Local meshless methods for second order elliptic interface problems with sharp corners
•Different types of RBFs are utilized for localized meshless methods in the context of interface PDEs.•Both sharp edged and smooth edged interfaces are taken into account.•Fully scattered and uniform nodal distributions are considered.•Numerical order of convergence are calculated.•Shape parameter s...
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| Vydané v: | Journal of computational physics Ročník 416; s. 109500 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Cambridge
Elsevier Inc
01.09.2020
Elsevier Science Ltd |
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| ISSN: | 0021-9991, 1090-2716, 1090-2716 |
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| Abstract | •Different types of RBFs are utilized for localized meshless methods in the context of interface PDEs.•Both sharp edged and smooth edged interfaces are taken into account.•Fully scattered and uniform nodal distributions are considered.•Numerical order of convergence are calculated.•Shape parameter sensitivity analysis of the meshless methods is performed.
In the present paper, we develop a local meshless procedure for solving a steady state two-dimensional interface problem having discontinuous coefficients and curved interfaces with sharp corners. The proposed local meshless methods are based on three types of radial basis functions (RBFs): a local meshless method based on multiquadric RBF (LMM1P), a local meshless method based on integrated multiquadric RBF (LMM2P) and a local meshless method based on hybrid Gaussian-Cubic RBF (LMM3P). Stencils are designed at the interface and interior regions to cope with discontinuities and sharp corners. Due to the localized nature of the procedure and a sparse matrix representation, the local meshless methods become computationally less expensive than global meshless methods. The methods are augmented with linear polynomial to improve accuracy and ensure stable computation. Comparison with some existing versions of finite element methods is also performed to show better accuracy of the proposed meshless methods. Accuracies of the proposed local meshless methods are also compared among themselves. Flexibility of the meshless methods with respect to complex geometries, adapting to different shapes of the interfaces and selection of the shape parameter is also considered. |
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| AbstractList | In the present paper, we develop a local meshless procedure for solving a steady state two-dimensional interface problem having discontinuous coefficients and curved interfaces with sharp corners. The proposed local meshless methods are based on three types of radial basis functions (RBFs): a local meshless method based on multiquadric RBF (LMM1P), a local meshless method based on integrated multiquadric RBF (LMM2P) and a local meshless method based on hybrid Gaussian-Cubic RBF (LMM3P). Stencils are designed at the interface and interior regions to cope with discontinuities and sharp corners. Due to the localized nature of the procedure and a sparse matrix representation, the local meshless methods become computationally less expensive than global meshless methods. The methods are augmented with linear polynomial to improve accuracy and ensure stable computation. Comparison with some existing versions of finite element methods is also performed to show better accuracy of the proposed meshless methods. Accuracies of the proposed local meshless methods are also compared among themselves. Flexibility of the meshless methods with respect to complex geometries, adapting to different shapes of the interfaces and selection of the shape parameter is also considered. •Different types of RBFs are utilized for localized meshless methods in the context of interface PDEs.•Both sharp edged and smooth edged interfaces are taken into account.•Fully scattered and uniform nodal distributions are considered.•Numerical order of convergence are calculated.•Shape parameter sensitivity analysis of the meshless methods is performed. In the present paper, we develop a local meshless procedure for solving a steady state two-dimensional interface problem having discontinuous coefficients and curved interfaces with sharp corners. The proposed local meshless methods are based on three types of radial basis functions (RBFs): a local meshless method based on multiquadric RBF (LMM1P), a local meshless method based on integrated multiquadric RBF (LMM2P) and a local meshless method based on hybrid Gaussian-Cubic RBF (LMM3P). Stencils are designed at the interface and interior regions to cope with discontinuities and sharp corners. Due to the localized nature of the procedure and a sparse matrix representation, the local meshless methods become computationally less expensive than global meshless methods. The methods are augmented with linear polynomial to improve accuracy and ensure stable computation. Comparison with some existing versions of finite element methods is also performed to show better accuracy of the proposed meshless methods. Accuracies of the proposed local meshless methods are also compared among themselves. Flexibility of the meshless methods with respect to complex geometries, adapting to different shapes of the interfaces and selection of the shape parameter is also considered. |
| ArticleNumber | 109500 |
| Author | Siraj-ul-Islam Larsson, Elisabeth Ahmad, Masood |
| Author_xml | – sequence: 1 givenname: Masood surname: Ahmad fullname: Ahmad, Masood email: masood.suf@gmail.com organization: Department of Basic Sciences, Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan – sequence: 2 orcidid: 0000-0001-8778-5688 surname: Siraj-ul-Islam fullname: Siraj-ul-Islam email: siraj-ul-islam@uetpeshawar.edu.pk organization: Department of Basic Sciences, Faculty of Architecture, Allied Sciences and Humanities, University of Engineering and Technology, Peshawar, Pakistan – sequence: 3 givenname: Elisabeth orcidid: 0000-0003-1154-9587 surname: Larsson fullname: Larsson, Elisabeth organization: Scientific Computing, Department of Information Technology, Uppsala University, Sweden |
| BackLink | https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-414049$$DView record from Swedish Publication Index (Uppsala universitet) |
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| Keywords | Sparse matrix Elliptic interface model Sharp-edged interface Local meshless method Radial basis functions Collocation |
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| Snippet | •Different types of RBFs are utilized for localized meshless methods in the context of interface PDEs.•Both sharp edged and smooth edged interfaces are taken... In the present paper, we develop a local meshless procedure for solving a steady state two-dimensional interface problem having discontinuous coefficients and... |
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| SubjectTerms | Accuracy Collocation Computational physics Corners Discontinuity Elliptic interface model Finite element method Interfaces Local meshless method Mathematical analysis Matrix representation Meshless methods Polynomials Radial basis function Radial basis functions Sharp-edged interface Sparse matrices Sparse matrix |
| Title | Local meshless methods for second order elliptic interface problems with sharp corners |
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