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<identifier>oai:HAL:hal-00763930v1</identifier>
<datestamp>2017-12-21</datestamp>
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<setSpec>subject:math</setSpec>
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<publisher>HAL CCSD</publisher>
<title lang=en>Equation-based interpolation and incremental unknowns for solving the three-dimensional Helmholtz equation</title>
<creator>Poullet, Pascal</creator>
<creator>Boag, Amir</creator>
<contributor>Laboratoire de Mathématiques Informatique et Applications (LAMIA) ; Université des Antilles et de la Guyane (UAG)</contributor>
<contributor>School of Electrical Engineering (TAU) ; Tel Aviv University [Tel Aviv]</contributor>
<identifier>hal-00763930</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00763930</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00763930/document</identifier>
<identifier>https://hal.univ-antilles.fr/hal-00763930/file/eci3D_3d.pdf</identifier>
<source>https://hal.univ-antilles.fr/hal-00763930</source>
<source>2012</source>
<language>en</language>
<subject lang=en>Helmholtz equation</subject>
<subject lang=en>Iterative methods</subject>
<subject lang=en>Preconditioning</subject>
<subject lang=en>Multilevel methods</subject>
<subject lang=en>Incremental Unknowns</subject>
<subject>[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]</subject>
<type>info:eu-repo/semantics/preprint</type>
<type>Preprints, Working Papers, ...</type>
<description lang=en>In an earlier paper, we developed an efficient incremental unknowns (IU) preconditioner for solving the two-dimensional (2D) Helmholtz problem in both high and low frequency (wavenumber) regimes. The multilevel preconditioning scheme involves separation of each grid into a coarser grid of the following level and a complementary grid on which the IUs are defined by interpolation. This approach is efficient as long as the mesh size of the coarsest grid is sufficiently small compared to the wavelength. In order to overcome this restriction, the authors introduced recently a modified IU method combining the conventional interpolation with the Helmholtz equation based interpolation (EBI). The EBI coefficients are derived numerically using a sufficiently large set of analytic solutions of the Helmholtz equation on a special hierarchy of stencils. The modified IUs using Helmholtz EBI are shown to provide improved preconditioning on the coarse scales where the conventional interpolation can not be employed. This study deals with the extension of this idea for solving the three-dimensional (3D) Helmholtz equation.</description>
<date>2012-12-11</date>
<rights>info:eu-repo/semantics/OpenAccess</rights>
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