Detecting Inverse Boundaries by Weighted High-Order Gradient Collocation Method

Judy P. Yang*, Hon Fung Samuel Lam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The weighted reproducing kernel collocation method exhibits high accuracy and efficiency in solving inverse problems as compared with traditional mesh-based methods. Nevertheless, it is known that computing higher order reproducing kernel (RK) shape functions is generally an expensive process. Computational cost may dramatically increase, especially when dealing with strong-from equations where high-order derivative operators are required as compared to weak-form approaches for obtaining results with promising levels of accuracy. Under the framework of gradient approximation, the derivatives of reproducing kernel shape functions can be constructed synchronically, thereby alleviating the complexity in computation. In view of this, the present work first introduces the weighted high-order gradient reproducing kernel collocation method in the inverse analysis. The convergence of the method is examined through the weights imposed on the boundary conditions. Then, several configurations of multiply connected domains are provided to numerically investigate the stability and efficiency of the method. To reach the desired accuracy in detecting the outer boundary for two special cases, special treatments including allocation of points and use of ghost points are adopted as the solution strategy. From four benchmark examples, the efficacy of the method in detecting the unknown boundary is demonstrated.

Original languageEnglish
Article number1297
Number of pages19
JournalMathematics
Volume8
Issue number8
DOIs
StatePublished - Aug 2020

Keywords

  • reproducing kernel approximation
  • gradient approximation
  • high-order gradient approximation
  • strong form collocation
  • inverse problem
  • multiply connected domain
  • KERNEL PARTICLE METHODS
  • ERROR ANALYSIS

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