We propose an efficient semi-Lagrangian characteristic mapping method for solving the one+one-dimensional Vlasov-Poisson equations with high precision on a coarse grid. The flow map is evolved numerically and exponential resolution in linear time is obtained. Global third-order convergence in space and time is shown and conservation properties are assessed. For benchmarking, we consider linear and nonlinear Landau damping and the two-stream instability. We compare the results with a Fourier pseudo-spectral method. The extreme fine-scale resolution features are illustrated showing the method's capabilities to efficiently treat filamentation in fusion plasma simulations.

翻译：我们提出了一种高效的半拉格朗日特征映射方法，用于在粗网格上高精度求解一维+一维Vlasov-Poisson方程。该方法通过数值演化流映射，在线性时间内实现了指数级分辨率。我们证明了其在空间和时间上均具有全局三阶收敛性，并评估了守恒性质。基准测试中，我们考虑了线性和非线性朗道阻尼以及双流不稳定性，并将结果与傅里叶伪谱法进行了对比。通过展示该方法在处理聚变等离子体模拟中丝化现象的高效能力，其极端细尺度分辨特性得到了充分说明。