Engineering topics
Roberts, Nathaniel David
Publications and source records attributed to Roberts, Nathaniel David.
DPG for Vlasov: Two Formulations and Selected Results.
Abstract not provided.
Neural-Network Based Collision Operators for the Boltzmann Equation.
Abstract not provided.
A DPG Space-Time Vlasov-Poisson Discretization with Adaptive Mesh Refinement.
Abstract not provided.
Hyperdimensional, Adaptive Finite Elements Using Camellia and Intrepid2.
Abstract not provided.
Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation
In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.