[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-202624-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-202624-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","albanyfelix-parallel-scalable-robust-finite-element-first-order-stokes-approximation-ice-sheet-solver","Albany/FELIX - parallel scalable robust finite element first-order Stokes approximation ice sheet solver","","This paper presents Albany/FELIX, a new parallel, scalable, and robust finite element solver for the first-order Stokes momentum balance equations governing ice flow. Built with a component-based code construction approach using modular Trilinos libraries, abstract interfaces, and template-based generic programming, the solver enables access to advanced analysis capabilities. The study reviews governing equations and boundary conditions, details discretization methods and implementation, and reports verification using manufactured-solution-based test cases and canonical benchmarks, followed by accuracy and convergence analyses on Greenland geometry. Scalability is further supported through a semi-coarsening algebraic multilevel preconditioner.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/albanyfelix-parallel-scalable-robust-finite-element-first-order-stokes-approximation-ice-sheet-solver/202624/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/albanyfelix-parallel-scalable-robust-finite-element-first-order-stokes-approximation-ice-sheet-solver/202624.png","ImageObject",300,407,{"name":42,"@type":43},"Oliver","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-09-04",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",14,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What problem does Albany/FELIX solve in ice-sheet modeling?","Question",{"text":63,"@type":64},"Albany/FELIX solves the first-order Stokes momentum balance equations for ice flow using a finite element approach.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How is the Albany/FELIX code constructed to support scalability and robustness?",{"text":68,"@type":64},"It is built using a component-based approach that combines mature, modular Trilinos libraries via abstract interfaces and template-based generic programming.",{"name":70,"@type":61,"acceptedAnswer":71},"What verification and benchmarking methods are used to assess accuracy?",{"text":72,"@type":64},"The paper reports verification with manufactured-solution-derived 2-D test cases and uses canonical ice-sheet modeling benchmarks.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},202624,1788549384,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":99,"preview_page_count":4},8796095461610,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Geosci. Model Dev., 8, 1–24, 2015  \n[www.geosci-model-dev.net/8/1/2015/](www.geosci-model-dev.net/8/1/2015/)[ ](www.geosci-model-dev.net/8/1/2015/)[doi:10.5194/gmd-8-1-2015](doi:10.5194/gmd-8-1-2015)  \n© Author(s) 2015 . CC Attribution 3.0 License.  \nAlbany/FELIX: a parallel, scalable and robust, finite element,first-order Stokes approximation ice sheet solver built for advanced analysis  \nI. K. Tezaur 1 , M. Perego2 , A. G. Salinger2 , R. S. Tuminaro2 , and S. F. Price3  \n1 Quantitative Modeling and Analysis Department, Sandia National Laboratories,  \nP.O. Box 969, MS 9159, Livermore, CA 94551, USA  \n2 Computational Mathematics Department, Sandia National Laboratories, P.O. Box 5800, MS 1320, Albuquerque, NM 87185, USA  \n3Fluid Dynamics and Solid Mechanics Group, Los Alamos National Laboratory,  \nP.O. Box 1663, MS B216, Los Alamos, NM 87545, USA  \nCorrespondence to: I. K. Tezaur ([ikalash@sandia.gov](ikalash@sandia.gov))  \nReceived: 30 September 2014 – Published in Geosci. Model Dev. Discuss.: 24 November 2014 Revised: 18 March 2015 – Accepted: 2 April 2015 – Published:  \nAbstract. This paper describes a new parallel, scalable and robust finite element based solver for the first-order Stokes momentum balance equations for ice flow. The solver, known as Albany/FELIX, is constructed using the component-based approach to building application codes, in which mature, modular libraries developed as a part of the Trilinos project are combined using abstract interfaces and template-based generic programming, resulting in a final code with access to dozens of algorithmic and advanced analysis capabilities. Following an overview of the relevant partial differential equations and boundary conditions, the numerical methods chosen to discretize the ice flow equations are described, along with their implementation. The results of several verification studies of the model accuracy are presented using (1) new test cases for simplified two-dimensional (2-D) versions ofthe governing equations derived using the method of manufactured solutions, and (2) canonical ice sheet modeling benchmarks. Model accuracy and convergence with respect to mesh resolution are then studied on problems involving a realistic Greenland ice sheet geometry discretized using hexahedral and tetrahedral meshes. Also explored as a part of this study is the effect of vertical mesh resolution on the solution accuracy and solver performance. The robustness and scalability of our solver on these problems is demonstrated. Lastly, we show that good scalability can be achieved by preconditioning the iterative linear solver using a new algebraic  \nmultilevel preconditioner, constructed based on the idea of semi-coarsening.  \n1 Introduction  \nIn its fourth assessment report (AR4), the Intergovernmental Panel on Climate Change (IPCC) declined to include estimates of future sea-level rise from ice sheet dynamics due to the inability of ice sheet models to mimic or explain observed dynamic behaviors, such as the acceleration and thinning then occurring on several of Greenland’s large outlet glaciers (IPCC, 2007) . Since the AR4, increased support from United States, United Kingdom, and European Union funding agencies has enabled concerted efforts towards improving the representation of ice dynamics in ice sheet models and towards their coupling to other components of Earth system models (ESMs) (Little, 2007; Lipscomb et al., 2008; van der Veen et al., 2010) . Thanks to this support, there has recently been tremendous progress in the development of“next generation” community-supported ice sheet models (e.g., Bueler and Brown, 2009; Rutt et al., 2009; Larour et al., 2012; Gagliardini et al., 2013; Brinkerhoff and Johnson, 2013; Lipscomb et al., 2013) able to perform realistic, highresolution, continental-scale simulations. These models run on massively parallel high-performance computing (HPC)  \nPublished by Copernicus Publications on behalf of the European Geosciences Union.  \n2 I .K. Tezaur e","cbCaid2mDd29IlY1","https://ap.wps.com/l/cbCaid2mDd29IlY1","pdf",3314875,24,"English","# Abstract\n# Introduction\n## Ice sheet modeling context and motivation\n## Solver development focus and modeling approaches","[{\"question\":\"What problem does Albany/FELIX solve in ice-sheet modeling?\",\"answer\":\"Albany/FELIX solves the first-order Stokes momentum balance equations for ice flow using a finite element approach.\"},{\"question\":\"How is the Albany/FELIX code constructed to support scalability and robustness?\",\"answer\":\"It is built using a component-based approach that combines mature, modular Trilinos libraries via abstract interfaces and template-based generic programming.\"},{\"question\":\"What verification and benchmarking methods are used to assess accuracy?\",\"answer\":\"The paper reports verification with manufactured-solution-derived 2-D test cases and uses canonical ice-sheet modeling benchmarks.\"}]","Albany/FELIX - parallel scalable robust finite element first-order Stokes approximation ice sheet solver | PDF"]