A physics-informed parametrization and its impact on 2D IGABEM analysis

Abstract

In this work, we study the effect of the geometry representation in the context of the IsoGeometric-Analysis-based Boundary Element Method (IGABEM) and we propose an algorithm for the construction of a physics-informed geometric representation which leads to approximation results of high accuracy that are comparable to known adaptive refinement schemes. As a model problem, we use a previously studied 2D potential flow problem around a cylinder; see Politis et al. (Proceedings of SIAM/ACM joint conference on geometric and physical modeling, California, pp 349–354, 2009. https://doi.org/10.1145/1629255.1629302L). This study involves a systematic examination of a series of transformations and reparametrizations and their effect on the achieved accuracy and convergence rate of the numerical solution to the problem at hand. Subsequently, a new parametrization is proposed based on a coarse-level approximation of the field-quantity solution, coupling in this way the geometry representation to the physics of the problem. Finally, the performance of our approach is compared against an exact-solution-driven adaptive refinement scheme and a posteriori error estimates for adaptive IGABEM methods. The proposed methodology delivers results of similar quality to the adaptive approaches, but without the computational cost of error estimates evaluation at each refinement step.