Parallel Smoothers for Matrix-based Multigrid Methods on Unstructured Meshes Using Multicore CPUs and GPUs

Multigrid methods are efficient and fast solvers for problems typically modeled by partial differential equations of elliptic type. For problems with complex geometries and local singularities stencil-type discrete operators on equidistant Cartesian grids need to be replaced by more flexible concepts for unstructured meshes in order to properly resolve all problem-inherent specifics and for maintaining a moderate number of unknowns. However, flexibility in the meshes goes along with severe drawbacks with respect to parallel execution – especially with respect to the definition of adequate smoothers. This point becomes in particular pronounced in the framework of fine-grained parallelism on GPUs with hundreds of execution units. We use the approach of matrixbased multigrid that has high flexibility and adapts well to the exigences of modern computing platforms. In this work we investigate multi-colored Gauß-Seidel type smoothers, the power(q)-pattern enhanced multi-colored ILU(p) smoothers with fillins

HONEI: A collection of libraries for numerical computations targeting multiple processor architectures.

We present HONEI, an open-source collection of libraries offering a hardware oriented approach to numerical calculations. HONEI abstracts the hardware, and applications written on top of HONEI can be executed on a wide range of computer architectures such as CPUs, GPUs and the Cell processor. We demonstrate the flexibility and performance of our approach with two test applications, a Finite Element multigrid solver for the Poisson problem and a robust and fast simulation of shallow water waves. By linking against HONEI's libraries, we achieve a two-fold speedup over straight forward C++ code using HONEI's SSE backend, and additional 3--4 and 4--16 times faster execution on the Cell and a GPU. A second important aspect of our approach is that the full performance capabilities of the hardware under consideration can be exploited by adding optimised application-specific operations to the HONEI libraries. HONEI provides all necessary infrastructure for development and evaluation of such kernels, significantly simplifying their development

Maximizing Communication Overlap with Dynamic Program Analysis

International audienceWe present a dynamic program analysis approach to optimize communication overlap in scientific applications. Our tool instruments the code to generate a trace of the application's memory and synchronization behavior. An offline analysis determines the program optimal points for maximal overlap when considering several programming constructs: nonblocking one-sided communication operations, non-blocking collectives and bespoke synchronization patterns and operations. Feedback about possible transformations is presented to the user and the tool can perform the directed transformations, which are supported by a lightweight runtime. The value of our approach comes from: 1) the ability to optimize across boundaries of software modules or libraries, while specializing for the intrinsics of the underlying communication runtime; and 2) providing upper bounds on the expected performance improvements after communication optimizations. We have reduced the time spent in communication by as much as 64% for several applications that were already aggressively optimized for overlap; this indicates that manual optimizations leave untapped performance. Although demonstrated mainly for the UPC programming language, the methodology can be easily adapted to any other communication and synchronization API