GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields

TL;DR

This paper presents a GPU-accelerated explicit time integration method for electro-quasistatic field problems, reducing computational complexity and enabling efficient parallel processing with iterative solvers.

Contribution

It introduces a novel explicit Runge-Kutta-Chebyshev scheme for electro-quasistatic problems that avoids Newton-Raphson iterations and leverages GPU parallelism.

Findings

Efficient solution of nonlinear electro-quasistatic problems using explicit methods.

Reduced computational time compared to implicit schemes.

Successful parallel implementation on multi-GPU systems.

Abstract

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.