Proceedings of 10th World Congress on Computational Mechanics 2014
DOI: 10.5151/meceng-wccm2012-19354
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Spectral Element Approximation of Fredholm Integral Eigenvalue Problems

Abstract: Abstract. The Karhunen-Loève expansion of a Gaussian process, a common tool on

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Cited by 3 publications
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“…Since exact eigenpairs are not known for this kernel, we consider as reference solutions the numerical approximations found with the spectral element method [2] of degree 16 on a spatial mesh of 161 Â 161 nodal points. Fig.…”
Section: Numerical Resultsmentioning
confidence: 99%
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“…Since exact eigenpairs are not known for this kernel, we consider as reference solutions the numerical approximations found with the spectral element method [2] of degree 16 on a spatial mesh of 161 Â 161 nodal points. Fig.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…We refer to [2,21,22] for details on the computation of exact eigenvalues for these kernels. Kernel (23) is a common benchmark for Fredholm integral eigenvalue problems [1,4,5,[22][23][24].…”
Section: Other Examples Of Kernelsmentioning
confidence: 99%
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“…[12,22,25]). From the UQ application point of view (especially for the computations of Karhunen-Lòeve approximations), one can refer to [21] for a finite element method combined with the fast multipole methods, to [19] for a wavelet Galerkin arpproach using Haar basis functions, to [18] for the finite cell method, to [17] for a spectral element approximation, to name a few.…”
Section: Introductionmentioning
confidence: 99%