A Local Macroscopic Conservative (LoMaC) low rank tensor method for the Vlasov-Maxwell system

The main computational challenges of solving the Vlasov-Maxwell (VM) system include the high dimensionality of the phase space, nonlinearity, inherent conservation properties, among others.

In this paper, we develop a novel Local Macroscopic Conservative (LoMaC) low rank tensor method for the VM system, as a continuation of our previous work (arXiv:2207.00518).

The method takes advantage of the tensor friendly structure of the Vlasov equation and employs the low rank hierarchical Tucker decomposition to approximate the Vlasov solution in high dimensions.

Hence, the curse of dimensionality can be mitigated.

Furthermore, to realize the LoMaC property, the algorithm simultaneously evolves the conservation laws of mass, momentum and energy alongside the Vlasov equation using a high order conservative method with the kinetic flux vector splitting.

By a conservative orthogonal projection, the low rank solution is guaranteed to have the same macroscopic observables updated from the conservation laws.

A collection of numerical tests on the VM system are presented to demonstrate the efficiency and efficacy of the proposed algorithm.