Optimal reduction of numerical dispersion for wave propagation problems. Application to isogeometric elements

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Abstract

Based on the optimal coefficients of the stencil equation, a numerical technique for the reduction of the numerical dispersion error has been suggested. New isogeometric elements with the reduced numerical dispersion error for wave propagation problems have been developed with the suggested approach. By the minimization of the order of the dispersion error of the stencil equation, the order of the dispersion error is improved from order 2p (the conventional isogeometric elements) to order 4p (the isogeometric elements with reduced dispersion) where p is the order of the polynomial approximations. Because all coefficients of the stencil equation are obtained from the minimization procedure, the obtained accuracy is maximum possible. The corresponding elemental mass and stiffness matrices of the isogeometric elements with reduced dispersion are calculated with help of the optimal coefficients of the stencil equation. The analysis of the dispersion error of the isogeometric elements with the lumped mass matrix has also shown that independent of the procedures for the calculation of the lumped mass matrix, the second order of the dispersion error cannot be improved with the conventional stiffness matrix. However, the dispersion error with the lumped mass matrix can be improved from the second order to order 2p by the modification of the stiffness matrix. The numerical examples confirm the computational efficiency of the isogeometric elements with reduced dispersion that significantly reduce the computation time at a given accuracy. The numerical results obtained by the new and conventional isogeometric elements may include spurious oscillations due to the dispersion error. These oscillations can be quantified and filtered by the two-stage time-integration technique developed recently. The approach developed can be directly applied to other space-discretization techniques with similar stencil equations.

Original languageEnglish
Title of host publicationCOMPDYN 2017 - Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering
EditorsM. Papadrakakis, Michalis Fragiadakis
PublisherNational Technical University of Athens
Pages946-954
Number of pages9
ISBN (Electronic)9786188284418
DOIs
StatePublished - 2017
Event6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2017 - Rhodes Island, Greece
Duration: Jun 15 2017Jun 17 2017

Publication series

NameCOMPDYN 2017 - Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering
Volume1

Conference

Conference6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2017
CountryGreece
CityRhodes Island
Period06/15/1706/17/17

Keywords

  • High-order Elements
  • Numerical Dispersion
  • Wave Propagation

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