000013280 001__ 13280
000013280 005__ 20161114160334.0
000013280 04107 $$aeng
000013280 046__ $$k2009-06-22
000013280 100__ $$aKoyama, T.
000013280 24500 $$aA geometric multigrid preconditioner for solving time-harmonic elastodynamics on unbounded domains with perfectly matched layers

000013280 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013280 260__ $$bNational Technical University of Athens, 2009
000013280 506__ $$arestricted
000013280 520__ $$2eng$$aA scalable geometric multigrid preconditioner applicable to solving large-scale time-harmonic elastodynamic systems on unbounded domains modeled by Perfectly Matched Layers (PMLs) is presented. To solve for the forced motion of the elastodynamic system under time-harmonic excitation, one must solve a linear system of equations where the coefficient matrix is the stiffness matrix shifted by the mass matrix. Application of PMLs to model the radiation boundary condition renders these mass and stiffness matrices complex-valued symmetric and large-scale for accurate solutions. Large-scale matrices require the use of iterative methods to solve the linear systems for tractable solution time and computational memory. Complexvalued symmetric linear systems can be in general extremely difficult to solve iteratively, due to the lack of standard efficient techniques. To solve this linear system, a geometric multigrid preconditioner which can be combined with iterative methods such as GMRES is developed. The prolongation operator is constructed geometrically by constructing a nested hierarchy of meshes within superblocks and evaluating fine grid nodes with coarse grid shape functions. The smoothing operator is chosen as a Chebyshev smoother or Gauss-Seidel smoother. For a desired accuracy, to obtain satisfactory convergence rates we observe a mild restriction on the selectable PML component parameters. Heuristics for selecting PML parameters given a desired error in approximating the radiation boundary condition are presented to complement this solvability requirement our method poses on the range of selectable PML parameters. Under these restrictions, we see superior convergence of the method. A microelectromechanical disk resonator device is used to display the effectiveness of our method.

000013280 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013280 653__ $$aPerfectly Matched Layers, Multigrid, Preconditioner, Time-harmonic elastodynamics. Abstract. A scalable geometric multigrid preconditioner applicable to solving large-scale time-harmonic elastodynamic systems on unbounded domains modeled by Perfectly Matched Layers (PMLs) is presented. To solve for the forced motion of the elastodynamic system under time-harmonic excitation, one must solve a linear system of equations where the coefficient matrix is the stiffness matrix shifted by the mass matrix. Application of PMLs to model the radiation boundary condition renders these mass and stiffness matrices complex-valued symmetric and large-scale for accurate solutions. Large-scale matrices require the use of iterative methods to solve the linear systems for tractable solution time and computational memory. Complexvalued symmetric linear systems can be in general extremely difficult to solve iteratively, due to the lack of standard efficient techniques. To solve this linear system, a geometric multigrid preconditioner which can be combined with iterative methods such as GMRES is developed. The prolongation operator is constructed geometrically by constructing a nested hierarchy of meshes within superblocks and evaluating fine grid nodes with coarse grid shape functions. The smoothing operator is chosen as a Chebyshev smoother or Gauss-Seidel smoother. For a desired accuracy, to obtain satisfactory convergence rates we observe a mild restriction on the selectable PML component parameters. Heuristics for selecting PML parameters given a desired error in approximating the radiation boundary condition are presented to complement this solvability requirement our method poses on the range of selectable PML parameters. Under these restrictions, we see superior convergence of the method. A microelectromechanical disk resonator device is used to display the effectiveness of our method.

000013280 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013280 720__ $$aKoyama, T.$$iGovindjee, S.
000013280 8560_ $$ffischerc@itam.cas.cz
000013280 8564_ $$s220988$$uhttps://invenio.itam.cas.cz/record/13280/files/CD420.pdf$$yOriginal version of the author's contribution as presented on CD, section: Computational methods for waves - ii (MS).
000013280 962__ $$r13074
000013280 980__ $$aPAPER