000021513 001__ 21513
000021513 005__ 20170622131249.0
000021513 04107 $$aeng
000021513 046__ $$k2017-06-15
000021513 100__ $$aIdesman, Alexander
000021513 24500 $$aOPTIMAL REDUCTION OF NUMERICAL DISPERSION FOR WAVE PROPAGATION PROBLEMS. APPLICATION TO ISOGEOMETRIC ELEMENTS.

000021513 24630 $$n6.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000021513 260__ $$bNational Technical University of Athens, 2017
000021513 506__ $$arestricted
000021513 520__ $$2eng$$aBased 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 timeintegration technique developed recently. The approach developed can be directly applied to other space-discretization techniques with similar stencil equations.

000021513 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000021513 653__ $$aHigh-order Elements, Wave Propagation, Numerical Dispersion.

000021513 7112_ $$aCOMPDYN 2017 - 6th International Thematic Conference$$cRhodes Island (GR)$$d2017-06-15 / 2017-06-17$$gCOMPDYN2017
000021513 720__ $$aIdesman, Alexander
000021513 8560_ $$ffischerc@itam.cas.cz
000021513 8564_ $$s302026$$uhttps://invenio.itam.cas.cz/record/21513/files/16785.pdf$$yOriginal version of the author's contribution as presented on CD, section: [MS10] Advances in Numerical Methods for Linear and Non-Linear Dynamics and Wave Propagation
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000021513 962__ $$r21500
000021513 980__ $$aPAPER