Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential equations, via the Isogeometric Analysis (IGA) paradigm. However, spectral accuracy in IGA is limited to relatively small NURBS patch degrees (roughly p≤8), since local condition numbers grow very rapidly for higher degrees. On the other hand, traditional Spectral Element Methods (SEM) guarantee spectral accuracy but often require complex and expensive meshing techniques, like transfinite mapping, that result anyway in inexact geometries. In this work we propose a hybrid NURBS-SEM approximation method that achieves spectral accuracy and maintains exact geometry representation by combining the advantages of IGA and SEM. As a prototypical problem on non trivial geometries, we consider the Laplace–Beltrami and Allen–Cahn equations on a surface. On these problems, we present a comparison of several instances of NURBS-SEM with the standard Galerkin and Collocation Isogeometric Analysis (IGA).

NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces / Pitton, Giuseppe; Heltai, Luca. - In: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. - ISSN 0045-7825. - 338:August(2018), pp. 440-462. [10.1016/j.cma.2018.04.039]

NURBS-SEM: A hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces

Pitton, Giuseppe;Heltai, Luca
2018

Abstract

Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years also for the approximation of partial differential equations, via the Isogeometric Analysis (IGA) paradigm. However, spectral accuracy in IGA is limited to relatively small NURBS patch degrees (roughly p≤8), since local condition numbers grow very rapidly for higher degrees. On the other hand, traditional Spectral Element Methods (SEM) guarantee spectral accuracy but often require complex and expensive meshing techniques, like transfinite mapping, that result anyway in inexact geometries. In this work we propose a hybrid NURBS-SEM approximation method that achieves spectral accuracy and maintains exact geometry representation by combining the advantages of IGA and SEM. As a prototypical problem on non trivial geometries, we consider the Laplace–Beltrami and Allen–Cahn equations on a surface. On these problems, we present a comparison of several instances of NURBS-SEM with the standard Galerkin and Collocation Isogeometric Analysis (IGA).
338
August
440
462
https://arxiv.org/abs/1804.08271
Pitton, Giuseppe; Heltai, Luca
File in questo prodotto:
File Dimensione Formato  
pitton_heltai_nurbs_sem.pdf

embargo fino al 04/05/2020

Tipologia: Documento in Post-print
Licenza: Creative commons
Dimensione 1.37 MB
Formato Adobe PDF
1.37 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/81737
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact