Fast Method of Fundamental Solution

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Fast Method of Fundamental Solution

• Xinrong Jiang, PhD candidate
• Wen Chen, Prof.
• C.S. Chen, Prof.
• NTU, Dec. 8, Taipei

Hohai University
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Outline

• Motivation
• Methodology
• Numerical Example
• Conclusion

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Motivation

• Radial Basis Functions (RBFs)
• Domain Type
• Kansas 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)

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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

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Motivation

• Fast algorithm
• Save memory
• Fast computing
• Efficiency ? Accuracy

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Methodology

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

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Methodology
collocation, source Points N Matrix NN
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Methodology

• Iterative Method
• ill-conditioned

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Methodology

• Krylov Subspace methodGMRES
• Generalized minimal residual method
• FMM-BEM
• Fail in FMM-MFS
• Iterator open issue

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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
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Numerical Examples
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Numerical Examples
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Numerical Examples
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Numerical Examples
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Numerical Examples
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GPU

• Further acceleration

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GPUCUDA

• CUDA Compute Unified Device Architecture

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Parallel

• Tree Structure
• Further Study

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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

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• End
• Thanks for your attention!
• Comments?
• ???
• Xinrong Jiang
• hhujiangxr_at_163.com
• 08/12/ 2011