Hybrid Method of Engineering Analysis: Combining Meshfree Method with Distance Fields and Collocation Technique

This paper describes a numerical technique for solving engineering analysis problems that combine radial basis functions and collocation technique with meshfree method with distance fields, also known as solution structure method. The proposed hybrid technique enables exact treatment of all prescribed boundary conditions at every point on the geometric boundary and can be efficiently implemented for both structured and unstructured grids of basis functions. Ability to use unstructured grids empowers the meshfree method with distance fields with higher level of geometric flexibility. By providing exact treatment of the boundary conditions, the new approach makes it possible to exclude boundary conditions from the collocation equations. This reduces the size of the algebraic system, which results in faster solutions. At the same time, the boundary collocation points can be used to enforce the governing equation of the problem, which enhances the solution’s accuracy. Application of the proposed method to solution of heat transfer problems is illustrated on a number of benchmark problems. Modeling results are compared with those obtained by the traditional collocation technique and meshfree method with distance fields.