English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We propose a variational splitting technique for the generalized-$\alpha$method to solve hyperbolic partial differential equations. We usetensor-product meshes to develop the splitting method, which has acomputational cost that grows linearly with respect to the total number ofdegrees of freedom for multi-dimensional problems. We consider standard $C^0$finite elements as well as smoother B-splines in isogeometric analysis for thespatial discretization. We also study the spectrum of the amplification matrixto establish the unconditional stability of the method. We then show that thestability behavior affects the overall behavior of the integrator on the entireinterval and not only at the limits $0$ and $\infty$. We use various examplesto demonstrate the performance of the method and the optimal approximationaccuracy. For the numerical tests, we compute the $L_2$ and $H^1$ norms to showthe optimal convergence of the discrete method in space and second-orderaccuracy in time.

Split generalized-$\alpha$ method: A linear-cost solver for a modified generalized-method for multi-dimensional second-order hyperbolic systems