Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully harness the synergy between Computer-Aided Design and Computer-Aided Engineering analyses. The existing methods often fix boundary parameters, leading to challenges in elongated geometries such as fluid channels and tubular reactors. This paper presents an innovative solution for the boundary parameter matching problem, specifically designed for analysis-suitable parameterizations. We employ a sophisticated Schwarz-Christoffel mapping technique, which is instrumental in computing boundary correspondences. A refined boundary curve reparameterization process complements this. Our dual-strategy approach maintains the geometric exactness and continuity of input physical domains, overcoming limitations often encountered with the existing reparameterization techniques. By employing our proposed boundary parameter method, we show that even a simple linear interpolation approach can effectively construct a satisfactory analysis-suitable parameterization. Our methodology offers significant improvements over traditional practices, enabling the generation of analysis-suitable and geometrically precise models, which is crucial for ensuring accurate simulation results. Numerical experiments show the capacity of the proposed method to enhance the quality and reliability of isogeometric analysis workflows.

翻译：等几何分析已在工程领域推动了计算仿真与几何设计融合的范式转变。该技术需要物理域的分析适用参数化，以充分发挥计算机辅助设计与计算机辅助工程分析的协同效应。现有方法通常固定边界参数，导致流体通道、管式反应器等细长几何体在参数化过程中面临挑战。本文针对分析适用参数化中的边界参数匹配问题，提出了一种创新解决方案。我们采用先进的Schwarz-Christoffel映射技术计算边界对应关系，并辅以精细化的边界曲线重参数化流程。这种双策略方法在保持输入物理域几何精确性与连续性的同时，突破了现有重参数化技术常见的技术瓶颈。研究表明，采用本文提出的边界参数方法后，即使简单的线性插值方法也能有效构建出令人满意的分析适用参数化。本方法较传统实践有显著改进，能够生成兼具分析适用性与几何精确性的模型，这对确保仿真结果的准确性至关重要。数值实验表明，所提方法能够有效提升等几何分析工作流程的质量与可靠性。