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Reproducing Polynomial Boundary Particle methods

This work by Chien-Ting Sun outlines the Reproducing Polynomial Particle (RPP) approach for solving boundary problems, focusing on its application to Boundary Integral Equations (BIE) relevant to the Poisson equation. It introduces the RPP shape function, discusses the placement and parameterization of nodes, and utilizes numerical integration techniques, including Gauss integration, to validate convergence through numerical examples. The importance of consistency and boundary conditions is emphasized, providing a comprehensive overview of RPP in computational methods.

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Reproducing Polynomial Boundary Particle methods

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  1. Reproducing Polynomial Boundary Particle methods Chien-Ting Sun 2013/06/13

  2. Outline • Reproducing Polynomial Particle (RPP) Shape function • Boundary Integral Equation (BIE) • Boundary Particle Method • Numerical Example

  3. Reproducing Polynomial Particle (RPP) Numerical Approximation Reproducing Polynomial Particle Approximation Reproducing Conditions (Consistency)

  4. Boundary Integral Equation (BIE) • For Poisson Equation:

  5. Boundary Particle Method • Where N is the number of line segment of edge-wise • NP is the number of RPP nodes

  6. Parameterized • Numerical integration • Then • By Gauss Integration

  7. Numerical Example • Poisson’s equation: • Analytical solution:

  8. Numerical Example • Convergence of

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