high performance computing on graphics processing units: hgpu.org

Efficient stencil operations are essential in explicit schemes for evolutionary PDEs. In particular, for conservation and balance laws, the solution will in many cases have non-constant values only in a portion of the grid. We present novel methods that through simple observation of the stencil and the distribution of conserved quantities, reduce both the memory footprint and the computational burden by only computing in cells in which the solution changes. To this end, we utilize sparse updating of grid cells, in which data values are not stored before they actually contribute in the simulation. This is motivated by the need to perform simulations over very large domains to model real-world dam breaks and various flooding scenarios. The methods are applied to a high-resolution shallow water simulator, but are also applicable to other stencil-based explicit solvers.