IsoGeometric Suitable Coupling Methods for Partitioned Multiphysics Simulation with Application to Fluid-Structure Interaction

TL;DR

This work introduces spline-based coupling methods for partitioned multiphysics simulations using isogeometric analysis (IGA) solvers to address interface data transfer across nonmatching meshes. It develops two strategies—a spline-vertex hybrid method and a fully isogeometric IGA-IGA approach—demonstrating reduced communication overhead and exact geometry transfer while preserving higher-order continuity. The authors provide theoretical overhead models and extensive verification/validation on benchmark problems, showing improved efficiency and geometric fidelity over vertex-based approaches. The methods are implemented in gsPreCICE within the preCICE framework and aimed at broad adoption in IGA-enabled simulation workflows.

Abstract

This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when applied to IGA solvers, including geometric accuracy issues, interpolation errors, and substantial communication overhead. The methodology draws on the IGA mathematical framework to deliver coupling solutions that preserve high-order continuity and exact geometric representation of splines. We develop two complementary strategies: (1) a spline-vertex coupling method enabling efficient interaction between IGA and conventional solvers, and (2) a fully isogeometric coupling approach maximizing accuracy for IGA-to-IGA communication. Both theoretical analysis and extensive numerical experiments demonstrate that our spline-based methods significantly reduce communication overhead compared to traditional approaches while enhancing geometric accuracy through exact boundary representation and maintaining higher-order solution continuity across coupled interfaces. We quantitatively confirm communication efficiency benefits through systematic measurements of transfer times and data volumes across various mesh refinement levels. Our benchmark studies demonstrate geometric fidelity advantages while highlighting how splines naturally preserve solution derivatives across interfaces without requiring additional computation. This work provides efficient coupling strategies tailored to IGA-based solvers and establishes a practical bridge between IGA and traditional discretization methods, enabling broader adoption of IGA in established simulation workflows.

Figures (18)

• Figure 1: Illustration of vertex-based solvers coupled with IGA-based solvers, with information exchanged at quadrature points/vertices.
• Figure 2: Spline-based coupling between IGA-based structural solver and vertex-based fluid solver, with interface data exchanged via continuous spline representation.
• Figure 3: IGA-IGA communication with spline representations on both fluid and structural domains, maximizing the benefits of isogeometric analysis.
• Figure 4: Constant load test setup for the vertical beam.
• Figure 5: Left: Comparison of tip displacement between reference solution and different coupling methods. Right: Relative $L^2$ error of different coupling methods compared to the reference solution.