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Numerical Methods for Partial Differential Equations, 2011
AbstractIn this article, we analyze the singular function boundary integral method (SFBIM) for a two‐dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick‐slip flow problem. In the SFBIM, the leading terms of the local asymptotic solution expansion near the singular point are used to approximate the solution ...
Christodoulou, Evgenia +7 more
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AbstractIn this article, we analyze the singular function boundary integral method (SFBIM) for a two‐dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick‐slip flow problem. In the SFBIM, the leading terms of the local asymptotic solution expansion near the singular point are used to approximate the solution ...
Christodoulou, Evgenia +7 more
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Singular boundary method for 2D dynamic poroelastic problems
Wave Motion, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun, Linlin +2 more
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Improved non-singular local boundary integral equation method
Applied Mathematics and Mechanics, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fu, Dong-Jie +2 more
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Regularized singular boundary method for 3D potential flow
Engineering Analysis with Boundary Elements, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kovářík, K. +3 more
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The singular function boundary integral method for biharmonic problems with crack singularities
Engineering Analysis with Boundary Elements, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Elliotis, Miltiades C. +5 more
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Evaluation of field singularities by an iterative boundary‐element method
Communications in Numerical Methods in Engineering, 1993AbstractA numerical method is presented for the evaluation of field singularities of the type (1/r1‐λ) using iterative solutions of standard boundary‐element analyses in a region surrounding the origin of singularity. Results for λ are presented for both two and three‐dimensional problems, and representative asymptotic fields for these examples are ...
Heyliger, P. R., Rudolphi, T. J.
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The Boundary Element Method with Singular Shape Functions
1992A class of singular potential problems using the boundary element algorithm with singular shape functions is investigated. In the proposed algorithm, an additional constraint equation is introduced in the global system making the stress intensity factor a degree of freedom.
N. G. Zamani, W. Sun
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Singular boundary method: A review and computer implementation aspects
Engineering Analysis with Boundary Elements, 2023Zhuojia Fu +11 more
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The Boundary Function Method for Singular Perturbation Problems
19951. Basic Ideas Regular and singular perturbations Asymptotic approximations Asymptotic and convergent series Examples of asymptotic expansions for solutions of regularly and singularly perturbed problems 2. Singularly perturbed ordinary differential equations Initial value problem The critical case Boundary value problems Spike-type solutions and other
Adelaida B. Vasil'eva +2 more
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The Dual Singular Function Method for 2D Boundary Integral Equations
Advances in Computational Mathematics, 2004The author investigates boundary element methods for the solution of elliptic boundary value problems on polygonal domains. In order to obtain an improved convergence behavior in the neighborhood of corner and collision points of the boundary he uses the dual singular function method.
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