Geodesic
Simulation of bubble dynamics in three-dimensional potential flows on heterogeneous computing systems using the fast multipole and boundary element methods
Numerical methods and programming, Tome 15 (2014) no. 2, pp. 239-257.

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The bubble dynamics in potential flows of incompressible liquid is studied. The proposed approach is based on the boundary element method for the Laplace equation, which is especially efficient for the 3D bubble dynamics. In order to increase the problem size and to accelerate computations, an efficient numerical algorithm is developed and implemented. Depending on the problem size, for the acceleration of computations we used the direct matrix-vector multiplication on graphics processors (GPU) or the fast multipole method (FMM) implemented on heterogeneous computing systems (multicore CPUs and graphics processors). For the simulation of bubble surfaces, a new method based on the filtration of spherical harmonics is proposed. The proposed approach allows one to directly calculate the 3D dynamics of a single bubble, two and three interacting bubbles as well as a bubble cluster with a high degree of surface discretization. The developed method can be used to solve a wide range of problems related to the potential flow of bubble liquids.
Keywords: bubble dynamics, potential flow, boundary element method, fast multipole method, parallel computing, graphics processors. 
@article{VMP_2014_15_2_a5,
     author = {Yu. A. Itkulova and O. A. Abramova and N. A. Gumerov and I. Sh. Akhatov},
     title = {Simulation of bubble dynamics in three-dimensional potential flows on heterogeneous computing systems using the fast multipole and boundary element methods},
     journal = {Numerical methods and programming},
     pages = {239--257},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a5/}
}
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Yu. A. Itkulova; O. A. Abramova; N. A. Gumerov; I. Sh. Akhatov. Simulation of bubble dynamics in three-dimensional potential flows on heterogeneous computing systems using the fast multipole and boundary element methods. Numerical methods and programming, Tome 15 (2014) no. 2, pp. 239-257. http://geodesic.mathdoc.fr/item/VMP_2014_15_2_a5/