基于GPU的电-准静态场显式时间积分方法
GPU Accelerated Explicit Time Integration Methods for Electro-Quasistatic Fields
AI总结：
本文提出利用显式Runge-Kutta-Chebyshev时间积分方案求解非线性材料电-准静态场问题，避免了全隐式方案中所需的牛顿-拉夫森迭代，通过常数预条件迭代求解多右端问题，实现高效的多GPU并行计算。
摘要：
涉及非线性材料的电-准静态场问题通常使用有限元法在空间上离散。本文提出通过显式Runge-Kutta-Chebyshev时间积分方案求解由此产生的常微分方程组。这消除了在全隐式时间积分方案中所需的牛顿-拉夫森迭代。然而，电-准静态常微分方程组具有拉普拉斯型质量矩阵，使得显式时间积分方案的一部分仍保持隐式。一个具有常数预条件器的迭代求解器被证明可以高效求解由此产生的多右端问题。这种方法允许在具有多个图形处理单元的系统上实现高效的并行实现。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
