{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T14:40:46Z","timestamp":1698072046257},"reference-count":10,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2007,9,5]],"date-time":"2007-09-05T00:00:00Z","timestamp":1188950400000},"content-version":"vor","delay-in-days":7187,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Systems &amp;amp; Computers in Japan"],"published-print":{"date-parts":[[1988,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the numerical computation of a partial differential equation, it is useful to employ a parallel computer, where a large number of processors are connected in a mesh form. Such a scheme is now realizable with the advent of modern VLSI technology. On the other hand, there arises a request for the fault tolerancy with the increase of the processing units. When a partial differential equation is to be solved by such a computer, the requirement is not severe for the completeness of the data, since the iterative method usually is employed. This paper considers a problem of this nature, and discusses the recovery from the fault within the execution. The method is to detect the fault, to modify the connections among the processing units, separating the processing unit in fault, and to continue the computation by modifying a part of the discrete algorithm. By the proposed method, the dynamic recovery from the fault is easily realized, and the degradation of the computation accuracy due to the fault is suppressed. The proposed scheme is implemented on the parallel computer PAX\u201032 with 32 processing units. The actual result of solving a two\u2010dimensional Poisson equation is presented, and a theoretical evaluation is made for the error in the one\u2010dimensional problem.<\/jats:p>","DOI":"10.1002\/scj.4690190403","type":"journal-article","created":{"date-parts":[[2009,11,19]],"date-time":"2009-11-19T21:12:52Z","timestamp":1258665172000},"page":"23-32","source":"Crossref","is-referenced-by-count":0,"title":["Fault\u2010Tolerant Scheme on Partial Differential Equations with Nearest\u2010Neighbor Mesh\u2010Connected Machines"],"prefix":"10.1002","volume":"19","author":[{"given":"Gyo","family":"Osawa","sequence":"first","affiliation":[]},{"given":"Toshio","family":"Kawai","sequence":"additional","affiliation":[]},{"given":"Hideo","family":"Aiso","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2007,9,5]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/357369.357370"},{"issue":"5","key":"e_1_2_1_3_2","first-page":"68","article-title":"An invitation to the world of PAX","volume":"19","author":"Hoshino T.","year":"1986","journal-title":"I.E.E.E. Computer"},{"key":"e_1_2_1_4_2","unstructured":"H. F.Jordan A special purpose architecture for finite element analysis ICASE Report 78\u20139(March1978)."},{"key":"e_1_2_1_5_2","unstructured":"L. M.Adams P.Mehrotraet al The FEM\u20102 design method Proc. 1983 Intl. Conf. on Parallel Processing pp.132\u2013134(Aug.1983)."},{"issue":"12","key":"e_1_2_1_6_2","first-page":"960","article-title":"The Lens interconnection strategy","volume":"30","author":"Lawrie D. H.","year":"1981","journal-title":"I.E.E.E. Trans. Comput."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1981.1675695"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1981.1675777"},{"key":"e_1_2_1_9_2","unstructured":"G.Osawa T.KawaiandH.Aiso Fault tolerant scheme on partial differential equations Proc. 1985 Intl. Conf. on Parallel Processing pp.413\u2013416(Aug.1986)."},{"issue":"6","key":"e_1_2_1_10_2","first-page":"1195","article-title":"Dynamic fault recovery of a parallel computer for numerical computation with mesh topology, Trans. (D) I.E.C.E.","volume":"68","author":"Yokota T.","year":"1985","journal-title":"Japan"},{"key":"e_1_2_1_11_2","first-page":"306","volume-title":"Mathematics for Natural Science Researchers","author":"Terazawa K.","year":"1983"}],"container-title":["Systems and Computers in Japan"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690190403","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fscj.4690190403","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/scj.4690190403","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,22]],"date-time":"2023-10-22T07:59:44Z","timestamp":1697961584000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/scj.4690190403"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1988,1]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1988,1]]}},"alternative-id":["10.1002\/scj.4690190403"],"URL":"https:\/\/doi.org\/10.1002\/scj.4690190403","archive":["Portico"],"relation":{},"ISSN":["0882-1666","1520-684X"],"issn-type":[{"value":"0882-1666","type":"print"},{"value":"1520-684X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1988,1]]}}}