This paper presents an end-to-end massively parallelized procedure for the solution of boundary value problems on Graphics Processing Units (GPU). The proposal is an integrated strategy that not only entails the calculation of nodal contributions, and the stiffness matrix assembly using the Meshless Local Petrov Galerkin Method (MLPG) but also the iterative solution of the system of algebraic equations in combination with methods from the Conjugate Gradient (CG) family. This end-to-end solution is fully developed using the Compute Unified Device Architecture (CUDA) platform without the need for extra data movement between the device and host after the matrix assembly. This is possible thanks to the parallel nature of the MLPG; each node designates a thread on the device. The introduced solution is wholly executed in the GPU, with minimal auxiliary structures or global synchronization points. The proposed approach was applied to the solution of a simple electromagnetic problem, and a sevenfold speedup was observed.
In this paper, a strategy to parallelize the meshless local Petrov-Galerkin (MLPG) method is developed. It is executed in a high parallel architecture, the well known graphics processing unit. The MLPG algorithm has many variations depending on which combination of trial and test functions is used. Two types of interpolation schemes are explored in this paper to approximate the trial functions and a Heaviside step function is used as test function. The first scheme approximates the trial function through a moving least squares interpolation, and the second interpolates using the radial point interpolation method with polynomial reproduction (RPIMp). To compare these two approaches, a simple electromagnetic problem is solved, and the number of nodes in the domain is increased while the time to assemble the system of equations is obtained. Results shows that with the parallel version of the algorithm it is possible to achieve an execution time 20 times smaller than the CPU execution time, for the MLPG using RPIMp versions of the method.Index Terms-Computer unified architecture (CUDA), meshless local Petrov-Galerkin (MLPG), parallel processing.
Complex flows involving waves and free-surfaces occur in several problems in hydrodynamics, such as fuel or water sloshing in tanks, waves breaking in ships, offshore platforms motions, wave action on harbors and coastal areas. The computation of such highly nonlinear flows is challenging since waves and free-surfaces commonly present merging, fragmentation and cusps, leading to the use of interface capturing Arbitrary Lagrangian-Eulerian (ALE) approaches. In such methods the interface between the two fluids is captured by the use of a marking function that is transported in a flow field. In this work we simulate these problems with a 3D incompressible SUPG/PSPG parallel edge-based finite element flow solver associated to the Volume-of-Fluid (VOF) method. The hyperbolic equation for the transport of the marking function is also solved by a fully implicit parallel edge-based SUPG finite element formulation. Global mass conservation is enforced adding or removing mass proportionally to the absolute value of the normal velocity at the interface. All those techniques were successfully implemented in a computational code, which has been suitably used to carry out several studies. The performance and accuracy of the proposed solution method is tested in the simulation waves and in the interaction between waves and a semisubmersible structure. Results count on the establishment of a relaxation zone close to the domain outflow, which partially absorbs incoming waves, avoiding their reflection.
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