {2014},
    month = jun,
    series = {\textbf{Invited talk under R. Moser}},
    location = {Institute for Computational Engineering and Sciences, University of Texas at Austin},
    url = {https://davidmoxey.uk/assets/talks/2014-06-ices.pdf}
  }
  

  In recent years, interest in using high-order finite element methods has increased dramatically in both academic and industrial fields alike. This class of methods offers both attractive dispersion properties and the potential to achieve highly accurate solutions at a lower computational cost in comparison to equivalently resolved low-order methods. One of the biggest hurdles to more widespread adoption of high-order methods is the additional complexity of implementation compared to low-order discretisations. There are a large number of implementation-related questions one may ask, such as: should one use continuous or discontinuous formulations, or implicit versus explicit timestepping? What basis functions should one use? What is the ‘most efficient’ polynomial order? There are also a number of seemingly mundane yet still challenging problems, such as developing techniques for the robust generation of curvilinear meshes which align with a given domain. Consequently, high-order codes are usually written for specific problems, and the reuse of code is low. New entrants to the high-order field therefore have a steep learning curve when trying to write new solvers for their particular problem. In this presentation, we give an overview of the Nektar++ framework, which aims to tackle these problems by providing a common platform for high-order finite element methods, and enables the development of software for a number of application areas including compressible and incompressible fluid dynamics, biomechanics and cardiac electrophysiology. We discuss how the design of our framework allows for a flexible approach to high-order solver development, and how this environment can help to investigate some of the implementation choices outlined above. We motivate this discussion by considering a specific application of these methods to high Reynolds number flow over complex three-dimensional aeronautical geometries, in which we highlight some of the numerical stabilisation and high-order meshing strategies which are needed to perform a successful simulation.
• Applications of the spectral/hp element method to CFD

  British Applied Mathematics Colloquium, Cardiff University, April 2014. BibTeX Abstract

  @booklet{bamc-2014,
    title = {Applications of the spectral/hp element method to CFD},
    year = {2014},
    month = apr,
    series = {British Applied Mathematics Colloquium},
    location = {Cardiff University},
    url = {https://davidmoxey.uk/assets/talks/2014-03-bamc.pdf}
  }
  

  The spectral/hp element method is an extension of the classical finite element method, which utilises a tensor product of high-order polynomials on two- and three-dimensional elements in order to obtain highly accurate spatial resolution within complex geometries. Such methods have in recent years become increasingly popular within both academia and industry, since they offer the potential to obtain highly accurate solutions at a lower computational cost than equivalent low-order finite element methods and also have attractive dispersion properties. In this presentation, we will discuss the application of the spectral/hp element method to a number of problems in the field of computational fluid dynamics. We will discuss some of the challenges which arise naturally within this application area, including the development techniques for the generation of valid curvilinear meshes which resolve the dynamics within very fine boundary layers, and how stabilisation techniques can be used in order to utilise these methods for industrially relevant aeronautics problems.

2013

• Investigation of flow over a 2D periodic hill

  2nd International Workshop on high-order CFD methods, Cologne, May 2013. BibTeX Abstract

  @booklet{how-2013,
    title = {Investigation of flow over a 2D periodic hill},
    year = {2013},
    month = may,
    series = {2nd International Workshop on high-order CFD methods},
    location = {Cologne},
    url = {https://davidmoxey.uk/assets/talks/2013-05-how.pdf}
  }
  

  https://davidmoxey.uk/assets/talks/2013-05-how-abs.pdf

2012

• High-order spectral/hp methods for aerodynamic applications

  European Congress on Computational Methods in Applied Sciences and Engineering, University of Vienna, September 2012. BibTeX Abstract

  @booklet{eccomas-2012,
    title = {High-order spectral/hp methods for aerodynamic applications},
    year = {2012},
    month = sep,
    series = {European Congress on Computational Methods in Applied Sciences and Engineering},
    location = {University of Vienna},
    url = {https://davidmoxey.uk/assets/talks/2012-09-eccomas.pdf}
  }
  

  https://davidmoxey.uk/assets/talks/2012-09-eccomas-abs.pdf

2011

• Onset of turbulence in pipe flow

  British Applied Mathematics Colloquium, University of Birmingham, April 2011. BibTeX Abstract

  @booklet{bamc-2011,
    title = {Onset of turbulence in pipe flow},
    year = {2011},
    month = apr,
    series = {British Applied Mathematics Colloquium},
    location = {University of Birmingham},
    url = {https://davidmoxey.uk/assets/talks/2011-04-bamc.pdf}
  }
  

  One of the most fundamental topics in fluid dynamics is the transition to turbulence in shear flows. Pipe flow provides an ideal geometry in which to study transition, since it is easily modelled by computer and can be well controlled in the laboratory, and yet the underlying dynamics are incredibly complex. The seminal works of Reynolds revealed that the transition depends on the now ubiqutous Reynolds number (Re); however, after being investigated for over 125 years, the question of a finding a critical Re below which turbulence cannot be sustained is still an open problem. Recently, a detailed statistical survey utilising both numerical and experimenal work has revealed that puffs – the localised structures found in the intermittent transitional regime – have finite lifetime regardless of Re. Whilst this may seem to suggest that all turbulence is perhaps transient, the decay process is entirely reliant on the temporal aspects of the flow and does not consider any spatial coupling. In this talk, we apply the same statistical techniques to investigate the phenomenon of puff splitting, in which more complex spatial dynamics are naturally incorporated. We show that this process is inherently stochastic and, in a similar fashion to decay studies, demonstrate that the process remains memory-less over a range of transitional Re. Using samples from both numerical and experimental studies, we construct the distribution governing the mean splitting time τas a function of Re. By comparing the distributions of both splitting and decay, we obtain a crossing point of Re_c ≈2036. Akin to other stochastic problems such as directed bond percolation, the transition in pipe flow then can be seen as two competing forces of puff decay and splitting. Below Re_c, a single puff will with all likelihood decay; above Re_c, splitting becomes the more probable outcome and turbulence ceases to be transient.
• Onset of turbulence in pipe flow

  Postgraduate Seminar Series, University of Warwick, March 2011. BibTeX Abstract

  @booklet{pgrad-2011,
    title = {Onset of turbulence in pipe flow},
    year = {2011},
    month = mar,
    series = {Postgraduate Seminar Series},
    location = {University of Warwick},
    url = {https://davidmoxey.uk/assets/talks/2011-03-postgrad.pdf}
  }
  

  One of the most fundamentally important topics in fluid dynamics is understanding the transition to turbulence in shear flows. Pipe flow provides an ideal geometry in which to study transition, since it is easily modelled by computer and can be well-controlled in the laboratory, yet the underlying dynamics remain incredibly complex. The seminal works of Reynolds revealed that the transition depends on the now ubiqutous Reynolds number (Re); however, after being investigated for over 125 years, the question of a finding a critical Re below which turbulence cannot be sustained is still an open problem. Thus far, much effort has been exerted on investigating puffs – localised pockets of turbulence found in the intermittent transitional regime. Recently, a detailed statistical survey revealed that puffs have finite lifetime regardless of Re. Whilst this may seem to suggest that all turbulence is transient, the decay process is entirely reliant on the temporal aspects of the flow and does not consider any spatial coupling. In this talk, I will introduce some basic numerical methods required to simulate the Navier-Stokes equations. Using these methods, we apply the same statistical techniques to obtain a distribution for the phenomenon of puff splitting, in which more complex spatial dynamics are naturally incorporated. By comparing this distribution to that of decay, we are able to finally obtain a value for the critical Reynolds number.

2010

• Investigating pipe flow using a spectral element method

  CSC@Lunch Seminar Series, University of Warwick, June 2010. BibTeX Abstract

  @booklet{csc-2010,
    title = {Investigating pipe flow using a spectral element method},
    year = {2010},
    month = jun,
    series = {CSC@Lunch Seminar Series},
    location = {University of Warwick},
    url = {https://davidmoxey.uk/assets/talks/2010-06-csc.pdf}
  }
  

  In this talk I will discuss the application of a spectral element method to the problem of fluid flow through a pipe, and briefly discuss some results obtained through direct numerical simulation of the underlying equations.

2009

• Numerical studies of the transition to turbulence in long pipes

  EPSRC Symposium Workshop on CFD, University of Warwick, September 2009. BibTeX

  @booklet{epsrc-2009,
    title = {Numerical studies of the transition to turbulence in long pipes},
    year = {2009},
    month = sep,
    series = {EPSRC Symposium Workshop on CFD},
    location = {University of Warwick},
    url = {https://davidmoxey.uk/assets/talks/2009-09-cfd.pdf}
  }
  

• A computational investigation of pipe flow at transitional Reynolds numbers

  British Applied Mathematics Colloquium, Nottingham University, April 2009. BibTeX Abstract

  @booklet{bamc-2009,
    title = {A computational investigation of pipe flow at transitional Reynolds numbers},
    year = {2009},
    month = apr,
    series = {British Applied Mathematics Colloquium},
    location = {Nottingham University},
    url = {https://davidmoxey.uk/assets/talks/2009-04-bamc.pdf}
  }
  

  Pipe flow is an intruiging problem in the field of fluid dynamics, and the understanding of transitional behaviour between turbulent and laminar flow remains an open question. Recently, interest has been re-ignited in the study of puffs, which are thought to have some connection with recently discovered travelling-wave solutions. Through some unknown mechanism, these turbulent structures are able to co-exist with a laminar solution and hence are of particular interest to those studying transition. Motivated by this, we have undertaken a detailed numerical simulation of the pipe flow problem at transitional Reynolds numbers. In particular, we study the re-laminarisation of a uniformly turbulent initial condition as the Reynolds number is slowly reduced, with a significant focus on the region 1900 ≤Re ≤2200. To this end, we consider several pipes from length L=25D to L=150D which are periodic in the streamwise direction and driven using a constant volumetric flux. The Navier-Stokes equations are solved independently in each using a highly accurate spectral-element/Fourier pseudo-spectral method. We report on the previously unseen spontaneous appearance of both multiple and single-puff states as the Re is reduced below 2100. Additionally, we have found this behaviour occurs in both L=50D and L=150D simulations. We conclude with some analysis of the puff states.
• A numerical study of the transition from turbulence in pipe flow

  Postgraduate Seminar Series, University of Warwick, January 2009. BibTeX Abstract

  @booklet{pgrad-2009,
    title = {A numerical study of the transition from turbulence in pipe flow},
    year = {2009},
    month = jan,
    series = {Postgraduate Seminar Series},
    location = {University of Warwick},
    url = {https://davidmoxey.uk/assets/talks/2009-01-postgrad.pdf}
  }
  

  Pipe flow is one of the most puzzling problems in fluid dynamics; whilst the laminar flow is most likely linearly stable, it easily becomes turbulent when exposed to small perturbations. Originally investigated by Reynolds in the 19th Century, many of the questions around this relatively simple problem still remain unanswered. One such question is the nature of the transition from a turbulent state back to a laminar flow. We have performed a numerical study of this problem, investigating the different states found in the Navier-Stokes equations during the transitional period. A short introduction to the pipe flow problem is given, then the corresponding algorithms are described before presenting some of the numerical results.

2008

• A numerical investigation of transition from turbulent to laminar flow in long pipes

  7th European Fluid Mechanics Conference, University of Manchester, September 2008. BibTeX Abstract

  @booklet{efmc7-2008,
    title = {A numerical investigation of transition from turbulent to laminar flow in long pipes},
    year = {2008},
    month = sep,
    series = {7th European Fluid Mechanics Conference},
    location = {University of Manchester},
    url = {https://davidmoxey.uk/assets/talks/2008-09-euromech.pdf}
  }
  

  https://davidmoxey.uk/assets/talks/2008-09-euromech-abs.pdf