A q-adaptive partition of unity finite element method for the solution of the 2-D Helmholtz equation

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    The Partition of Unity Finite Element Method (PUFEM) is used to solve a wave scattering problem governed by the Helmholtz equation. The number q of the enriching plane waves is usually considered to be constant all over the computational domain which is a reasonable choice when a uniform mesh grid is considered. However, for nonuniform mesh grids where the element size may well vary throughout the computational domain this choice can considerably increase the condition number of the resulting linear system. It is shown that varying the number q as the element size varies may significantly reduce the required total number of degrees of freedom and improve the conditioning, when a fixed accuracy is considered.

    Original languageEnglish
    Article number012148
    Pages (from-to)-
    Number of pages8
    JournalIOP Conference Series: Materials Science and Engineering
    Issue number1
    Publication statusPublished - 5 Jul 2010
    Event9th World Congress on Computational Mechanics/4th Asian Pacific Congress on Computational Mechanics - Sydney, Australia
    Duration: 19 Jul 201023 Jul 2010

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