论文标题
时间自适应多发性多学 - Neumann波形松弛方法，用于异质耦合热方程
A time adaptive multirate Dirichlet-Neumann waveform relaxation method for heterogeneous coupled heat equations
论文作者
论文摘要
我们考虑用于异质耦合热方程的分区时间集成。得出了第一阶和二阶的多阶段以及时间自适应的dirichlet-neumann波形松弛（DNWR）方法。在1D和隐式Euler时间集成中，我们通过分析确定完全离散方案的最佳松弛参数。 我们在2D中测试了二阶多培训方法上弛豫参数的鲁棒性。 DNWR被证明非常健壮，并且始终产生快速收敛速率，而密切相关的Neumann-Neumann波形Relaxtion（NNWR）方法较慢甚至分歧。 波形方法自然允许子问题中的不同时间段。在DNWR的性能比较中，由于自动找到合适的步骤尺寸比例，时间自适应方法主导了多段方法。总体而言，我们获得了一个快速，健壮，多胎和时间自适应分区求解器，用于不稳定的共轭传热。
We consider partitioned time integration for heterogeneous coupled heat equations. First and second order multirate, as well as time-adaptive Dirichlet-Neumann Waveform relaxation (DNWR) methods are derived. In 1D and for implicit Euler time integration, we analytically determine optimal relaxation parameters for the fully discrete scheme. We test the robustness of the relaxation parameters on the second order multirate method in 2D. DNWR is shown to be very robust and consistently yielding fast convergence rates, whereas the closely related Neumann-Neumann Waveform relaxtion (NNWR) method is slower or even diverges. The waveform approach naturally allows for different timesteps in the subproblems. In a performance comparison for DNWR, the time-adaptive method dominates the multirate method due to automatically finding suitable stepsize ratios. Overall, we obtain a fast, robust, multirate and time adaptive partitioned solver for unsteady conjugate heat transfer.
