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

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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.

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Notes

  1. Note that by flipping the direction of \(\textbf{n}\) we may substitute the two minus signs with pluses.

  2. \(m=2\) may be also included, assuming control points at infinity are allowed.

  3. Note that using higher-order representations of the circle would allow it.

  4. Note that if the coarse approximation of the unknown field quantity is not adequate, a few steps of a uniform refinement process may be applied before following the procedure described above.

  5. insert knots.

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Funding

This work has received funding from Nazarbayev University, Kazakhstan under the Grant: “SOFFA - PHYS: Shape Optimization of Free-form Functional surfaces using isogeometric Analysis and Physics-Informed Surrogate Models”(Grant award Nr. 11022021FD2927).

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Nazarbayev University, 53 Kabanbay Batyr, 010000, Astana, Akmola, Kazakhstan

    Konstantinos V. Kostas & Issa Zhanabay

  2. Department of Naval Architecture, University of West Attica, Ag. Spyridonos, 12243, Egaleo, Attica, Greece

    Constantinos G. Politis

  3. Department of Naval Architecture, Ocean and Marine Engineering, University of Strathclyde, 16 Richmond Street, Glasgow, G1 1XQ, UK

    Panagiotis D. Kaklis

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  1. Konstantinos V. Kostas
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Correspondence to Konstantinos V. Kostas.

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Kostas, K.V., Politis, C.G., Zhanabay, I. et al. A physics-informed parametrization and its impact on 2D IGABEM analysis. Engineering with Computers 40, 3663–3682 (2024). https://doi.org/10.1007/s00366-024-02037-4

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