Multi-level meshless methods based on direct multi-elliptic interpolation

Gáspár, Csaba

doi:10.1016/j.cam.2008.08.005

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…The technique can easily be combined with a Seidel-type iteration in a natural way. For the 2D Laplace equation, this result in the following local scheme (for details, see [7]):…”

Section: Localization Techniquesmentioning

confidence: 99%

A Localized Version of the Method of Fundamental Solutions in a Multi-level Context

Gáspár

2023

Period. Polytech. Civil Eng.

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The Method of Fundamental Solutions is applied to the Laplace equation. Instead of using the traditional approach with external source points and boundary collocation points, the original domain decomposed into a lot of smaller, overlapping subdomains, and the Method of Fundamental Solutions is used to the individual local subdomains. After eliminating the local source points, local schemes are obtained. Instead of constructing a global scheme, the local subproblems are solved sequentially, in an iterative way. This mimics a multiplicative Schwarz method with overlapping subdomains, which assures the convergence of the method. Combining the iteration with a simple Seidel-type method, the resulting iteration is used as a smoothing procedure of a multi-level method. The points belonging to the coarse and fine levels are defined by a quadtree-generated cell system controlled by the boundary of the original domain. The multi-level character of the obtained method makes it possible to reduce the necessary number of iterations, that is, the overall computational cost can be significantly reduced. Moreover, the solution of large and ill-conditioned systems is completely avoided. The method is illustrated through several numerical test examples.

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“…The technique can easily be combined with a Seidel-type iteration in a natural way. For the 2D Laplace equation, this result in the following local scheme (for details, see [7]):…”

Section: Localization Techniquesmentioning

confidence: 99%

A Localized Version of the Method of Fundamental Solutions in a Multi-level Context

Gáspár

2023

Period. Polytech. Civil Eng.

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Some Regularized Versions of the Method of Fundamental Solutions

Gáspár

2012

Meshfree Methods for Partial Differential Equations VI

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Numerical Solution to Coupled Burgers’ Equations by Gaussian-Based Hermite Collocation Scheme

Chuathong

Kaennakham

2018

Journal of Applied Mathematics

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One of the most challenging PDE forms in fluid dynamics namely Burgers equations is solved numerically in this work. Its transient, nonlinear, and coupling structure are carefully treated. The Hermite type of collocation mesh-free method is applied to the spatial terms and the 4th-order Runge Kutta is adopted to discretize the governing equations in time. The method is applied in conjunction with the Gaussian radial basis function. The effect of viscous force at high Reynolds number up to 1,300 is investigated using the method. For the purpose of validation, a conventional global collocation scheme (also known as “Kansa” method) is applied parallelly. Solutions obtained are validated against the exact solution and also with some other numerical works available in literature when possible.

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Multi-level meshless methods based on direct multi-elliptic interpolation

Cited by 3 publications

References 13 publications

A Localized Version of the Method of Fundamental Solutions in a Multi-level Context

A Localized Version of the Method of Fundamental Solutions in a Multi-level Context

Some Regularized Versions of the Method of Fundamental Solutions

Numerical Solution to Coupled Burgers’ Equations by Gaussian-Based Hermite Collocation Scheme

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