The emergence of accelerators as standard computing resources on supercomputers and the subsequent architectural complexity increase revived the need for high-level parallel programming paradigms. Sequential task-based programming model has been shown to efficiently meet this challenge on a single multicore node possibly enhanced with accelerators, which motivated its support in the OpenMP 4.0 standard. In this paper, we show that this paradigm can also be employed to achieve high performance on modern supercomputers composed of multiple such nodes, with extremely limited changes in the user code. To prove this claim, we have extended the StarPU runtime system with an advanced inter-node data management layer that supports this model by posting communications automatically. We illustrate our discussion with the task-based tile Cholesky algorithm that we implemented on top of this new runtime system layer. We show that it enables very high productivity while achieving a performance competitive with both the pure Message Passing Interface (MPI)-based ScaLAPACK Cholesky reference implementation and the DPLASMA Cholesky code, which implements another (non-sequential) task-based programming paradigm.
This paper deals with some improvements of the Waveform Relaxation method for large power systems transient stability analysis. In this context, the classical Waveform Relaxation iterative method is usually not efficient due to its slow convergence. The convergence speed depends on a lot of parameters such as the model, the disturbance nature, the number of subdomains created by the decomposition, the initialization, the time domain length, etc. In order to make the method competitive with usual and mastered sequential methods, some important points are here investigated such as an initialization of nonlinear integrations with linear solutions and a preconditioning technique to deal with a large number of subsystems. These innovative methods can bring interesting speedups for large power systems as illustrated in the presented numerical experiments on a large and realistic European power system.
Dense matrix multiplication involving a symmetric input matrix (SYMM) is implemented in reference distributed-memory codes with the same data distribution as its general analogue (GEMM). We show that, when the symmetric matrix is dominant, such a 2D block-cyclic (2D BC) scheme leads to a lower arithmetic intensity (AI) of SYMM than that of GEMM by a factor of 2. We propose alternative data distributions preserving the memory benefit of SYMM of storing only half of the matrix while achieving up to the same AI as GEMM. We also show that, in the case we can afford the same memory footprint as GEMM, SYMM can achieve a higher AI. We propose a task-based design of SYMM independent of the data distribution. This design allows for scalable A-stationary SYMM with which all discussed data distributions, may they be very irregular, can be easily assessed. We have integrated the resulting code in a reduction dimension algorithm involving a randomized singular value decomposition dominated by SYMM. An experimental study shows a compelling impact on performance.
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