波传播数值模拟中Hermite方法的GPU加速
GPU Acceleration of Hermite Methods for the Simulation of Wave Propagation
摘要：
Goodrich，Hagstrom和Lorenz（2006）的Hermite方法使用Hermite插值来构造双曲型初值问题的高阶数值方法。该方法的结构有几个有利的特点，并行计算。在这项工作中，我们提出了算法，利用众核架构的图形处理单元。该算法利用紧凑的模板的Hermite方法，并使用数据结构，允许有效的数据加载和存储。此外，高度本地化的埃尔米特方法的进化算子，使我们能够结合多阶段的时间步长方法在新的算法，从而导致最小的访问全局内存。以标量线性波动方程为例，将Hermite插值和演化作为独立的核函数，并将它们交替组合成一个整体核函数。对于这两种方法，我们展示了提高性能的策略。我们的数值实验表明，虽然两个内核的方法允许更好的性能在硬件上，单片内核可以提供一个可比的时间解决方案，更少的全局内存使用。
英文摘要：
The Hermite methods of Goodrich, Hagstrom, and Lorenz (2006) use Hermite interpolation to construct high order numerical methods for hyperbolic initial value problems. The structure of the method has several favorable features for parallel computing. In this work, we propose algorithms that take advantage of the many-core architecture of Graphics Processing Units. The algorithm exploits the compact stencil of Hermite methods and uses data structures that allow for efficient data load and stores. Additionally the highly localized evolution operator of Hermite methods allows us to combine multi-stage time-stepping methods within the new algorithms incurring minimal accesses of global memory. Using a scalar linear wave equation, we study the algorithm by considering Hermite interpolation and evolution as individual kernels and alternatively combined them into a monolithic kernel. For both approaches we demonstrate strategies to increase performance. Our numerical experiments show that although a two kernel approach allows for better performance on the hardware, a monolithic kernel can offer a comparable time to solution with less global memory usage.
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