2017/01/01 by Marcus J. Grote, Grote, Marcus J., Michaela Mehlin +3 · 1 citation
Engineering · Mathematics · #Electromagnetic Simulation and Numerical Methods #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics
paper · pdf · doi:10.48550/arxiv.1703.07965
Local adaptivity and mesh refinement are key to the efficient simulation of\nwave phenomena in heterogeneous media or complex geometry. Locally refined\nmeshes, however, dictate a small time-step everywhere with a crippling effect\non any explicit time-marching method. In [18] a leap-frog (LF) based explicit\nlocal time-stepping (LTS) method was proposed, which overcomes the severe\nbottleneck due to a few small elements by taking small time-steps in the\nlocally refined region and larger steps elsewhere. Here a rigorous convergence\nproof is presented for the fully-discrete LTS-LF method when combined with a\nstandard conforming finite element method (FEM) in space. Numerical results\nfurther illustrate the usefulness of the LTS-LF Galerkin FEM in the presence of\ncorner singularities.\n