Hardware Adapted Numerics

14. January 2016

Computer hardware has changed dramatically over the last decade with the advent of parallel and massively parallel architectures. Hardware adapted numerics is at the core of this challenge, and considers the interplay between mathemathics and computer hardware.

Shallow Water Simulations and Hyperbolic Conservation Laws

Graphics processing units have shown to be highly suited for simulation on Cartesian grids. SINTEF ICT started working with the shallow water equations on GPUs in 2004, and showed speed-ups of 25x in these early experiments.

We have since 2010 revisited the shallow water equations, and gone from the early proof of concepts into fully verified and validated simulator code, capable of faster than real-time performance.

The shallow water equations are one set of equations in a class called hyperbolic conservation laws, and we have further worked on similar types of problems such as the Euler equations for ideal gasses and CO₂ sequestration.

Smoothed Particle Hydrodynamics

SINTEF ICT has worked with the smoothed particle hydrodynamics (SPH) method on GPUs since 2011, starting with the SCORE project. The massively parallel nature of the SPH method maps very well to the architecture of GPUs and multi-core CPUs.

The focus in our work has been on developing code that runs on both CPUs and GPUs without duplicating the numerics, and the method can be applied to problems within everything from fracturing of solids to waves breaking onto ship hulls.