A modified bubble placement method and its application in solving elliptic problem with discontinuous coefficients adaptively

Abstract

To solve the elliptic problem with discontinuous coefficients adaptively and efficiently which has strong singularity, one of the key steps is to generate mesh adaptively near region with discontinuous coefficients according to an a posteriori error estimator. For bubble placement method, the previous interaction force function used to obtain a high-quality nodes set is only determined by the ratio ω of the real and desired distance between bubbles, which is not suitable to generate mesh with a very small size. In this study, the force function is modified and it is determined both by the ratio ω and the sizes of bubbles. Meanwhile, in consideration of the quality of nodes and the computational efficiency, the equation of motion used to calculate the positions of bubbles is also modified. Moreover, a constrained bubble-type local mesh generation (BLMG) method is developed. The modified node placement method and constrained BLMG strategy are applied to solve elliptic problem with discontinuous coefficients adaptively. Several numerical experiments are reported to demonstrate that the adaptive method can be applied to various kinds of complicated geometries, and the triangles remain very well shaped at any particular refinement levels, even though the mesh size varies by several orders of magnitude. ARTICLE HISTORY

A novel progressive grid generation method for free-form grid structure design and case studies

“…In research by Persson and Strang [27], an iterative technique was developed for the mesh generation based on a physical analogy between a simplex mesh and a truss structure. Similar to the physical analogy, Shimada and Gossard et al [28][29] invented an interesting grid generation method called bubble mesh generation. In its actual implementation, the bubble method generated node configurations that yielded virtually no ill-shaped triangles or tetrahedrals.…”

Provably size-guaranteed mesh generation with superconvergence

“…[14,15,16]. The advantage of BPM is to generate high-quality grids on many complexly bounded 2D and 3D domains and can be easily used in adaptive finite element method and anisotropic problems [17,18,19,20,21]. In addition, due to the natural parallelism of BPM, computational efficiency has been improved greatly to solve large-scale problems [22].…”