{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:36:21Z","timestamp":1648568181742},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2009,2,27]],"date-time":"2009-02-27T00:00:00Z","timestamp":1235692800000},"content-version":"unspecified","delay-in-days":6054,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["AIEDAM"],"published-print":{"date-parts":[[1992,8]]},"abstract":"<jats:p>This paper presents a knowledge-based problem solving environment for numerical simulation of problems described by partial differential equations (PDEs). The system aims to facilitate the simulation requirements of different user groups that include engineers, mathematicians and numerical analysts. To attain this objective, a flexible multi-perspective modelling environment is proposed which incorporates three natural modelling platforms, namely; a physical model, a mathematical model and a numerical model. The modelling environment is integrated with a sophisticated numerical solver. We believe that combination of an open modelling system with a basic numerical simulator provides a powerful problem solving environment capable of meeting the needs of these different user groups. The overall system architecture is based on automatic transformation using mathematical and numerical knowledge bases between the three identified models. The knowledge bases are organized in a frame based manner to reflect the hierarchical nature of the knowledge in PDEs and numerical algorithms. The object oriented paradigm is used to bind local rule bases to each frame and for implementing a global inference mechanism which works over the hierarchical knowledge structures. Evaluation of the modelling environment has indicated that engineers can tackle PDE based engineering problems without the necessity for detailed knowledge of mathematics or numerical techniques and mathematicians can examine the mathematical properties of PDEs without the requirement of numerical expertise.<\/jats:p>","DOI":"10.1017\/s0890060400003073","type":"journal-article","created":{"date-parts":[[2010,3,31]],"date-time":"2010-03-31T13:47:59Z","timestamp":1270043279000},"page":"199-212","source":"Crossref","is-referenced-by-count":1,"title":["AI-DEQSOL. A knowledge-based environment for numerical simulation of engineering problems described by partial differential equations"],"prefix":"10.1017","volume":"6","author":[{"given":"D. P.","family":"Finn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N. J.","family":"Hurley","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"N.","family":"Sagawa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2009,2,27]]},"reference":[{"key":"S0890060400003073_ref014","unstructured":"Yip K. M.-K. 1991. Computer-aided heuristic and qualitative reasoning in fluid mechanics. In: Proceedings of IMACS 13th World Congress on Computation and Applied Mathematics, pp. 1022\u20131027."},{"key":"S0890060400003073_ref013","volume-title":"Object Oriented Programming in Artificial Intelligence","author":"Tello","year":"1990"},{"key":"S0890060400003073_ref012","doi-asserted-by":"publisher","DOI":"10.1115\/1.3151889"},{"key":"S0890060400003073_ref011","first-page":"353","volume-title":"Intelligent Mathematical Software Systems","author":"Schonauer","year":"1988"},{"key":"S0890060400003073_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0954-1810(91)90013-E"},{"key":"S0890060400003073_ref007","unstructured":"Houstis E. N. and Rice J. R. 1991 b. Parallel ELLPACK: a development and problem solving environment for high performance computing machines. Proceedings of IFIP Working Conference on Programming Environments for High-Level Scientific Problem Solving, pp. 229\u2013242."},{"key":"S0890060400003073_ref010","first-page":"33","volume-title":"Intelligent Mathematical Software Systems","author":"Kowalski","year":"1988"},{"key":"S0890060400003073_ref009","first-page":"15","article-title":"Automatic code generation method of DEQSOL (differential equation solver language)","volume":"11","author":"Konno","year":"1987","journal-title":"Journal of Information Processing"},{"key":"S0890060400003073_ref001","volume-title":"Proceedings of the Second International Conference on Expert Systems for Numerical Computing","author":"Barras","year":"1990"},{"key":"S0890060400003073_ref006","first-page":"1037","article-title":"The engineering of modern interfaces for PDE solvers","volume":"3","author":"Houstis","year":"1991","journal-title":"Proceedings of IMACS 13th World Congress on Computation and Applied Mathematics"},{"key":"S0890060400003073_ref002","volume-title":"Object Oriented Design","author":"Booch","year":"1991"},{"key":"S0890060400003073_ref003","first-page":"1035","article-title":"XELLPACK: a distributed problem solving environment for elliptic partial differential equations","volume":"3","author":"Buis","year":"1991","journal-title":"Proceedings of IMACS 13th World Congress on Computation and Applied Mathematics"},{"key":"S0890060400003073_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0954-1810(91)90009-D"},{"key":"S0890060400003073_ref005","first-page":"579","volume-title":"Proceedings of the 2nd International Conference on Artificial Intelligence in Design","author":"Finn","year":"1992"}],"container-title":["Artificial Intelligence for Engineering Design, Analysis and Manufacturing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0890060400003073","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T21:02:45Z","timestamp":1558040565000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0890060400003073\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,8]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,8]]}},"alternative-id":["S0890060400003073"],"URL":"https:\/\/doi.org\/10.1017\/s0890060400003073","relation":{},"ISSN":["0890-0604","1469-1760"],"issn-type":[{"value":"0890-0604","type":"print"},{"value":"1469-1760","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,8]]}}}