Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence

Parallel 3D ADI Scheme for Partially Dimension Reduced Heat Conduction Problem

“…First the factorization algorithm for 3D problems severely depends on data movement in the memory of computers (from and to in different levels of the memory). Only few arithmetical operations are done with each small size portion of data, therefore cost of data movement is very important issue (see, Guo and Lu, 2016;Otero et al, 2020). Second, nonlocality of some parts of the discrete scheme lead to modifications of the standard factorization algorithm and these changes should be resolved efficiently by the parallel algorithm (see Čiegis et al, 2014, where a parallel ADI algorithm is constructed to solve multidimensional parabolic problems with nonlocal boundary conditions).…”

“…Third, different approaches of parallelization can be used for different architectures of parallel computers. At least three main classes can be considered, including GPU processors (Imankulov et al, 2021;Xue and Feng, 2018;Otero et al, 2020), shared memory processors (multicore processors) and general global memory parallel machines, when implementation of parallel algorithms can be done, e.g. by using MPI library (Čiegis et al, 2014).…”

Loop Selection for Multilevel Nested Loops Using a Genetic Algorithm

“…However, the dependence analysis ability of the hardware was limited, and thus, the Mathematical Problems in Engineering success rate of these techniques in stimulating multithreaded parallel execution in multilevel nested loops was not high [1,4,[33][34][35][36][37]. In [31,[38][39][40][41], a multilevel nested loop threadlevel parallelization scheme that combines static analysis and dynamic scheduling was adopted. Most of these methods used traditional compilation techniques to assess the benefits of the loops to obtain information on parallelization and made corresponding dynamic adjustments on various program behaviors caused by different platforms and different input data in actual operations, which is also the main direction of the current studies.…”

“…However, reliance on only traditional compilation techniques cannot give accurate loop-level parallelization prompts for multilevel nested loops. erefore, the methods described in these references lack generality [31,[38][39][40][41]. As reported in [32,[42][43][44] the relevant features, such as the number of loop iterations of multilevel nested loops and the number of nested layers, were extracted from the intermediate representation of the compiler to construct the loop selection assessment model of multilevel nested loops.…”