[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84206-en":3,"doc-seo-84206-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84206,962075114765,"Quinn","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","A framework for generating nonconforming triangular meshes with multiple discretization layers","A framework generates nonconforming triangular meshes with multiple discretization layers using structural properties of meshes produced by a frontal Delaunay algorithm with uniform element size. The meshes feature an unstructured boundary layer and a bulk region resembling a regular triangular lattice. The bulk can be coarsened by grouping elements into connected composite elements, repeated to yield multiple layers. For complex geometries, the method builds composite multidomain meshes with layers per subdomain and supports postprocessing for refinement, coarsening, and AMR integration.","arXiv :2607 .07242v1 [math .NA] 8 Jul 2026  \nA framework for generating nonconforming triangular meshes with multiple discretization layers  \nI. L. Semenov and M. M. Becker  \nLeibniz Institute for Plasma Science and Technology, Felix-Hausdorff-Str. 2, Greifswald,  \n17489, Germany.  \nAbstract  \nWe present a framework for generating nonconforming triangular meshes with multiple discretization layers. The framework exploits characteristic structural properties of meshes produced by a frontal Delaunay algorithm with uniform element size. The bulk region of such meshes exhibits a structured pattern resembling a regular triangular lattice. Owing to this structure, the bulk region can be coarsened by grouping elements into connected subsets of larger composite elements. When applied repeatedly, this procedure produces a mesh with multiple discretization layers. For complex geometries, the framework can be used to create composite multidomain meshes, where multiple discretization layers are generated within each subdomain. We present examples of meshes generated by the proposed framework and discuss postprocessing strategies for their refinement and coarsening. The resulting meshes are well suited for the application of adaptive mesh refinement techniques. The proposed framework can be readily integrated with existing mesh generators and finite-element solvers that support nonconforming triangular meshes.  \nKeywords: nonconforming triangular meshes, mesh generation, frontal Delaunay algorithm, adaptive mesh refinement  \n1 Introduction  \nNonconforming (irregular) meshes are meshes in which elements do not necessarily share complete common edges or faces. Such meshes are typically used in the context of adaptive mesh refinement (AMR) and are supported by most modern finiteelement solvers [1–4] .  \nThe most common form of nonconforming AMR is implemented on logically structured meshes using hierarchical data structures such as quadtrees or octrees [5, 6] . On unstructured meshes, nonconforming AMR can be realized using the red-refinement approach [7–9], in which elements of the background mesh are subdivided into subelements that can later be coarsened. This  \napproach, however, is less efficient than in the structured case when the background mesh does not possess a suitable hierarchy of discretization layers. Creating such layers therefore requires the development of new algorithmic approaches that operate in fully unstructured settings.  \nNonconforming meshes also provide a flexible alternative to nonuniform conforming meshes for resolving geometrically complex regions of the computational domain. In this regard, a transition from logically structured to unstructured settings for nonconforming mesh generation offers greater flexibility as well.  \nIn an unstructured setting, generating a nonconforming mesh with multiple discretization layers involves two key aspects. First, it is necessary  \nto identify an appropriate data structure capable of representing nonconforming element interfaces within a mesh. Such a data structure should be sufficiently flexible to allow the straightforward implementation of basic combinatorial operationson mesh elements. Second, it is necessary to provide an approach for constructing a hierarchy of discretization layers within the mesh that resolves the geometry of the computational domain while aiming to minimize the total number of mesh elements. Such a discretization can then serve as a basis for AMR techniques.  \nIn this paper, we address the aforementioned aspects in the context of triangular meshes. We present a framework for generating nonconforming triangular meshes with multiple discretization layers in domains with relatively simple geometry. The proposed framework builds on the following observation. The application of a frontal Delaunay algorithm [10] to triangular mesh generation with a uniform element size results in meshes exhibiting a characteristic two-region structure. The first region is an","cbCaikIVBijjUYa7","https://ap.wps.com/l/cbCaikIVBijjUYa7","pdf",1528735,3,1,18,"English","en",105,"# Introduction\n## Nonconforming meshes and AMR background\n## Two key aspects for unstructured layer hierarchy\n## Core observation from frontal Delaunay meshes\n## Representation of nonconforming interfaces\n## Scope and contributions","[{\"question\":\"What problem does the framework address?\",\"answer\":\"It addresses how to generate nonconforming triangular meshes that contain multiple discretization layers in fully unstructured settings, enabling efficient adaptive mesh refinement.\"},{\"question\":\"How does the framework produce multiple discretization layers?\",\"answer\":\"It starts from meshes produced by a frontal Delaunay algorithm with uniform element size, coarsens the bulk region by grouping elements into connected composite elements, and repeats the coarsening procedure to create multiple layers.\"},{\"question\":\"How are nonconforming interfaces represented for implementation?\",\"answer\":\"Nonconforming element interfaces are represented as zero-area triangles, so the mesh remains conforming in a combinatorial sense while treating nonconformity as a limiting case of conforming meshes geometrically.\"}]",1784193944,45,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"a-framework-for-generating-nonconforming-triangular-meshes-with-multiple-discretization-layers","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/a-framework-for-generating-nonconforming-triangular-meshes-with-multiple-discretization-layers/84206/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem does the framework address?","Question",{"text":75,"@type":76},"It addresses how to generate nonconforming triangular meshes that contain multiple discretization layers in fully unstructured settings, enabling efficient adaptive mesh refinement.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the framework produce multiple discretization layers?",{"text":80,"@type":76},"It starts from meshes produced by a frontal Delaunay algorithm with uniform element size, coarsens the bulk region by grouping elements into connected composite elements, and repeats the coarsening procedure to create multiple layers.",{"name":82,"@type":73,"acceptedAnswer":83},"How are nonconforming interfaces represented for implementation?",{"text":84,"@type":76},"Nonconforming element interfaces are represented as zero-area triangles, so the mesh remains conforming in a combinatorial sense while treating nonconformity as a limiting case of conforming meshes 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