[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-278599-105":53,"doc-detail-278599-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","algorithm-3-iteration-of-a-stencil-function-over-an-extruded-mesh","Algorithm 3 Iteration of a stencil function over an extruded mesh","","Algorithm 3 specifies how to iterate a stencil function across degrees of freedom on an extruded mesh. The procedure iterates over a base mesh entity set V, then over vertical iteration entities determined by the vertical dimension d2 and the number of vertical intervals. For each entity and vertical level, it applies the stencil function S to the field f at selected degrees of freedom, and performs updates by combining local dof values with a vertical offset offsetS;fs per function space fs.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/algorithm-3-iteration-of-a-stencil-function-over-an-extruded-mesh/278599/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/algorithm-3-iteration-of-a-stencil-function-over-an-extruded-mesh/278599.png","ImageObject",442,249,{"name":88,"@type":89},"Marry","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-09-20","2026-09-15",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What does Algorithm 3 iterate over on the extruded mesh?","Question",{"text":108,"@type":109},"It iterates over base mesh entities in V and, for each, over vertical levels defined by d2 and the number of vertical intervals.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How is the stencil function S applied to the field f?",{"text":113,"@type":109},"For each selected set of degrees of freedom, S is evaluated using the corresponding components of f.",{"name":115,"@type":106,"acceptedAnswer":116},"What role does offsetS;fs play in updating degrees of freedom?",{"text":117,"@type":109},"It provides a vertical offset for function space fs given stencil S, which is added to dof values during the update step.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},278599,1789510953,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":125,"read_time":4},5909892079670,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","| Algorithm 3 Iteration of a stencil function over an extruded mesh |\n| --- |\n| Require: V: iteration set of base mesh entities\u003Cbr>Require: d2 : the dimension of vertical iteration entities\u003Cbr>Require: 􀀕 : the number of vertical intervals\u003Cbr>Require: S: stencil function to be applied to the degrees of freedom of field f\u003Cbr>Require: L fs: set of explicit lists of degrees of freedom for function space fs\u003Cbr>Require: offsetS;fs: the vertical offset for function space fs given stencil S\u003Cbr>for v in V do\u003Cbr>.dof 0 ; dof 1;:::;dofk􀀀1/ Lfs.v/\u003Cbr>for l in f0 ; 1;:::;􀀕 􀀀 d2g do\u003Cbr>S.f.dof 0/;f.dof 1/;:::;f.dofk􀀀1//\u003Cbr>for j in f0 ; 1;:::;k 􀀀 1g do\u003Cbr>dof j dof j C offsetS;fs.j/\u003Cbr>end for\u003Cbr>end for\u003Cbr>end for |","cbCairl5wrLChKNK","https://ap.wps.com/l/cbCairl5wrLChKNK","pdf",83711,"English","# Algorithm 3\n## Iteration sets and parameters\n## Nested iteration over entities and vertical intervals\n## Stencil application and degree-of-freedom update","[{\"question\":\"What does Algorithm 3 iterate over on the extruded mesh?\",\"answer\":\"It iterates over base mesh entities in V and, for each, over vertical levels defined by d2 and the number of vertical intervals.\"},{\"question\":\"How is the stencil function S applied to the field f?\",\"answer\":\"For each selected set of degrees of freedom, S is evaluated using the corresponding components of f.\"},{\"question\":\"What role does offsetS;fs play in updating degrees of freedom?\",\"answer\":\"It provides a vertical offset for function space fs given stencil S, which is added to dof values during the update step.\"}]","Algorithm 3 Iteration of a stencil function over an extruded mesh | PDF"]