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a b s t r a c tThis is the first in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source MATLAB/GNU Octave toolbox. The intention of this ongoing project is to provide a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix/vector operations and is carefully documented; in addition, a direct mapping between discretization terms and code routines is maintained throughout. The present work focuses on a two-dimensional time-dependent diffusion equation with space/time-varying coefficients. The spatial discretization is based on the local discontinuous Galerkin formulation. Approximations of orders zero through four based on orthogonal polynomials have been implemented; more spaces of arbitrary type and order can be easily accommodated by the code structure.

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This is the second in a series of papers on implementing a discontinuous Galerkin (DG) method as an open source MATLAB / GNU Octave toolbox. The intention of this ongoing project is to offer a rapid prototyping package for application development using DG methods. The implementation relies on fully vectorized matrix / vector operations and is comprehensively documented. Particular attention was paid to maintaining a direct mapping between discretization terms and code routines as well as to supporting the full code functionality in GNU Octave. The present work focuses on a two-dimensional time-dependent linear advection equation with space / time-varying coefficients, and provides a general order implementation of several slope limiting schemes for the DG method.

Abstract. A study of the scalability of the Finite-volumE Sea ice–Ocean circulation Model, Version 2.0 (FESOM2), the first mature global model of its kind formulated on unstructured meshes, is presented. This study includes an analysis of the main computational kernels with a special focus on bottlenecks in parallel scalability. Several model enhancements improving this scalability for large numbers of processes are described and tested. Model grids at different resolutions are used on four high-performance computing (HPC) systems with differing computational and communication hardware to demonstrate the model's scalability and throughput. Furthermore, strategies for improvements in parallel performance are presented and assessed. We show that, in terms of throughput, FESOM2 is on a par with state-of-the-art structured ocean models and, in a realistic eddy-resolving configuration (1/10∘ resolution), can achieve about 16 years per day on 14 000 cores. This suggests that unstructured-mesh models are becoming very competitive tools in high-resolution climate modeling. We show that the main bottlenecks of FESOM2 parallel scalability are the two-dimensional components of the model, namely the computations of the external (barotropic) mode and the sea-ice model. It is argued that these bottlenecks are shared with other general ocean circulation models.

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Abstract. A study of the scalability of the Finite-volumE Sea ice-Ocean circulation Model, Version 2.0 (FESOM2), the first mature global model of its kind formulated on unstructured meshes, is presented. This study includes an analysis of main computational kernels with a special focus on bottlenecks in parallel scalability. Several model enhancements, improving this scalability for large numbers of processes, are described and tested. Model grids at different resolutions are used on four HPC systems with differing computation and communication hardware to demonstrate model's scalability and throughput. Furthermore, strategies for improvements in parallel performance are presented and assessed. We show that in terms of throughput FESOM2.0 is on par with the state-of-the-art structured ocean models and in realistic eddy resolving configuration (1/10° resolution) can produce about 16 years per day on 14 000 cores. This suggests that unstructured-mesh models are becoming extremely competitive tools in high-resolution climate modelling. It is shown that main bottlenecks of FESOM parallel scalability are the two-dimensional components of the model, namely the computations of external (barotropic) mode and the sea-ice model. It is argued that these bottlenecks are shared with other general ocean circulation models.