GPU accelerated high order reconstruction of signed distance function of the level set method is studied. The flow based reinitialization equation is discretized in space by using a nodal discontinuous Galerkin method on adaptive unstructured grids. Artificial diffusion with a modal decay rate based regularity estimator is used to damp out high frequency solution components near kinks, where mesh adaptivity is applied. A two rate Adams-Bashforth time integrator is developed to avoid time step restrictions resulting from artificial diffusion stabilization and local mesh refinement. Platform independence of the solver is achieved by using an extensible multi-threading programming API that allows runtime selection of different computing devices (GPU and CPU) and threading interfaces (CUDA, OpenCL and OpenMP). Overall, a highly scalable numerical scheme that preserves the simplicity of the original level set method is obtained. Performance and accuracy of the method to construct signed distance function on highly disturbed initial data with smooth and non-smooth interfaces are tested through distinct two- and three-dimensional problems.