Generalized finite differences using fundamental solutions

作者：Leitao V M A^*

来源：International Journal for Numerical Methods in Engineering, 2010, 81(5): 564-583.

DOI：10.1002/nme.2697

• solids
• finite difference methods
• mesh-free methods
• fundamental solutions
• collocation

It is well known that solutions for linear partial differential equations may be given in terms of fundamental solutions. The fundamental solutions solve the homogeneous equation exactly and are obtained from the solution of the inhomogeneous equation where the inhomogeneous term is described by a Dirac delta distribution. Fundamental solutions are the building blocks of the boundary element method and of the method of fundamental solutions and are traditionally used to build boundary-only global approximations in the domain of interest. In this work the same characteristic of the fundamental solutions, that of solving the homogeneous equation exactly, is used but not to build a global approximation. On the contrary, local approximations are built in such a manner that it is possible to construct finite difference operators that are free from any form of structured grid.

• 出版日期2010-1-29