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All major weather and climate applications are currently developed using languages such as Fortran or C++. This is typical in the domain of high performance computing (HPC), where efficient execution is an important concern. Unfortunately, this approach leads to implementations that intermix optimizations for specific hardware architectures with the high-level numerical methods that are typical for the domain. This leads to code that is verbose, difficult to extend and maintain, and difficult to port to different hardware architectures. Here, we propose a different strategy based on GT4Py (GridTools for Python). GT4Py is a Python framework to write weather and climate applications that includes a high-level embedded domain specific language (DSL) to write stencil computations. The toolchain integrated in GT4Py enables automatic code-generation,to obtain the performance of state-of-the-art C++ and CUDA implementations. The separation of concerns between the mathematical definitions and the actual implementations allows for performance portability of the computations on a wide range of computing architectures, while being embedded in Python allows easy access to the tools of the Python ecosystem to enhance the productivity of the scientists and facilitate integration in complex workflows. Here, the initial release of GT4Py is described, providing an overview of the current state of the framework and performance results showing how GT4Py can outperform pure Python implementations by orders of magnitude., Comment: 12 pages

Matrix factorizations are among the most important building blocks of scientific computing. State-of-the-art libraries, however, are not communication-optimal, underutilizing current parallel architectures. We present novel algorithms for Cholesky and LU factorizations that utilize an asymptotically communication-optimal 2.5D decomposition. We first establish a theoretical framework for deriving parallel I/O lower bounds for linear algebra kernels, and then utilize its insights to derive Cholesky and LU schedules, both communicating N^3/(P*sqrt(M)) elements per processor, where M is the local memory size. The empirical results match our theoretical analysis: our implementations communicate significantly less than Intel MKL, SLATE, and the asymptotically communication-optimal CANDMC and CAPITAL libraries. Our code outperforms these state-of-the-art libraries in almost all tested scenarios, with matrix sizes ranging from 2,048 to 262,144 on up to 512 CPU nodes of the Piz Daint supercomputer, decreasing the time-to-solution by up to three times. Our code is ScaLAPACK-compatible and available as an open-source library., Comment: 15 pages (including references), 11 figures. arXiv admin note: substantial text overlap with arXiv:2010.05975

Communication-avoiding algorithms for Linear Algebra have become increasingly popular, in particular for distributed memory architectures. In practice, these algorithms assume that the data is already distributed in a specific way, thus making data reshuffling a key to use them. For performance reasons, a straightforward all-to-all exchange must be avoided. Here, we show that process relabeling (i.e. permuting processes in the final layout) can be used to obtain communication optimality for data reshuffling, and that it can be efficiently found by solving a Linear Assignment Problem (Maximum Weight Bipartite Perfect Matching). Based on this, we have developed a Communication-Optimal Shuffle and Transpose Algorithm (COSTA): this highly-optimised algorithm implements $A=\alpha\cdot \operatorname{op}(B) + \beta \cdot A,\ \operatorname{op} \in \{\operatorname{transpose}, \operatorname{conjugate-transpose}, \operatorname{identity}\}$ on distributed systems, where $A, B$ are matrices with potentially different (distributed) layouts and $\alpha, \beta$ are scalars. COSTA can take advantage of the communication-optimal process relabeling even for heterogeneous network topologies, where latency and bandwidth differ among nodes. The implementation not only outperforms the best available ScaLAPACK redistribute and transpose routines multiple times, but is also able to deal with more general matrix layouts, in particular it is not limited to block-cyclic layouts. Finally, we use COSTA to integrate a communication-optimal matrix multiplication algorithm into the CP2K quantum chemistry simulation package. This way, we show that COSTA can be used to unlock the full potential of recent Linear Algebra algorithms in applications by facilitating interoperability between algorithms with a wide range of data layouts, in addition to bringing significant redistribution speedups., Comment: To be published in the proceedings of the 36th International Conference on High Performance Computing, ISC High Performance 2021. The implementation of the algorithm is available at: https://github.com/eth-cscs/COSTA

Non-linear phase field models are increasingly used for the simulation of fracture propagation models. The numerical simulation of fracture networks of realistic size requires the efficient parallel solution of large coupled non-linear systems. Although in principle efficient iterative multi-level methods for these types of problems are available, they are not widely used in practice due to the complexity of their parallel implementation. Here, we present Utopia, which is an open-source C++ library for parallel non-linear multilevel solution strategies. Utopia provides the advantages of high-level programming interfaces while at the same time a framework to access low-level data-structures without breaking code encapsulation. Complex numerical procedures can be expressed with few lines of code, and evaluated by different implementations, libraries, or computing hardware. In this paper, we investigate the parallel performance of our implementation of the recursive multilevel trust-region (RMTR) method based on the Utopia library. RMTR is a globally convergent multilevel solution strategy designed to solve non-convex constrained minimization problems. In particular, we solve pressure-induced phase-field fracture propagation in large and complex fracture networks. Solving such problems is deemed challenging even for a few fractures, however, here we are considering networks of realistic size with up to 1000 fractures., Comment: CCF Trans. HPC (2021)

Materials Cloud is a platform designed to enable open and seamless sharing of resources for computational science, driven by applications in materials modelling. It hosts 1) archival and dissemination services for raw and curated data, together with their provenance graph, 2) modelling services and virtual machines, 3) tools for data analytics, and pre-/post-processing, and 4) educational materials. Data is citable and archived persistently, providing a comprehensive embodiment of the FAIR principles that extends to computational workflows. Materials Cloud leverages the AiiDA framework to record the provenance of entire simulation pipelines (calculations performed, codes used, data generated) in the form of graphs that allow to retrace and reproduce any computed result. When an AiiDA database is shared on Materials Cloud, peers can browse the interconnected record of simulations, download individual files or the full database, and start their research from the results of the original authors. The infrastructure is agnostic to the specific simulation codes used and can support diverse applications in computational science that transcend its initial materials domain., Comment: 19 pages, 8 figures

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular and biological systems. It is especially aimed at massively-parallel and linear-scaling electronic structure methods and state-of-the-art ab-initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2k to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension., Comment: 51 pages, 5 figures

We propose COSMA: a parallel matrix-matrix multiplication algorithm that is near communication-optimal for all combinations of matrix dimensions, processor counts, and memory sizes. The key idea behind COSMA is to derive an optimal (up to a factor of 0.03\% for 10MB of fast memory) sequential schedule and then parallelize it, preserving I/O optimality. To achieve this, we use the red-blue pebble game to precisely model MMM dependencies and derive a constructive and tight sequential and parallel I/O lower bound proofs. Compared to 2D or 3D algorithms, which fix processor decomposition upfront and then map it to the matrix dimensions, it reduces communication volume by up to $\sqrt{3}$ times. COSMA outperforms the established ScaLAPACK, CARMA, and CTF algorithms in all scenarios up to 12.8x (2.2x on average), achieving up to 88\% of Piz Daint's peak performance. Our work does not require any hand tuning and is maintained as an open source implementation., Comment: 18 pages, 29 figures, short version submitted to the SC'19 conference

The capabilities of CP2K, a density-functional theory package and OMEN, a nano-device simulator, are combined to study transport phenomena from first-principles in unprecedentedly large nanostructures. Based on the Hamiltonian and overlap matrices generated by CP2K for a given system, OMEN solves the Schroedinger equation with open boundary conditions (OBCs) for all possible electron momenta and energies. To accelerate this core operation a robust algorithm called SplitSolve has been developed. It allows to simultaneously treat the OBCs on CPUs and the Schroedinger equation on GPUs, taking advantage of hybrid nodes. Our key achievements on the Cray-XK7 Titan are (i) a reduction in time-to-solution by more than one order of magnitude as compared to standard methods, enabling the simulation of structures with more than 50000 atoms, (ii) a parallel efficiency of 97% when scaling from 756 up to 18564 nodes, and (iii) a sustained performance of 15 DP-PFlop/s.

Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed. If matrices are sparse, with application-specific sparsity patterns, the optimal implementation remains an open question. Here, we explore the performance of communication reducing 2.5D algorithms and one-sided MPI communication in the context of linear scaling electronic structure theory. In particular, we extend the DBCSR sparse matrix library, which is the basic building block for linear scaling electronic structure theory and low scaling correlated methods in CP2K. The library is specifically designed to efficiently perform block-sparse matrix-matrix multiplication of matrices with a relatively large occupation. Here, we compare the performance of the original implementation based on Cannon's algorithm and MPI point-to-point communication, with an implementation based on MPI one-sided communications (RMA), in both a 2D and a 2.5D approach. The 2.5D approach trades memory and auxiliary operations for reduced communication, which can lead to a speedup if communication is dominant. The 2.5D algorithm is somewhat easier to implement with one-sided communications. A detailed description of the implementation is provided, also for non ideal processor topologies, since this is important for actual applications. Given the importance of the precise sparsity pattern, and even the actual matrix data, which decides the effective fill-in upon multiplication, the tests are performed within the CP2K package with application benchmarks. Results show a substantial boost in performance for the RMA based 2.5D algorithm, up to 1.80x, which is observed to increase with the number of involved processes in the parallelization., Comment: In Proceedings of PASC '17, Lugano, Switzerland, June 26-28, 2017, 10 pages, 4 figures

The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious approximations. Even though recent developments have significantly reduced the overhead for modelling the quantum nature of the nuclei, the cost is still prohibitive when combined with advanced electronic structure methods. Here we present how multiple time step integrators can be combined with ring-polymer contraction techniques (effectively, multiple time stepping in imaginary time) to reduce virtually to zero the overhead of modelling nuclear quantum effects, while describing inter-atomic forces at high levels of electronic structure theory. This is demonstrated for a combination of MP2 and semi-local DFT applied to the Zundel cation. The approach can be seamlessly combined with other methods to reduce the computational cost of path integral calculations, such as high-order factorizations of the Boltzmann operator, or generalized Langevin equation thermostats.