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Träfflista för sökning "hsv:(NATURVETENSKAP) hsv:(Matematik) hsv:(Beräkningsmatematik) ;pers:(Larsson Elisabeth)"

Sökning: hsv:(NATURVETENSKAP) hsv:(Matematik) hsv:(Beräkningsmatematik) > Larsson Elisabeth

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  • Bernal, Francisco, et al. (författare)
  • A radial basis function partition of unity method for steady flow simulations
  • 2024
  • Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 503
  • Tidskriftsartikel (refereegranskat)abstract
    • A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The compressed domain is then discretised, regardless of its final shape, via the radial basis function partition of unity method. Finally, the system of nonlinear algebraic collocation equations is solved with the trust-region algorithm, taking advantage of analytically derived Jacobians. We validate the methodology on a benchmark of computational fluid mechanics: the steady viscous flow past a circular cylinder. The resulting flow characteristics compare very well with the literature. Then, we stress-test the methodology on less smooth obstacles-rounded and sharp square cylinders. As expected, in the latter scenario the solution is polluted by spurious oscillations, owing to the presence of boundary singularities.
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  • Buhmann, Martin D., et al. (författare)
  • A note on radial basis function interpolant limits
  • 2010
  • Ingår i: IMA Journal of Numerical Analysis. - : Oxford University Press (OUP). - 0272-4979 .- 1464-3642. ; 30, s. 543-554
  • Tidskriftsartikel (refereegranskat)
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  • Cacciani, Nicola, et al. (författare)
  • A first meshless approach to simulation of the elastic behaviour of the diaphragm
  • 2020
  • Ingår i: Spectral and High Order Methods for Partial Differential Equations. - Cham : Springer. - 9783030396466 ; , s. 501-512
  • Konferensbidrag (refereegranskat)abstract
    • The diaphragm is the main muscle that regulates the human respiration. When a patient is put under controlled mechanical ventilation, the diaphragm is exposed to forces that damage the muscle function. The long-term aim of this work is to study this process through numerical simulation. Here, we take the first steps in developing a meshless numerical simulation method for the diaphragm. We describe how the diaphragm geometry can be extracted from medical images, and then be used in the meshless method. We show that for a thin volume like the diaphragm, the resolution of the thin dimension is highly relevant for the accuracy of the approximation, and we also show that the method converges for a test case, where realistic displacements are used as boundary conditions.
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  • Fornberg, Bengt, et al. (författare)
  • A new class of oscillatory radial basis functions
  • 2006
  • Ingår i: Computers and Mathematics with Applications. - : Elsevier BV. - 0898-1221 .- 1873-7668. ; 51, s. 1209-1222
  • Tidskriftsartikel (refereegranskat)
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  • Fornberg, Bengt, et al. (författare)
  • Stable computations with Gaussian radial basis functions in 2-D
  • 2009
  • Rapport (övrigt vetenskapligt/konstnärligt)abstract
    • Radial basis function (RBF) approximation is an extremely powerful tool for representing smooth functions in non-trivial geometries, since the method is meshfree and can be spectrally accurate. A perceived practical obstacle is that the interpolation matrix becomes increasingly ill-conditioned as the RBF shape parameter becomes small, corresponding to flat RBFs. Two stable approaches that overcome this problem exist, the Contour-Padé method and the RBF-QR method. However, the former is limited to small node sets and the latter has until now only been formulated for the surface of the sphere. This paper contains an RBF-QR formulation for planar two-dimensional problems. The algorithm is perfectly stable for arbitrarily small shape parameters and can be used for up to a thousand node points in double precision and for several thousand node points in quad precision. A sample MATLAB code is provided.
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