Vectorized numerical algorithms for the solution of continuum mechanics problems
The aim of the work is to study the possibilities provided by new information technologies, object-oriented programming tools and modern operating systems for solving boundary value problems of continuum mechanics described by partial differential equations. To discretize the basic equations, we app...
Gespeichert in:
| Veröffentlicht in: | Nauchno-tekhnicheskiĭ vestnik informat͡s︡ionnykh tekhnologiĭ, mekhaniki i optiki Jg. 22; H. 1; S. 193 - 205 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
ITMO University
01.12.2024
|
| Schlagworte: | |
| ISSN: | 2226-1494, 2500-0373 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | The aim of the work is to study the possibilities provided by new information technologies, object-oriented programming tools and modern operating systems for solving boundary value problems of continuum mechanics described by partial differential equations. To discretize the basic equations, we applied the method of finite differences and finite volumes, which are widely used to solve problems in the mechanics of liquids and gases. The paper considers the implementation of the finite difference methods and the finite volume method with vectorized grid structures, including access to the inner and boundary cells of the grid, as well as the features of the implementation of algorithms at singular points of the computational domain. To solve boundary value problems described by partial differential equations, we developed an approach to the construction of vectorized algorithms and considered the features of their software implementation in the MATLAB package. Vectorization in such tasks, excluding nested loops, is ensured by appropriate data organization and the use of vectorized operations. On the one hand, the developed algorithms widely use MATLAB functions designed for processing vectors and sparse matrices, and on the other hand, they are distinguished by high efficiency and computation speed, comparable to those of programs written in C/C++. The main results imply the numerical solution of a number of problems in continuum mechanics associated with the calculation of stresses in a separate body and the calculation of the field of velocity and temperature in the flow of a viscous incompressible fluid. The features of discretization of the basic equations and the implementation of the corresponding finite-difference and finite-volume algorithms are shown. The use of the MATLAB system opens up new possibilities for the formalization and implementation of finite-difference and finite-volume methods for the numerical solution of boundary value problems in continuum mechanics. Despite the fact that the capabilities of the developed algorithms are illustrated by the example of solving fairly simple problems, they admit a relatively simple generalization to more complex problems, for example, solving the Euler equations and Navier–Stokes equations. As part of the work, computational modules were prepared with user programming tools that expand the capabilities of the package and are focused on solving problems in continuum mechanics. |
|---|---|
| AbstractList | The aim of the work is to study the possibilities provided by new information technologies, object-oriented programming tools and modern operating systems for solving boundary value problems of continuum mechanics described by partial differential equations. To discretize the basic equations, we applied the method of finite differences and finite volumes, which are widely used to solve problems in the mechanics of liquids and gases. The paper considers the implementation of the finite difference methods and the finite volume method with vectorized grid structures, including access to the inner and boundary cells of the grid, as well as the features of the implementation of algorithms at singular points of the computational domain. To solve boundary value problems described by partial differential equations, we developed an approach to the construction of vectorized algorithms and considered the features of their software implementation in the MATLAB package. Vectorization in such tasks, excluding nested loops, is ensured by appropriate data organization and the use of vectorized operations. On the one hand, the developed algorithms widely use MATLAB functions designed for processing vectors and sparse matrices, and on the other hand, they are distinguished by high efficiency and computation speed, comparable to those of programs written in C/C++. The main results imply the numerical solution of a number of problems in continuum mechanics associated with the calculation of stresses in a separate body and the calculation of the field of velocity and temperature in the flow of a viscous incompressible fluid. The features of discretization of the basic equations and the implementation of the corresponding finite-difference and finite-volume algorithms are shown. The use of the MATLAB system opens up new possibilities for the formalization and implementation of finite-difference and finite-volume methods for the numerical solution of boundary value problems in continuum mechanics. Despite the fact that the capabilities of the developed algorithms are illustrated by the example of solving fairly simple problems, they admit a relatively simple generalization to more complex problems, for example, solving the Euler equations and Navier–Stokes equations. As part of the work, computational modules were prepared with user programming tools that expand the capabilities of the package and are focused on solving problems in continuum mechanics. |
| Author | Emelyanov, V.N. Brykov, N.A. Volkov, K.N. |
| Author_xml | – sequence: 1 givenname: N.A. surname: Brykov fullname: Brykov, N.A. – sequence: 2 givenname: K.N. surname: Volkov fullname: Volkov, K.N. – sequence: 3 givenname: V.N. surname: Emelyanov fullname: Emelyanov, V.N. |
| BookMark | eNo9kEtLAzEUhYNUsNb-hyzcRvOaF7iR4qNQ0IW6DUnmpk2ZmZRkZqG_3rQ-4HLPPYfLWXyXaDaEARC6ZvSGVUVd3nLOS8JkIwmnnJM8jLBGZFecoTkvKCVUVGKW77_PC7RMaU8pZVVenM_R6wfYMUT_BS0eph6it7rDutvmbNz1CbsQ8bgDnEI3jT4MODhswzD6YZp63IPd6cHbhA8xmA76dIXOne4SLH91gd4fH95Wz2Tz8rRe3W-IZZUoCActbVnStqyZ41QCFNTUUkhXU6qdaxswde2s5QDGOONaTY1oBBitRVFxsUDrn9426L06RN_r-KmC9uoUhLhVOo7edqAAWidrJqvK0qxMl7JkreTgmJPGidx199NlY0gpgvvvY1SdYKsjQnVEqI6ws1VMZdjZFeIbVCN2pA |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.17586/2226-1494-2022-22-1-193-205 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 2500-0373 |
| EndPage | 205 |
| ExternalDocumentID | oai_doaj_org_article_eedf481477c04811a6461d42ef1f4bf3 10_17586_2226_1494_2022_22_1_193_205 |
| GroupedDBID | 642 AAYXX ADBBV AFKRA ALMA_UNASSIGNED_HOLDINGS BCNDV BENPR BPHCQ BYOGL CITATION GROUPED_DOAJ KQ8 PIMPY PQQKQ PROAC VCL VIT |
| ID | FETCH-LOGICAL-c1735-2ea4c660d681f204ee50b8434f800affd9eb88fcc2eebbfbfda0b393ebaa35723 |
| IEDL.DBID | DOA |
| ISSN | 2226-1494 |
| IngestDate | Mon Nov 03 22:07:14 EST 2025 Sat Nov 29 03:57:44 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c1735-2ea4c660d681f204ee50b8434f800affd9eb88fcc2eebbfbfda0b393ebaa35723 |
| OpenAccessLink | https://doaj.org/article/eedf481477c04811a6461d42ef1f4bf3 |
| PageCount | 13 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_eedf481477c04811a6461d42ef1f4bf3 crossref_primary_10_17586_2226_1494_2022_22_1_193_205 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-12-01 |
| PublicationDateYYYYMMDD | 2024-12-01 |
| PublicationDate_xml | – month: 12 year: 2024 text: 2024-12-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationTitle | Nauchno-tekhnicheskiĭ vestnik informat͡s︡ionnykh tekhnologiĭ, mekhaniki i optiki |
| PublicationYear | 2024 |
| Publisher | ITMO University |
| Publisher_xml | – name: ITMO University |
| SSID | ssj0001700022 ssib026971427 |
| Score | 2.2757032 |
| Snippet | The aim of the work is to study the possibilities provided by new information technologies, object-oriented programming tools and modern operating systems for... |
| SourceID | doaj crossref |
| SourceType | Open Website Index Database |
| StartPage | 193 |
| SubjectTerms | векторизация математическое моделирование механика сплошной среды численный алгоритм |
| Title | Vectorized numerical algorithms for the solution of continuum mechanics problems |
| URI | https://doaj.org/article/eedf481477c04811a6461d42ef1f4bf3 |
| Volume | 22 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2500-0373 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0001700022 issn: 2226-1494 databaseCode: DOA dateStart: 20010101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1La9wwEBYhhNAeSpO0dPsIOuRqYlkPy8e2dOkhhBySkJvQYybZsusN690c-uszsp1le8ql4IsENuKbQfONNfqGsTPjAcsGYmFKGfMxYyoamaBI0TY-apR2sPRFfXlp7-6aq51WX7kmbJAHHoA7pz0clRWqrmOWNhHeKCOSqgAFqoC9ziexnp1kijypMk0t1Khv-WcQicnRKneaI75RUFqgDtlZ3jGIL5vz7SQ5DSVn9IiCmA2N9D_xakfWv48_0_fs3Ugc-fdhwUdsD9pj9nZHTvCEXd32v-BnfyHxdjMcxcy5n9_T3Pph0XEiqJwIH3_xN75EnmvVZ-1ms-ALyLeAZ7HjY5eZ7gO7mf66_vm7GDsmFFHUUhcVeBWNKZOxAqtSAegyWCUVEi_0iKmBYC3GWAGEgAGTL4NsJATvpa4r-ZHtt8sWPjFOsZxSL195sMSY0AfUMqEFtI32NlYTpl9wcY-DMIbLCUXG02U8XcbTZTxp6IQjPGmkJ-xHBnH7Tpa37ifI6G40unvN6J__x0e-sDe0OjXUpnxl--vVBr6xg_i0nnWr096fngGcysqh |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Vectorized+numerical+algorithms+for+the+solution+of+continuum+mechanics+problems&rft.jtitle=Nauchno-tekhnicheski%C4%AD+vestnik+informat%CD%A1s%EF%B8%A1ionnykh+tekhnologi%C4%AD%2C+mekhaniki+i+optiki&rft.au=N.+A.+Brykov&rft.au=K.+N.+Volkov&rft.au=V.+N.+Emelyanov&rft.date=2024-12-01&rft.pub=ITMO+University&rft.issn=2226-1494&rft.eissn=2500-0373&rft.volume=22&rft.issue=1&rft.spage=193&rft.epage=205&rft_id=info:doi/10.17586%2F2226-1494-2022-22-1-193-205&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_eedf481477c04811a6461d42ef1f4bf3 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2226-1494&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2226-1494&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2226-1494&client=summon |