2016/09/30 by Arturo Vargas, Jesse Chan, Vargas, Arturo +5 · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #FOS: Computer and information sciences #FOS: Mathematics #Mathematical Software (cs.MS) #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1609.09841
openalex publication_date 2016/09/30 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28
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.