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The paper develops a spectrum of techniques based on a family of place-transition nets aimed at the computing and communication structure design for fast mass-parallel numerical solving of PDEs. For the HPC domain, we develop models of interconnects in the form of infinite nets and graphical programs in the form of Sleptsov nets. For the embedded control domain, we develop specialized lattices for fast numerical solving PDE based on integer number approximation specified with Sleptsov-Salwicki nets to be implemented on dedicated hardware, which we prototype on FPGAs. For mass-parallel solving of PDEs, we employ ad-hoc finite-difference schemes and iteration methods that allow us to recalculate the lattice values in a single time cycle suitable for control of hypersonic objects and thermonuclear reactions. <\/jats:p>","DOI":"10.1142\/s0129626425500045","type":"journal-article","created":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T03:32:21Z","timestamp":1746761541000},"source":"Crossref","is-referenced-by-count":0,"title":["Computing and Communication Structure Design for Fast Mass-Parallel Numerical Solving PDE"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5698-7324","authenticated-orcid":false,"given":"Dmitry A.","family":"Zaitsev","sequence":"first","affiliation":[{"name":"The University of Derby, Derby, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4799-3842","authenticated-orcid":false,"given":"Tatiana R.","family":"Shmeleva","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Software Systems, Kaiserslautern, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3503-4836","authenticated-orcid":false,"given":"Alexander A.","family":"Kostikov","sequence":"additional","affiliation":[{"name":"Technical University \u201dMetinvest Polytechnic\u201d LLC, Zaporizhzhia, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,5,9]]},"reference":[{"key":"S0129626425500045BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-031-69630-5"},{"key":"S0129626425500045BIB002","doi-asserted-by":"publisher","DOI":"10.1201\/9780203908518"},{"volume-title":"Finite Difference Schemes and Partial Differential Equations","year":"2007","author":"Strikwerda J.","key":"S0129626425500045BIB003"},{"key":"S0129626425500045BIB004","doi-asserted-by":"publisher","DOI":"10.1002\/9781119667889"},{"volume-title":"High Performance Computing: Modern Systems and Practices","year":"2024","author":"Sterling Thomas","key":"S0129626425500045BIB005"},{"volume-title":"A Hands-On Guide to Designing Embedded Systems","year":"2021","author":"Taylor Adam","key":"S0129626425500045BIB006"},{"first-page":"646","volume-title":"Proc. 2018 IEEE International Conference on Cluster Computing (CLUSTER)","author":"Ajima Y.","key":"S0129626425500045BIB007"},{"first-page":"1","volume-title":"Proc. 2020 IEEE Asian Solid-State Circuits Conference (A-SSCC)","author":"Shimizu T.","key":"S0129626425500045BIB008"},{"key":"S0129626425500045BIB010","doi-asserted-by":"publisher","DOI":"10.1109\/MCSE.2008.153"},{"key":"S0129626425500045BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-13-0824-6"},{"key":"S0129626425500045BIB012","doi-asserted-by":"publisher","DOI":"10.1201\/9781315219547"},{"key":"S0129626425500045BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2015.2444414"},{"key":"S0129626425500045BIB014","doi-asserted-by":"publisher","DOI":"10.25088\/ComplexSystems.26.2.157"},{"key":"S0129626425500045BIB015","doi-asserted-by":"publisher","DOI":"10.25088\/ComplexSystems.26.4.341"},{"volume-title":"Computer-Aided Design of Flexible Computer-Aided Manufacturing Systems","year":"1986","author":"Sleptsov A. 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