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Fast Method of Fundamental Solution

Fast Method of Fundamental Solution. Xinrong Jiang, PhD candidate Wen Chen, Prof. C.S. Chen, Prof. NTU, Dec. 8, Taipei. Hohai University. Outline. Motivation Methodology Numerical Example Conclusion. Motivation. Radial Basis Functions (RBFs) : Domain Type Kansa’s Method

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Fast Method of Fundamental Solution

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  1. Fast Method of Fundamental Solution Xinrong Jiang, PhD candidate Wen Chen, Prof. C.S. Chen, Prof. NTU, Dec. 8, Taipei Hohai University

  2. Outline • Motivation • Methodology • Numerical Example • Conclusion

  3. Motivation • Radial Basis Functions (RBFs) : • Domain Type • Kansa’s Method • Local Method of Particular Solution (LMPS) • Boundary Type • Method of Fundamental Solution (MFS) • Regularized Meshless Method (RMM) • Boundary Knot Method (BKM) • Boundary Particle Method (BPM) • Singular Boundary Method (SBM)

  4. Motivation • Dense Matrix • Large-scale problem • Infinite domain … • Speed up ^_^ iterative method • Mainframe T_T • expensive, computer volume large, electricity • PC T_T • Memory, CPU flops

  5. Motivation • Fast algorithm • Save memory • Fast computing • Efficiency  Accuracy

  6. Methodology • Fast Multipole Method (FMM) • 1987, 1997 new version, Rokhlin and Greengard • Nlog(N)->N • Adaptive • Fast Fourier Transform (FFT) • Precorrected FFT, J White • N*log(N) • Uniform • Hierarchical Matrix,Adaptive Cross-Approximation, etc

  7. Methodology collocation, source Points: N Matrix: N*N

  8. Methodology • Iterative Method • ill-conditioned

  9. Methodology • Krylov Subspace method::GMRES • Generalized minimal residual method • FMM-BEM • Fail in FMM-MFS • Iterator: open issue

  10. MFS easy-to-program, exponential convergence, highly accuracy, geometric flexibility and so on infinite domain problems, large deformation problems, dynamic crack propagation etc FMM-MFS

  11. Numerical Examples

  12. Numerical Examples

  13. Numerical Examples

  14. Numerical Examples

  15. Numerical Examples

  16. GPU • Further acceleration

  17. GPU::CUDA • CUDA: Compute Unified Device Architecture

  18. Parallel • Tree Structure • Further Study

  19. Conclusion • FMM-MFS • implement successfully • high precision and speed • high wave number requires wide band • high frequency • large domain with low frequency • ill-conditioned requires suitable iterative method

  20. End Thanks for your attention! Comments? 姜欣榮 Xinrong Jiang hhujiangxr@163.com 08/12/ 2011

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