2019/11/11 by Pouria Behnoudfar, Behnoudfar, Pouria, Quanling Deng +3
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1911.04125
openalex publication_date 2019/11/11 · openalex created_date 2022/09/14 · openalex updated_date 2026/07/28
We propose a variational splitting technique for the generalized-\α\nmethod to solve hyperbolic partial differential equations. We use\ntensor-product meshes to develop the splitting method, which has a\ncomputational cost that grows linearly with respect to the total number of\ndegrees of freedom for multi-dimensional problems. We consider standard C0\nfinite elements as well as smoother B-splines in isogeometric analysis for the\nspatial discretization. We also study the spectrum of the amplification matrix\nto establish the unconditional stability of the method. We then show that the\nstability behavior affects the overall behavior of the integrator on the entire\ninterval and not only at the limits 0 and \∞. We use various examples\nto demonstrate the performance of the method and the optimal approximation\naccuracy. For the numerical tests, we compute the L2 and H1 norms to show\nthe optimal convergence of the discrete method in space and second-order\naccuracy in time.\n