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Reproducing Polynomial Boundary Particle methods

Reproducing Polynomial Boundary Particle methods. Chien-Ting Sun 2013/06/13. Outline. Reproducing Polynomial Particle (RPP) Shape function Boundary Integral Equation (BIE) Boundary Particle Method Numerical Example. Reproducing Polynomial Particle (RPP). Numerical Approximation

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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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