A meshless method for nonhomogeneous polyharmonic problems using method of fundamental solution coupled with quasi-interpolation technique

作者：Li, Xiaolin^*; Li, Shuling

来源：Applied Mathematical Modelling, 2011, 35(8): 3698-3709.

DOI：10.1016/j.apm.2011.01.042

• Meshless
• Method of fundamental solutions
• Quasi-interpolation
• Nonhomogeneous
• Biharmonic equation
• Error estimate

This paper proposes a meshless method based on coupling the method of fundamental solutions (MFS) with quasi-interpolation for the solution of nonhomogeneous polyharmonic problems. The original problems are transformed to homogeneous problems by subtracting a particular solution of the governing differential equation. The particular solution is approximated by quasi-interpolation and the corresponding homogeneous problem is solved using the MFS. By applying quasi-interpolation, problems connected with interpolation can be avoided. The error analysis and convergence study of this meshless method are given for solving the boundary value problems of nonhomogeneous harmonic and biharmonic equations. Numerical examples are also presented to show the efficiency of the method.

• 出版日期2011-8
• 单位重庆师范大学