Spike-Layer Simulation for Steady-State Coupled Schrödinger Equations (East Asian Journal on Applied Mathematics, 2018)
An adaptive finite element method is adopted to simulate the steady statecoupled Schrödinger equations with a small parameter. We use damped Newton iterationto solve the nonlinear algebraic system. When the solution domain is elliptic, ournumerical results with Dirichlet or Neumann boundary conditions are consistent withprevious theoretical results. For the dumbbell and circular ring domains with Dirichletboundary conditions, we obtain some new results that may be compared with futuretheoretical analysis.
Keywords: Schrödinger equations; damped Newton iteration; adaptive finite element method; spike-layer solution.