Lukasz Szustak

Adaptation of MPDATA heterogeneous stencil computation to Intel Xeon Phi coprocessor

The multidimensional positive definite advection transport algorithm (MPDATA) belongs to the group of nonoscillatory forward-in-time algorithms and performs a sequence of stencil computations. MPDATA is one of the major parts of the dynamic core of the EULAG geophysical model. In this work, we outline an approach to adaptation of the 3D MPDATA algorithm to the Intel MIC architecture. In order to utilize available computing resources, we propose the (3 + 1)D decomposition of MPDATA heterogeneous stencil computations. This approach is based on combination of the loop tiling and fusion techniques. It allows us to ease memory/communication bounds and better exploit the theoretical floating point efficiency of target computing platforms. An important method of improving the efficiency of the (3 + 1)D decomposition is partitioning of available cores/threads into work teams. It permits for reducing inter-cache communication overheads. This method also increases opportunities for the efficient distribution of MPDATA computation onto available resources of the Intel MIC architecture, as well as Intel CPUs. We discuss preliminary performance results obtained on two hybrid platforms, containing two CPUs and Intel Xeon Phi. The top-of-the-line Intel Xeon Phi 7120P gives the best performance results, and executes MPDATA almost 2 times faster than two Intel Xeon E5-2697v2 CPUs.

Adaptation of fluid model EULAG to graphics processing unit architecture

The goal of this study is to adapt the multiscale fluid solver EULerian or LAGrangian framewrok (EULAG) to future graphics processing units (GPU) platforms. The EULAG model has the proven record of successful applications, and excellent efficiency and scalability on conventional supercomputer architectures. Currently, the model is being implemented as the new dynamical core of the COSMO weather prediction framework. Within this study, two main modules of EULAG, namely the multidimensional positive definite advection transport algorithm (MPDATA) and the variational generalized conjugate residual, elliptic pressure solver Generalized Conjugate Residual (GCR) are analyzed and optimized. In this paper, a method is proposed, which ensures a comprehensive analysis of the resource consumption including registers, shared, and global memories. This method allows us to identify bottlenecks of the algorithm, including data transfers between host and global memory, global and shared memories, as well as GPU occupancy. We put the emphasis on providing a fixed memory access pattern, padding as well as organizing computation in the MPDATA algorithm. The testing and validation of the new GPU implementation have been carried out based on modeling decaying turbulence of a homogeneous incompressible fluid in a triply‐periodic cube. Simulations performed using the standard version of EULAG and its new GPU implementation give similar solutions. Preliminary results show a promising increase in terms of computational efficiency. Copyright

Using Intel Xeon Phi Coprocessor to Accelerate Computations in MPDATA Algorithm

The multidimensional positive definite advection transport algorithm (MPDATA) belongs to the group of nonoscillatory forward-in-time algorithms, and performs a sequence of stencil computations. MPDATA is one of the major parts of the dynamic core of the EULAG geophysical model.

Parallelization of 2D MPDATA EULAG algorithm on hybrid architectures with GPU accelerators

Abstract EULAG (Eulerian/semi-Lagrangian fluid solver) is an established computational model developed for simulating thermo-fluid flows across a wide range of scales and physical scenarios. The dynamic core of EULAG includes the multidimensional positive definite advection transport algorithm (MPDATA) and elliptic solver. In this work we investigate aspects of an optimal parallel version of the 2D MPDATA algorithm on modern hybrid architectures with GPU accelerators, where computations are distributed across both GPU and CPU components. Using the hybrid OpenMP–OpenCL model of parallel programming opens the way to harness the power of CPU–GPU platforms in a portable way. In order to better utilize features of such computing platforms, comprehensive adaptations of MPDATA computations to hybrid architectures are proposed. These adaptations are based on efficient strategies for memory and computing resource management, which allow us to ease memory and communication bounds, and better exploit the theoretical floating point efficiency of CPU–GPU platforms. The main contributions of the paper are: • method for the decomposition of the 2D MPDATA algorithm as a tool to adapt MPDATA computations to hybrid architectures with GPU accelerators by minimizing communication and synchronization between CPU and GPU components at the cost of additional computations; • method for the adaptation of 2D MPDATA computations to multicore CPU platforms, based on space and temporal blocking techniques; • method for the adaptation of the 2D MPDATA algorithm to GPU architectures, based on a hierarchical decomposition strategy across data and computation domains, with support provided by the developed GPU task scheduler allowing for the flexible management of available resources; • approach to the parametric optimization of 2D MPDATA computations on GPUs using the autotuning technique, which allows us to provide a portable implementation methodology across a variety of GPUs. Hybrid platforms tested in this study contain different numbers of CPUs and GPUs – from solutions consisting of a single CPU and a single GPU to the most elaborate configuration containing two CPUs and two GPUs. Processors of different vendors are employed in these systems – both Intel and AMD CPUs, as well as GPUs from NVIDIA and AMD. For all the grid sizes and for all the tested platforms, the hybrid version with computations spread across CPU and GPU components allows us to achieve the highest performance. In particular, for the largest MPDATA grids used in our experiments, the speedups of the hybrid versions over GPU and CPU versions vary from 1.30 to 1.69, and from 1.95 to 2.25, respectively.

Model-Based Optimization of EULAG Kernel on Intel Xeon Phi Through Load Imbalancing

Load balancing is a widely accepted technique for performance optimization of scientific applications on parallel architectures. Indeed, balanced applications do not waste processor cycles on waiting at points of synchronization and data exchange, maximizing this way the utilization of processors. In this paper, we challenge the universality of the load-balancing approach to optimization of the performance of parallel applications. First, we formulate conditions that should be satisfied by the performance profile of an application in order for the application to achieve its best performance via load balancing. Then we use a real-life scientific application, EULAG MPDATA kernel, to demonstrate that its performance profile on a modern parallel architecture, Intel Xeon Phi, significantly deviates from these conditions. Based on this observation, we propose a method of performance optimization of scientific applications through load imbalancing. In the case of data parallel application, the method uses functional performance models of the application to find partitioning that minimizes its computation time but not necessarily balances the load of processors. We apply this method to optimization of MPDATA on Intel Xeon Phi. Experimental results demonstrate that the performance of this carefully optimized load-balanced application can be further improved by 15percent using the proposed load-imbalancing technique.

Parallelization of EULAG model on multicore architectures with GPU accelerators

EULAG (Eulerian/semi-Lagrangian fluid solver) is an established computational model developed by the group headed by Piotr K. Smolarkiewicz for simulating thermo-fluid flows across a wide range of scales and physical scenarios. In this paper we focus on development of the most time-consuming calculations of the EULAG model, which is multidimensional positive definite advection transport algorithm (MPDATA). Our work consists of two parts. The first part is based on the GPU parallelization using ATI Radeon HD 5870 GPU, NVIDIA Tesla C1060 GPU, and Fermi based NVIDIA Tesla M2070-Q, while the second one assumes the multicore CPU parallelization using AMD Phenom II X6 CPU, and Intel Xeon E3-1200 CPU with Sandy Bridge architecture. In our work, we use such standards for multicore and GPGPU programming as OpenCL and OpenMP. The GPU parallelization is based on decomposition of the algorithm into several smaller tasks called kernels. They are executed in a FIFO order corresponding to the dependency tree expressing data dependencies between kernels. To optimize performance of the resulting implementation, we utilize the extensive vectorization of each kernel, as well as overlapping of data transfer with computations. At the same time, when considering CPU parallelization we focus on multicore processing, vectorization and cache reusing. To achieve high efficiency of computations, the SIMD processing is applied using standard SSE and new AVX extensions. In this paper we provide performance analysis based on the Roofline Model, which shows inherent hardware limitations for MPDATA, as well as potential benefit and priority of optimizations. In order to alleviate memory bottleneck and improve efficient cache reusing, we propose to use the loop tiling technique.

Towards Efficient Decomposition and Parallelization of MPDATA on Hybrid CPU-GPU Cluster

EULAG (Eulerian/semi-Lagrangian fluid solver) is an established computational model for simulating thermo-fluid flows across a wide range of scales and physical scenarios. The multidimensional positive definite advection transport algorithm (MPDATA) is among the most time-consuming components of EULAG.

Performance Analysis for Stencil-Based 3D MPDATA Algorithm on GPU Architecture

EULAG (Eulerian/semi-Lagrangian fluid solver) is an established computational model for simulating thermo-fluid flows across a wide range of scales and physical scenarios. The multidimensional positive defined advection transport algorithm (MPDATA) is among the most time-consuming components of EULAG.

Toward Parallel Modeling of Solidification Based on the Generalized Finite Difference Method Using Intel Xeon Phi

Modern heterogeneous computing platforms have become powerful HPC solutions, which could be applied for a wide range of applications. In particular, the hybrid platforms equipped with Intel Xeon Phi coprocessors offers performance advantages over conventional homogeneous solutions based on CPUs, while supporting practically the same parallel programming model. However, there is still an open issue how scientific applications can utilize efficiently the hybrid platforms equipped with Intel coprocessors.

Porting and optimization of solidification application for CPU–MIC hybrid platforms:

Modern heterogeneous computing platforms have become powerful HPC solutions, which could be applied to a wide range of real-life applications. In particular, the hybrid platforms equipped with Intel Xeon Phi coprocessors offer the advantages of massively parallel computing, while supporting practically the same parallel programming model as conventional homogeneous solutions. However, there is still an open issue as to how scientific applications can efficiently utilize hybrid platforms with Intel MIC coprocessors. In this article, we propose an approach for porting a real-life scientific application to such hybrid platforms, assuming no significant modifications of the application code. It allows us to take advantage of all the computing components, including two CPUs and two coprocessors, for the parallel execution of computational workloads. In this study, we focus on the parallel implementation of a numerical model of the dendritic solidification process in isothermal conditions. We develop a sequence of steps that are necessary for the porting and optimization of the solidification application to hybrid platforms with Intel coprocessors. The main challenges include not only overlapping data movements with computations, but also ensuring adequate utilization of cores/threads and vector units of processors, as well as coprocessors. To reach this aim, we propose an efficient and flexible method for the workload distribution between heterogeneous computing components. For implementing the potential benefits of the proposed approach, we choose a heterogeneous programming model based on a combination of the offload mode for Intel MIC and OpenMP programming standard. The developed approach allows us to execute the whole application up to 9.33× faster than the original parallel version that uses two CPUs. Furthermore, the CPU–MIC hybrid platforms enable achieving the speedup of about 1.9× that of the CPU platform with 24 cores based on the Ivy Bridge architecture, and about 1.5× that of the Haswell-based CPU platform with 36 cores.