A technique for generating adapted discretizations to solve partial differential equations with the generalized finite difference method

The generalized finite difference method is a meshless method for solving partial differential equations that allows arbitrary discretizations of points. Typically, the discretizations have the same density of points in the domain. We propose a technique to get adapted discretizations for the solution of partial differential equations. This strategy allows using a smaller number of points and, therefore, a lower computational cost, to achieve the same accuracy that would be obtained with a regular discretization.

Automated summary

The study proposes an adaptive discretization technique that allows using fewer points for solving partial differential equations, resulting in lower computational cost while maintaining the same accuracy as regular discretization.