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@@ -55,8 +55,8 @@ The features of SEMs are now well-established. Like low order finite element met
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What some are now calling “classical” spectral element methods use tensor product bases on quadrilateral or hexahedral meshes. These bases lead to very efficient implementations and have high order quadratures that can be used to approximate the integrals found in weak forms of the equations. Of the widely available spectral element packages, SemTex, Sem2dPack, Nek5000, FLEXI, FLUXO, Trixi.jl, and HORSES3D primarily or exclusively use quadrilateral and hexahedral meshes.
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Unfortunately, unstructured meshes for quad/hex elements are difficult to generate even for low order finite elements [@Bommes:2013lc].
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The advantages not withstanding, a major impediment to the application of SEMs has been the availability of appropriate general purpose mesh generation software that can generate elements of arbitrary order, especially in open-source form.
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<!-- A survey of the literature, practitioners, and user manuals for available spectral element software packages highlights these difficulties. In 2002 Sherwin and Peiro [@Sherwin:2002vx] wrote: "The development of robust unstructured high-order methods is currently limited by the inability to consistently generate valid computational meshes for complex geometries without user intervention." This has remained true particularly for quadrilateral and hexahedral meshes.-->
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The advantages not withstanding, a major impediment to the application of SEMs has been the availability of appropriate general purpose mesh generation software that can generate elements of arbitrary order, especially in open-source form.
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In 2002 Sherwin and Peiro [@Sherwin:2002vx] wrote: "The development of robust unstructured high-order methods is currently limited by the inability to consistently generate valid computational meshes for complex geometries without user intervention." This has remained true particularly for quadrilateral and hexahedral meshes.
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For these reasons, HOHQMesh was developed to generate all-quadrilateral and extruded hexahedral meshes suitable for use with spectral element methods. HOHQMesh is a direct quadrilateral mesher, which generates quadrilateral elements by the subdivision method of Schneiders [@schneiders2000algorithms] rather than indirectly from a triangular mesh or by curving a low order mesh. It also sizes and curves the elements based on the length scales in the model, rather than try to modify an existing low order mesh.
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# Features
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The preprocessor HOPR [@HOPR] can also read and modify quad meshes generated by HOHQMesh.
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HOHQMesh can be used with the graphical front end HOHQMesh.jl [@kopriva2024hohqmeshjl]
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HOHQMesh.jl is a wrapper package written in the Julia programming language [@bezanson2017julia].
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With it one can use the mesh generator directly in Julia, without having to install HOHQMesh or any
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of its dependencies manually. HOHQMesh.jl augments HOHQMesh with interactive functionality that
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gives a user the ability to create, visualize, and generate high-order meshes. It further allows one
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to seamlessly integrate meshes generated by HOHQMesh into a Julia-based simulation workflow. Like
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HOHQMesh itself, HOHQMesh.jl is available on Linux, macOS, and Windows.
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HOHQMesh can be used with the graphical front end HOHQMesh.jl [@kopriva2024hohqmeshjl].
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It is a wrapper package that augments HOHQMesh with interactive functionality
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giving a user the ability to create and visualize the meshes without the need to compile from source.
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