GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields
For researchers in computational electromagnetics, this work offers a GPU-accelerated explicit time integration method that reduces computational cost compared to implicit schemes, but it is an incremental improvement combining existing techniques.
The paper proposes using explicit Runge-Kutta-Chebyshev time integration for electro-quasistatic field problems with nonlinear materials, avoiding Newton-Raphson iterations. The method achieves efficient parallel implementation on multiple GPUs by solving the resulting multiple right-hand side problem with an iterative solver and constant preconditioner.
Electro-quasistatic field problems involving nonlinear materials are commonly discretized in space using finite elements. In this paper, it is proposed to solve the resulting system of ordinary differential equations by an explicit Runge-Kutta-Chebyshev time-integration scheme. This mitigates the need for Newton-Raphson iterations, as they are necessary within fully implicit time integration schemes. However, the electro-quasistatic system of ordinary differential equations has a Laplace-type mass matrix such that parts of the explicit time-integration scheme remain implicit. An iterative solver with constant preconditioner is shown to efficiently solve the resulting multiple right-hand side problem. This approach allows an efficient parallel implementation on a system featuring multiple graphic processing units.