Geodesic
Numerical methods for black box software
Numerical methods and programming, Tome 20 (2019) no. 2, pp. 147-169

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A number of requirements are formulated to the numerical algorithms for black box software intended for mathematical modeling in continuum mechanics. An analysis of applied properties of the classical multigrid methods and robust multigrid technique in the framework of “robustness-efficiency-parallelism” problem is performed. It is shown that a close-to-optimal complexity with the least number of problem-dependent components and high parallel efficiency can be achieved with the robust multigrid technique on globally structured grids. Application of unstructured grids requires the accurate definition of two problem-dependent components (intergrid operators) that strongly affect on the complexity of an algorithm.
Keywords: parallel and high performance computing, boundary value problems, multigrid methods, black box software. 
@article{VMP_2019_20_2_a6,
     author = {S. I. Martynenko},
     title = {Numerical methods for black box software},
     journal = {Numerical methods and programming},
     pages = {147--169},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_2_a6/}
}
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S. I. Martynenko. Numerical methods for black box software. Numerical methods and programming, Tome 20 (2019) no. 2, pp. 147-169. http://geodesic.mathdoc.fr/item/VMP_2019_20_2_a6/