The recent advent of novel multi- and many-core architectures forces application programmers to deal with hardware-specific implementation details and to be familiar with software optimisation techniques to benefit from new high-performance computing machines. Extra care must be taken for communication-intensive algorithms, which may be a bottleneck for forthcoming era of exascale computing. This paper aims to present a high-level stencil framework implemented for the EULerian or LAGrangian

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... l (EULAG) that efficiently utilises multi- and many-cores architectures. Only an efficient usage of both many-core processors (CPUs) and graphics processing units (GPUs) with the flexible data decomposition method can lead to the maximum performance that scales the communication-intensive Generalized Conjugate Residual (GCR) elliptic solver with preconditioner.