{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T02:02:57Z","timestamp":1776132177184,"version":"3.50.1"},"reference-count":67,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T00:00:00Z","timestamp":1624665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Slovenian Research Agency","doi-asserted-by":"crossref","award":["P2-0095"],"award-info":[{"award-number":["P2-0095"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Young Researcher program","award":["PR-08346"],"award-info":[{"award-number":["PR-08346"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Math. Softw."],"published-print":{"date-parts":[[2021,9,30]]},"abstract":"<jats:p>Medusa, a novel library for implementation of non-particle strong form mesh-free methods, such as GFDM or RBF-FD, is described. We identify and present common parts and patterns among many such methods reported in the literature, such as node positioning, stencil selection, and stencil weight computation. Many different algorithms exist for each part and the possible combinations offer a plethora of possibilities for improvements of solution procedures that are far from fully understood. As a consequence there are still many unanswered questions in the mesh-free community resulting in vivid ongoing research in the field. Medusa implements the core mesh-free elements as independent blocks, which offers users great flexibility in experimenting with the method they are developing, as well as easily comparing it with other existing methods. The article describes the chosen abstractions and their usage, illustrates aspects of the philosophy and design, offers some executions time benchmarks and demonstrates the application of the library on cases from linear elasticity and fluid flow in irregular 2D and 3D domains.<\/jats:p>","DOI":"10.1145\/3450966","type":"journal-article","created":{"date-parts":[[2021,6,26]],"date-time":"2021-06-26T16:14:12Z","timestamp":1624724052000},"page":"1-25","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":38,"title":["Medusa"],"prefix":"10.1145","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6405-7976","authenticated-orcid":false,"given":"Jure","family":"Slak","sequence":"first","affiliation":[{"name":"Jo\u017eef Stefan Institute, Slovenia and Faculty of Mathematics and Physics, University of Ljubljana, Slovenia"}]},{"given":"Gregor","family":"Kosec","sequence":"additional","affiliation":[{"name":"Jo\u017eef Stefan Institute, Slovenia"}]}],"member":"320","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"AIP Conference Proceedings","volume":"1389","author":"Ahnert Karsten","year":"2011","unstructured":"Karsten Ahnert and Mario Mulansky . 2011 . Odeint\u2013solving ordinary differential equations in C++ . In AIP Conference Proceedings , Vol. 1389 . American Institute of Physics, 1586\u20131589. DOI:https:\/\/doi.org\/10.1063\/1.3637934 Karsten Ahnert and Mario Mulansky. 2011. Odeint\u2013solving ordinary differential equations in C++. In AIP Conference Proceedings, Vol. 1389. American Institute of Physics, 1586\u20131589. DOI:https:\/\/doi.org\/10.1063\/1.3637934"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/1268776.1268779"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2016.12.008"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5194\/gmd-8-3007-2015"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.07.008"},{"key":"e_1_2_1_6_1","unstructured":"Jan Bender. 2016. SPlisHSPlasH. Retrieved from https:\/\/github.com\/InteractiveComputerGraphics\/SPlisHSPlasH. Jan Bender. 2016. SPlisHSPlasH. Retrieved from https:\/\/github.com\/InteractiveComputerGraphics\/SPlisHSPlasH."},{"key":"e_1_2_1_7_1","volume-title":"The Numerical Modelling of Nonlinear Stellar Pulsations","author":"Benz W.","unstructured":"W. Benz . 1990. Smooth particle hydrodynamics: A review . In The Numerical Modelling of Nonlinear Stellar Pulsations . Springer , 269\u2013288. DOI:https:\/\/doi.org\/10.1007\/978-94-009-0519-1_16 W. Benz. 1990. Smooth particle hydrodynamics: A review. In The Numerical Modelling of Nonlinear Stellar Pulsations. Springer, 269\u2013288. DOI:https:\/\/doi.org\/10.1007\/978-94-009-0519-1_16"},{"key":"e_1_2_1_8_1","volume-title":"The LifeV library: Engineering mathematics beyond the proof of concept. arXiv preprint arXiv:1710.06596","author":"Bertagna Luca","year":"2017","unstructured":"Luca Bertagna , Simone Deparis , Luca Formaggia , Davide Forti , and Alessandro Veneziani . 2017. The LifeV library: Engineering mathematics beyond the proof of concept. arXiv preprint arXiv:1710.06596 ( 2017 ). Luca Bertagna, Simone Deparis, Luca Formaggia, Davide Forti, and Alessandro Veneziani. 2017. The LifeV library: Engineering mathematics beyond the proof of concept. arXiv preprint arXiv:1710.06596 (2017)."},{"key":"e_1_2_1_9_1","unstructured":"Jose Luis Blanco and Pranjal Kumar Rai. 2014. nanoflann: A C++ header-only fork of FLANN a library for Nearest Neighbor (NN) with KD-trees. Retrieved from https:\/\/github.com\/jlblancoc\/nanoflann. Jose Luis Blanco and Pranjal Kumar Rai. 2014. nanoflann: A C++ header-only fork of FLANN a library for Nearest Neighbor (NN) with KD-trees. Retrieved from https:\/\/github.com\/jlblancoc\/nanoflann."},{"key":"e_1_2_1_10_1","unstructured":"Evan Bollig. 2014. Radial Basis Function Finite Differences on the GPU. Retrieved from https:\/\/github.com\/bollig\/rbffd_gpu\/. Evan Bollig. 2014. Radial Basis Function Finite Differences on the GPU. Retrieved from https:\/\/github.com\/bollig\/rbffd_gpu\/."},{"key":"e_1_2_1_11_1","volume-title":"5th US National Congress on Computational Mechanics.","author":"Choi Y.","unstructured":"Y. Choi and S. Kim . 1999. Node generation scheme for meshfree method by Voronoi diagram and weighted bubble packing . In 5th US National Congress on Computational Mechanics. Y. Choi and S. Kim. 1999. Node generation scheme for meshfree method by Voronoi diagram and weighted bubble packing. In 5th US National Congress on Computational Mechanics."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1080\/10407790050051146"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2014.10.004"},{"key":"e_1_2_1_14_1","unstructured":"Dassault Syst\u00e8mes. 2012. Abaqus Unified FEA. Retrieved from https:\/\/www.3ds.com\/products-services\/simulia\/products\/abaqus\/. Dassault Syst\u00e8mes. 2012. Abaqus Unified FEA. Retrieved from https:\/\/www.3ds.com\/products-services\/simulia\/products\/abaqus\/."},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compchemeng.2008.03.009"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1145\/1966895.1966900"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2015.01.009"},{"key":"e_1_2_1_18_1","unstructured":"Chris Foster et\u00a0al. 2011. tinyformat: Minimal type safe printf replacement library for C++. Retrieved from http:\/\/rapidxml.sourceforge.net. Chris Foster et\u00a0al. 2011. tinyformat: Minimal type safe printf replacement library for C++. Retrieved from http:\/\/rapidxml.sourceforge.net."},{"key":"e_1_2_1_19_1","unstructured":"Fraunhofer Gesellschaft. 1999. MESHFREE. Retrieved from https:\/\/www.meshfree.eu\/. Fraunhofer Gesellschaft. 1999. MESHFREE. Retrieved from https:\/\/www.meshfree.eu\/."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0017-9310(91)90295-P"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0307-904X(03)00091-X"},{"key":"e_1_2_1_22_1","volume-title":"Jared Wyles, Chedy Najjar, Simon Brand, and Filipe Cabecinhas.","author":"Godbolt Matt","year":"2019","unstructured":"Matt Godbolt , Rub\u00e9n Rinc\u00f3n , Patrick Quist , Austin Morton , Jared Wyles, Chedy Najjar, Simon Brand, and Filipe Cabecinhas. 2019 . Compiler explorer. Retrieved from https:\/\/github.com\/mattgodbolt\/compiler-explorer. Matt Godbolt, Rub\u00e9n Rinc\u00f3n, Patrick Quist, Austin Morton, Jared Wyles, Chedy Najjar, Simon Brand, and Filipe Cabecinhas. 2019. Compiler explorer. Retrieved from https:\/\/github.com\/mattgodbolt\/compiler-explorer."},{"key":"e_1_2_1_23_1","volume-title":"Beno\u00eet Jacob et\u00a0al","author":"Guennebaud Ga\u00ebl","year":"2010","unstructured":"Ga\u00ebl Guennebaud , Beno\u00eet Jacob et\u00a0al . 2010 . Eigen v3. Retrieved from http:\/\/eigen.tuxfamily.org. Ga\u00ebl Guennebaud, Beno\u00eet Jacob et\u00a0al. 2010. Eigen v3. Retrieved from http:\/\/eigen.tuxfamily.org."},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1515\/jnum-2012-0013"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1145\/1089014.1089020"},{"key":"e_1_2_1_26_1","volume-title":"RBF: Python package containing the tools necessary for radial basis function (RBF) applications.","author":"Hines Trever","year":"2015","unstructured":"Trever Hines . 2015 . RBF: Python package containing the tools necessary for radial basis function (RBF) applications. Retrieved from https:\/\/github.com\/treverhines\/RBF. Trever Hines. 2015. RBF: Python package containing the tools necessary for radial basis function (RBF) applications. Retrieved from https:\/\/github.com\/treverhines\/RBF."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2014.06.006"},{"key":"e_1_2_1_28_1","unstructured":"Inpartik & ITM University of Stuttgart. 2008. Pasimodo. Retrieved from https:\/\/www.itm.uni-stuttgart.de\/en\/software\/pasimodo\/. Inpartik & ITM University of Stuttgart. 2008. Pasimodo. Retrieved from https:\/\/www.itm.uni-stuttgart.de\/en\/software\/pasimodo\/."},{"key":"e_1_2_1_29_1","unstructured":"Marcin Kalicinski. 2011. RapidXml. Retrieved from https:\/\/github.com\/c42f\/tinyformat. Marcin Kalicinski. 2011. RapidXml. Retrieved from https:\/\/github.com\/c42f\/tinyformat."},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.advengsoft.2016.05.010"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1108\/09615530810898999"},{"key":"e_1_2_1_32_1","doi-asserted-by":"crossref","unstructured":"Gregor Kosec Jure Slak Matja Depolli Roman Trobec Kyvia Pereira Satyendra Tomar Thibault Jacquemin St\u00e9phane P. A. Bordas and Magd Abdel Wahab. 2019. Weak and strong from meshless methods for linear elastic problem under fretting contact conditions. Tribol. Internat. (2019). DOI:https:\/\/doi.org\/10.1016\/j.triboint.2019.05.041 Gregor Kosec Jure Slak Matja Depolli Roman Trobec Kyvia Pereira Satyendra Tomar Thibault Jacquemin St\u00e9phane P. A. Bordas and Magd Abdel Wahab. 2019. Weak and strong from meshless methods for linear elastic problem under fretting contact conditions. Tribol. Internat. (2019). DOI:https:\/\/doi.org\/10.1016\/j.triboint.2019.05.041","DOI":"10.1016\/j.triboint.2019.05.041"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-98-00974-0"},{"key":"e_1_2_1_34_1","volume-title":"Mulay","author":"Li Hua","year":"2013","unstructured":"Hua Li and Shantanu S . Mulay . 2013 . Meshless Methods and Their Numerical Properties. CRC Press . Hua Li and Shantanu S. Mulay. 2013. Meshless Methods and Their Numerical Properties. CRC Press."},{"key":"e_1_2_1_35_1","volume-title":"Mesh Free Methods: Moving Beyond the Finite Element Method","author":"Liu Gui-Rong","unstructured":"Gui-Rong Liu . 2002. Mesh Free Methods: Moving Beyond the Finite Element Method . CRC Press . DOI:https:\/\/doi.org\/10.1201\/9781420040586 Gui-Rong Liu. 2002. Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press. DOI:https:\/\/doi.org\/10.1201\/9781420040586"},{"key":"e_1_2_1_36_1","first-page":"89","article-title":"Node placement method by bubble simulation and its application","volume":"55","author":"Liu Ying","year":"2010","unstructured":"Ying Liu , Yufeng Nie , Weiwei Zhang , and Lei Wang . 2010 . Node placement method by bubble simulation and its application . Comput. Model. Eng. Sci. 55 , 1 (2010), 89 . Ying Liu, Yufeng Nie, Weiwei Zhang, and Lei Wang. 2010. Node placement method by bubble simulation and its application. Comput. Model. Eng. Sci. 55, 1 (2010), 89.","journal-title":"Comput. Model. Eng. Sci."},{"key":"e_1_2_1_37_1","doi-asserted-by":"publisher","DOI":"10.1145\/1731022.1731030"},{"key":"e_1_2_1_38_1","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1068"},{"key":"e_1_2_1_39_1","doi-asserted-by":"crossref","unstructured":"M. Maksi\u0107 V. Djurica A. Souvent J. Slak M. Depolli and G. Kosec. 2019. Cooling of overhead power lines due to the natural convection. Int. J. Electric. Power Energy Syst. 113 (Dec. 2019) 333\u2013343. DOI:https:\/\/doi.org\/10.1016\/j.ijepes.2019.05.005 M. Maksi\u0107 V. Djurica A. Souvent J. Slak M. Depolli and G. Kosec. 2019. Cooling of overhead power lines due to the natural convection. Int. J. Electric. Power Energy Syst. 113 (Dec. 2019) 333\u2013343. DOI:https:\/\/doi.org\/10.1016\/j.ijepes.2019.05.005","DOI":"10.1016\/j.ijepes.2019.05.005"},{"key":"e_1_2_1_40_1","unstructured":"Ltd. MIDAS Information Technology Co.2018. midas MeshFree. Retrieved from http:\/\/www.midasmeshfree.com\/. Ltd. MIDAS Information Technology Co.2018. midas MeshFree. Retrieved from http:\/\/www.midasmeshfree.com\/."},{"key":"e_1_2_1_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-012-9614-6"},{"key":"e_1_2_1_42_1","first-page":"487","article-title":"Coordinate free numerics: Closing the gap between \u201cpure\u201d and \u2018applied\u201d mathematics. ZAMM Z. angew","volume":"76","author":"Munthe-Kaas H.","year":"1996","unstructured":"H. Munthe-Kaas and M. Haveraaen . 1996 . Coordinate free numerics: Closing the gap between \u201cpure\u201d and \u2018applied\u201d mathematics. ZAMM Z. angew . Math. Mech 76 , S1 (1996), 487 \u2013 488 . H. Munthe-Kaas and M. Haveraaen. 1996. Coordinate free numerics: Closing the gap between \u201cpure\u201d and \u2018applied\u201d mathematics. ZAMM Z. angew. Math. Mech 76, S1 (1996), 487\u2013488.","journal-title":"Math. Mech"},{"key":"e_1_2_1_43_1","unstructured":"Nextflow Software. 2015. SPH-flow. Retrieved from https:\/\/www.nextflow-software.com\/solvers\/sphflow\/. Nextflow Software. 2015. SPH-flow. Retrieved from https:\/\/www.nextflow-software.com\/solvers\/sphflow\/."},{"key":"e_1_2_1_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2008.01.003"},{"key":"e_1_2_1_45_1","unstructured":"NOGRID GmbH. 2006. NOGRID. Retrieved from https:\/\/www.nogrid.com\/. NOGRID GmbH. 2006. NOGRID. Retrieved from https:\/\/www.nogrid.com\/."},{"key":"e_1_2_1_46_1","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.amc.2017.06.006","article-title":"Adaptive RBF-FD method for elliptic problems with point singularities in 2D","volume":"313","author":"Oanh Dang Thi","year":"2017","unstructured":"Dang Thi Oanh , Oleg Davydov , and Hoang Xuan Phu . 2017 . Adaptive RBF-FD method for elliptic problems with point singularities in 2D . Appl. Math. Comput. 313 (2017), 474 \u2013 497 . DOI:https:\/\/doi.org\/10.1016\/j.amc.2017.06.006 Dang Thi Oanh, Oleg Davydov, and Hoang Xuan Phu. 2017. Adaptive RBF-FD method for elliptic problems with point singularities in 2D. Appl. Math. Comput. 313 (2017), 474\u2013497. DOI:https:\/\/doi.org\/10.1016\/j.amc.2017.06.006","journal-title":"Appl. Math. Comput."},{"key":"e_1_2_1_47_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7949(01)00067-0"},{"key":"e_1_2_1_48_1","unstructured":"OneZero Software. 2008. Fluidix. Retrieved from https:\/\/www.fluidix.ca\/. OneZero Software. 2008. Fluidix. Retrieved from https:\/\/www.fluidix.ca\/."},{"key":"e_1_2_1_49_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.05.022"},{"key":"e_1_2_1_50_1","volume-title":"Chandrashekhar Kaushik et\u00a0al","author":"Ramachandran Prabhu","year":"2019","unstructured":"Prabhu Ramachandran , Kunal Puri , Aditya Bhosale , A. Dinesh , Abhinav Muta , Pawan Negi , Rahul Govind , Suraj Sanka , Pankaj Pandey , Chandrashekhar Kaushik et\u00a0al . 2019 . PySPH: A Python-based framework for smoothed particle hydrodynamics. arXiv preprint arXiv:1909.04504 (2019). Prabhu Ramachandran, Kunal Puri, Aditya Bhosale, A. Dinesh, Abhinav Muta, Pawan Negi, Rahul Govind, Suraj Sanka, Pankaj Pandey, Chandrashekhar Kaushik et\u00a0al. 2019. PySPH: A Python-based framework for smoothed particle hydrodynamics. arXiv preprint arXiv:1909.04504 (2019)."},{"key":"e_1_2_1_51_1","doi-asserted-by":"publisher","DOI":"10.1145\/2998441"},{"key":"e_1_2_1_52_1","article-title":"GetFEM: Automated FE modeling of multiphysics problems based on a generic weak form language","volume":"47","author":"Renard Yves","year":"2020","unstructured":"Yves Renard and Konstantinos Poulios . 2020 . GetFEM: Automated FE modeling of multiphysics problems based on a generic weak form language . ACM Trans. Math. Softw. 47 , 1 (2020). Yves Renard and Konstantinos Poulios. 2020. GetFEM: Automated FE modeling of multiphysics problems based on a generic weak form language. ACM Trans. Math. Softw. 47, 1 (2020).","journal-title":"ACM Trans. Math. Softw."},{"key":"e_1_2_1_53_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.softx.2017.07.002"},{"key":"e_1_2_1_54_1","volume-title":"SWIFT: SPH with inter-dependent fine-grained tasking","author":"Schaller Matthieu","year":"2018","unstructured":"Matthieu Schaller , Pedro Gonnet , Peter W. Draper , Aidan B. G. Chalk , Richard G. Bower , James Willis , and Lo\u00efc Hausammann . 2018 . SWIFT: SPH with inter-dependent fine-grained tasking . Astrophysics Source Code Library ( 2018), ascl\u20131805. Matthieu Schaller, Pedro Gonnet, Peter W. Draper, Aidan B. G. Chalk, Richard G. Bower, James Willis, and Lo\u00efc Hausammann. 2018. SWIFT: SPH with inter-dependent fine-grained tasking. Astrophysics Source Code Library (2018), ascl\u20131805."},{"key":"e_1_2_1_55_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2018.06.036"},{"key":"e_1_2_1_56_1","doi-asserted-by":"publisher","DOI":"10.1137\/17M114090X"},{"key":"e_1_2_1_57_1","doi-asserted-by":"publisher","DOI":"10.23919\/MIPRO.2018.8400034"},{"key":"e_1_2_1_58_1","doi-asserted-by":"publisher","DOI":"10.1137\/18M1231456"},{"key":"e_1_2_1_59_1","volume-title":"Refined meshless local strong form solution of Cauchy\u2013Navier equation on an irregular domain. Eng. Anal. Bound. Elem. 100 (Mar","author":"Slak Jure","year":"2019","unstructured":"Jure Slak and Gregor Kosec . 2019b. Refined meshless local strong form solution of Cauchy\u2013Navier equation on an irregular domain. Eng. Anal. Bound. Elem. 100 (Mar 2019 ), 3\u201313. DOI:https:\/\/doi.org\/10.1016\/j.enganabound.2018.01.001 Jure Slak and Gregor Kosec. 2019b. Refined meshless local strong form solution of Cauchy\u2013Navier equation on an irregular domain. Eng. Anal. Bound. Elem. 100 (Mar 2019), 3\u201313. DOI:https:\/\/doi.org\/10.1016\/j.enganabound.2018.01.001"},{"key":"e_1_2_1_60_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2019.04.030"},{"key":"e_1_2_1_61_1","volume-title":"Meshfree Methods for Partial Differential Equations","author":"Tiwari Sudarshan","unstructured":"Sudarshan Tiwari and J\u00f6rg Kuhnert . 2003. Finite pointset method based on the projection method for simulations of the incompressible Navier-Stokes equations . In Meshfree Methods for Partial Differential Equations . Springer , 373\u2013387. DOI:https:\/\/doi.org\/10.1007\/978-3-642-56103-0_26 Sudarshan Tiwari and J\u00f6rg Kuhnert. 2003. Finite pointset method based on the projection method for simulations of the incompressible Navier-Stokes equations. In Meshfree Methods for Partial Differential Equations. Springer, 373\u2013387. DOI:https:\/\/doi.org\/10.1007\/978-3-642-56103-0_26"},{"key":"e_1_2_1_62_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00466-003-0501-9"},{"key":"e_1_2_1_63_1","volume-title":"Fast variable density 3-D node generation. arXiv:1906.00636 [math.NA]","author":"van der Sande Kiera","year":"2019","unstructured":"Kiera van der Sande and Bengt Fornberg . 2019. Fast variable density 3-D node generation. arXiv:1906.00636 [math.NA] ( 2019 ). Kiera van der Sande and Bengt Fornberg. 2019. Fast variable density 3-D node generation. arXiv:1906.00636 [math.NA] (2019)."},{"key":"e_1_2_1_64_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2012.08.017"},{"key":"e_1_2_1_65_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijheatmasstransfer.2017.05.057"},{"key":"e_1_2_1_66_1","volume-title":"Scattered Data Approximation","author":"Wendland Holger","unstructured":"Holger Wendland . 2004. Scattered Data Approximation . Vol. 17 . Cambridge University Press . Holger Wendland. 2004. Scattered Data Approximation. Vol. 17. Cambridge University Press."},{"key":"e_1_2_1_67_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2018.03.031"}],"container-title":["ACM Transactions on Mathematical Software"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3450966","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3450966","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T17:49:24Z","timestamp":1750268964000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3450966"}},"subtitle":["A C++ Library for Solving PDEs Using Strong Form Mesh-free Methods"],"short-title":[],"issued":{"date-parts":[[2021,6,26]]},"references-count":67,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9,30]]}},"alternative-id":["10.1145\/3450966"],"URL":"https:\/\/doi.org\/10.1145\/3450966","relation":{},"ISSN":["0098-3500","1557-7295"],"issn-type":[{"value":"0098-3500","type":"print"},{"value":"1557-7295","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,26]]},"assertion":[{"value":"2019-01-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-09-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-06-26","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}