An improved numerical manifold method and its application

Abstract

The conventional numerical manifold method is improved in generating manifold elements. In this framework, the concept of mathematical element is underlying, and manifold elements are generated by intersecting mathematical elements with physical features. On one hand, each mathematical cover is recovered by the mathematical elements with the same node (and hence the node is the star of mathematical cover). On the other hand, each physical cover is eventually recovered by piecewise pasting the manifold elements within the same mathematical cover with the same physical feature. After this improvement, generation of manifold elements can bypass the overlapping procedure of irregular and complicated physical covers, leading to the effect as simple as the finite element method. Compared with the conventional numerical manifold method, this improvement can attain “what you see is what you get” in generating manifold elements, and construction of weight functions is theoretically straightforward. In addition, local mesh refinement becomes more convenient when necessary. Two examples are conducted to validate the improved numerical manifold method.