A Meshless Boundary Element Technique Based On Multi-level Iterated Helmholtz-type Interpolation
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A special scattered data interpolation technique is introduced. The interpolation problem is converted to a higher order auxiliary PDE, typically to an iterated Laplace or Helmholtz equation. To solve this PDE, robust multi-level methods are used which are based on a quadtree / octtree subdivision algorithm. Thus, the solution of large interpolalion equations are avoided. Using this interpolation method, meshless techniques are constructed which require a set of boundary points only, without any structure. Theoretical results as well as numerical examples are also presented.