1,429 research outputs found
Efficient multicore-aware parallelization strategies for iterative stencil computations
Stencil computations consume a major part of runtime in many scientific
simulation codes. As prototypes for this class of algorithms we consider the
iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient
parallel implementations for cache-based multicore architectures. Temporal
cache blocking is a known advanced optimization technique, which can reduce the
pressure on the memory bus significantly. We apply and refine this optimization
for a recently presented temporal blocking strategy designed to explicitly
utilize multicore characteristics. Especially for the case of Gauss-Seidel
smoothers we show that simultaneous multi-threading (SMT) can yield substantial
performance improvements for our optimized algorithm.Comment: 15 pages, 10 figure
CRAFT: A library for easier application-level Checkpoint/Restart and Automatic Fault Tolerance
In order to efficiently use the future generations of supercomputers, fault
tolerance and power consumption are two of the prime challenges anticipated by
the High Performance Computing (HPC) community. Checkpoint/Restart (CR) has
been and still is the most widely used technique to deal with hard failures.
Application-level CR is the most effective CR technique in terms of overhead
efficiency but it takes a lot of implementation effort. This work presents the
implementation of our C++ based library CRAFT (Checkpoint-Restart and Automatic
Fault Tolerance), which serves two purposes. First, it provides an extendable
library that significantly eases the implementation of application-level
checkpointing. The most basic and frequently used checkpoint data types are
already part of CRAFT and can be directly used out of the box. The library can
be easily extended to add more data types. As means of overhead reduction, the
library offers a build-in asynchronous checkpointing mechanism and also
supports the Scalable Checkpoint/Restart (SCR) library for node level
checkpointing. Second, CRAFT provides an easier interface for User-Level
Failure Mitigation (ULFM) based dynamic process recovery, which significantly
reduces the complexity and effort of failure detection and communication
recovery mechanism. By utilizing both functionalities together, applications
can write application-level checkpoints and recover dynamically from process
failures with very limited programming effort. This work presents the design
and use of our library in detail. The associated overheads are thoroughly
analyzed using several benchmarks
Poisson cohomology of 3D Lie algebras
We compute the Poisson cohomology associated with several three dimensional
Lie algebras. Together with existing results and the classification of three
dimensional Lie algebras, this provides the Poisson cohomology of all linear
Poisson structures in dimension 3.Comment: 37 pages, 8 figure
Dynamical low-rank approximation of the Vlasov-Poisson equation with piecewise linear spatial boundary
We consider dynamical low-rank approximation (DLRA) for the numerical
simulation of Vlasov--Poisson equations based on separation of space and
velocity variables, as proposed in several recent works. The standard approach
for the time integration in the DLRA model uses a splitting of the tangent
space projector for the low-rank manifold according to the separated variables.
It can also be modified to allow for rank-adaptivity. A less studied aspect is
the incorporation of boundary conditions in the DLRA model. We propose a
variational formulation of the projector splitting which allows to handle
inflow boundary conditions on spatial domains with piecewise linear boundary.
Numerical experiments demonstrate the principle feasibility of this approach
- …