We propose a new family of high-order explicit generalized-α methods for hyperbolic problems with the feature of dissipation control. Our k-stage approach delivers 2k,k∈N accuracy order in time by solving k matrix systems explicitly and updating 2k variables at each time-step. The user can control the numerical dissipation in the discrete spectrum's high-frequency regions by adjusting the method's coefficients. We study the method's spectral behaviour and show that the CFL condition is independent of the accuracy. The stability region remains invariant while increasing the number of stages, that is, the accuracy order. Next, we exploit efficient preconditioners for the isogeometric matrix to minimize the computational cost. These preconditioners use a diagonal-scaled Kronecker product of univariate parametric mass matrices; they have a robust performance with respect to the spline degree and the mesh size, and their decomposition structure implies that their application is faster than a matrix–vector product involving the fully-assembled mass matrix. Our high-order schemes require simple modifications of the available implementations of the generalized-α method. Finally, we present numerical examples demonstrating the methodology's performance regarding single- and multi-patch IGA discretizations.
Explicit high-order generalized-α methods for isogeometric analysis of structural dynamics
Loli G.;Reali A.;Sangalli G.;
2022-01-01
Abstract
We propose a new family of high-order explicit generalized-α methods for hyperbolic problems with the feature of dissipation control. Our k-stage approach delivers 2k,k∈N accuracy order in time by solving k matrix systems explicitly and updating 2k variables at each time-step. The user can control the numerical dissipation in the discrete spectrum's high-frequency regions by adjusting the method's coefficients. We study the method's spectral behaviour and show that the CFL condition is independent of the accuracy. The stability region remains invariant while increasing the number of stages, that is, the accuracy order. Next, we exploit efficient preconditioners for the isogeometric matrix to minimize the computational cost. These preconditioners use a diagonal-scaled Kronecker product of univariate parametric mass matrices; they have a robust performance with respect to the spline degree and the mesh size, and their decomposition structure implies that their application is faster than a matrix–vector product involving the fully-assembled mass matrix. Our high-order schemes require simple modifications of the available implementations of the generalized-α method. Finally, we present numerical examples demonstrating the methodology's performance regarding single- and multi-patch IGA discretizations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
