{"title":"三角剖分中三角元退化估计的一种方法","authors":"Yu. A. Kriksin, V. F. Tishkin","doi":"10.1134/S106456242370076X","DOIUrl":null,"url":null,"abstract":"<p>A quantitative estimate for the quality of a triangular element—the triangle degeneration index—is proposed. To apply this estimate, a simple model triangulation is constructed in which the vertex coordinates are obtained as the sum of the corresponding node coordinates in a given regular grid and their random increments. For various parameter values, the empirical distribution function of the triangle degeneration index is calculated, which is considered a quantitative characteristic of the quality of triangular elements in the constructed triangulation.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"107 2","pages":"126 - 129"},"PeriodicalIF":0.5000,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On One Approach to the Estimation of a Triangular Element Degeneration in a Triangulation\",\"authors\":\"Yu. A. Kriksin, V. F. Tishkin\",\"doi\":\"10.1134/S106456242370076X\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A quantitative estimate for the quality of a triangular element—the triangle degeneration index—is proposed. To apply this estimate, a simple model triangulation is constructed in which the vertex coordinates are obtained as the sum of the corresponding node coordinates in a given regular grid and their random increments. For various parameter values, the empirical distribution function of the triangle degeneration index is calculated, which is considered a quantitative characteristic of the quality of triangular elements in the constructed triangulation.</p>\",\"PeriodicalId\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":\"107 2\",\"pages\":\"126 - 129\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S106456242370076X\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S106456242370076X","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On One Approach to the Estimation of a Triangular Element Degeneration in a Triangulation
A quantitative estimate for the quality of a triangular element—the triangle degeneration index—is proposed. To apply this estimate, a simple model triangulation is constructed in which the vertex coordinates are obtained as the sum of the corresponding node coordinates in a given regular grid and their random increments. For various parameter values, the empirical distribution function of the triangle degeneration index is calculated, which is considered a quantitative characteristic of the quality of triangular elements in the constructed triangulation.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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