Solving Inverse Laplace Equation with Singularity by Weighted Reproducing Kernel Collocation Method

Judy Ping Yang*, Pai Chen Guan, Chia Ming Fan

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

This work introduces the weighted collocation method with reproducing kernel approximation to solve the inverse Laplace equations. As the inverse problems in consideration are equipped with over-specified boundary conditions, the resulting equations yield an overdetermined system. Following our previous work, the weighted collocation method using a least-squares minimization has shown to solve the inverse Cauchy problems efficiently without using techniques such as iteration and regularization. In this work, we further consider solving the inverse problems of Laplace type and introduce the Shepard functions to deal with singularity. Numerical examples are provided to demonstrate the validity of the method.

Original languageEnglish
Article number1750065
JournalInternational Journal of Applied Mechanics
Volume9
Issue number5
DOIs
StatePublished - 1 Jul 2017

Keywords

  • Inverse Laplace equation
  • collocation method
  • reproducing kernel approximation
  • singularity
  • strong form

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