A meshless polyharmonic-type boundary interpolation method for solving boundary integral equations
A boundary interpolation technique is introduced based on multi-elliptic partial differential equations. The interpolation problem is converted to a special higher order partial differential equation which is completely independent of the geometry of the original problem. Based on this interpolation method, meshless methods are constructed for the 2D LaplacePoisson equation. The presented approach makes it possible to avoid solving large and dense interpolation equations. The auxiliary higher order partial differential equation is solved by robust, quadtree-based multi-level methods. The results can be easily generalized to 3D problems as well.
meshless methods scattered data interpolation biharmonic interpolation polyharmonic interpolation quadtree