{"title":"Irregular domains: Special coordinates for a pseudospectral method","authors":"O. Guimarães, Leandro Cunha, José R.C. Piqueira","doi":"10.1016/j.enganabound.2024.105921","DOIUrl":null,"url":null,"abstract":"<div><p>Working with a special coordinate system, this study demonstrates how to obtain numerical solutions with geometric convergence for the eigenstates of a Laplacian operator in irregular prismatic domains (both annular and single) that are simply connected. An appropriate coordinate system, which defines a tightly bounded domain, allows for a fair mesh for series approximation nodes. Three independent criteria were used to verify the consistency of the solutions: the Rayleigh quotient, the divergence theorem, and a partial derivative equation (PDE) transformed from an eigenvalue problem to a boundary value problem with Robin conditions. Supporting the proposed method, examples show a few hundred eigenstates obtained in a single computation, with at least 10 significant figures and a low computational cost.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"168 ","pages":"Article 105921"},"PeriodicalIF":4.2000,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0955799724003953","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Working with a special coordinate system, this study demonstrates how to obtain numerical solutions with geometric convergence for the eigenstates of a Laplacian operator in irregular prismatic domains (both annular and single) that are simply connected. An appropriate coordinate system, which defines a tightly bounded domain, allows for a fair mesh for series approximation nodes. Three independent criteria were used to verify the consistency of the solutions: the Rayleigh quotient, the divergence theorem, and a partial derivative equation (PDE) transformed from an eigenvalue problem to a boundary value problem with Robin conditions. Supporting the proposed method, examples show a few hundred eigenstates obtained in a single computation, with at least 10 significant figures and a low computational cost.
期刊介绍：
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.
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