Adaptive Multiresolution Refinement With Distance Fields

This paper describes a multiresolution approach to field modeling that can be used with any meshfree or mesh based method for adaptive solution refinement. The refined solution is represented as a superposition of a coarse (unrefined) solution and a sequence of refinements that provide additional degrees of freedom with higher spatial or functional resolution. Each refinement is treated as a solution to a boundary value problem within a specified refinement window. The proposed approach is based on the meshfree method with distance fields [19, 29] and guarantees C continuity of the refined solutions with matching or non-matching grids. The method does not restrict the shape of the refinement window and does not place any constraints on the type of basis functions, or relative position and resolution of the refinement grids. Combining the proposed approach with hierarchical space decompositions and a posteriori error estimators results in an effective tool for automatic solution refinement. Carefully chosen numerical examples illustrate the power and advantages of the proposed approach.