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Performance tests and analyses are critical to effective HPC softwaredevelopment and are central components in the design and implementation ofcomputational algorithms for achieving faster simulations on existing andfuture computing architectures for large-scale application problems. In thispaper, we explore performance and space-time trade-offs for importantcompute-intensive kernels of large-scale numerical solvers for PDEs that governa wide range of physical applications. We consider a sequence of PDE- motivatedbake-off problems designed to establish best practices for efficient high-ordersimulations across a variety of codes and platforms. We measure peakperformance (degrees of freedom per second) on a fixed number of nodes andidentify effective code optimization strategies for each architecture. Inaddition to peak performance, we identify the minimum time to solution at 80%parallel efficiency. The performance analysis is based on spectral and p-typefinite elements but is equally applicable to a broad spectrum of numerical PDEdiscretizations, including finite difference, finite volume, and h-type finiteelements.

Scalability of High-Performance PDE Solvers