Exploring Critical Collapse in the Semilinear Wave Equation using Space-Time Finite Elements
1 Department of Mathematics and Statistics, South Dakota State University, Brookings, SD 57007, USA and2 Center for Research in Extreme Scale Technologies,Indiana University, Bloomington, IN 47405, USA(Dated: October 8, 2014)A fully implicit numerical approach based on the space-time nite element method is implementedfor the semilinear wave equation in 1(space) + 1(time) dimensions to explore critical collapse andsearch for self-similar solutions. Previous work studied this behavior by exploring the threshold ofsingularity formation using time marching nite di erence techniques while this work introducesan adaptive time parallel numerical method to the problem. The semilinear wave equation witha p = 7 term is examined in spherical symmetry. The impact of mesh re nement and the timeadditive Schwarz preconditioner in conjunction with Krylov Subspace Methods are examined.I. INTRODUCTION