A Parallel Implementation of an Iterative Substructuring Algorithm for Problems in Three Dimensions

1993 ◽  
Vol 14 (2) ◽  
pp. 406-423 ◽  
Author(s):  
Barry F. Smith
Keyword(s):  
Parallel Implementation ◽  
Three Dimensions ◽  
Iterative Substructuring

scholarly journals Efficient Parallel Algorithms for 3D Laplacian Smoothing on the GPU

2019 ◽  
Vol 9 (24) ◽  
pp. 5437
Author(s):  
Lei Xiao ◽  
Guoxiang Yang ◽  
Kunyang Zhao ◽  
Gang Mei
Keyword(s):  
Large Scale ◽  
Graphics Processing Unit ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Smoothing Method ◽  
Three Dimensions ◽  
Processing Unit ◽  
Mesh Quality ◽  
Mesh Smoothing ◽  
Laplacian Smoothing

In numerical modeling, mesh quality is one of the decisive factors that strongly affects the accuracy of calculations and the convergence of iterations. To improve mesh quality, the Laplacian mesh smoothing method, which repositions nodes to the barycenter of adjacent nodes without changing the mesh topology, has been widely used. However, smoothing a large-scale three dimensional mesh is quite computationally expensive, and few studies have focused on accelerating the Laplacian mesh smoothing method by utilizing the graphics processing unit (GPU). This paper presents a GPU-accelerated parallel algorithm for Laplacian smoothing in three dimensions by considering the influence of different data layouts and iteration forms. To evaluate the efficiency of the GPU implementation, the parallel solution is compared with the original serial solution. Experimental results show that our parallel implementation is up to 46 times faster than the serial version.

An Iterative Substructuring Method for Raviart--Thomas Vector Fields in Three Dimensions

2000 ◽  
Vol 37 (5) ◽  
pp. 1657-1676 ◽  
Author(s):  
Barbara I. Wohlmuth ◽  
Andrea Toselli ◽  
Olof B. Widlund
Keyword(s):  
Vector Fields ◽  
Three Dimensions ◽  
Iterative Substructuring

Schwarz Analysis of Iterative Substructuring Algorithms for Elliptic Problems in Three Dimensions

1994 ◽  
Vol 31 (6) ◽  
pp. 1662-1694 ◽  
Author(s):  
Maksymilian Dryja ◽  
Barry F. Smith ◽  
Olof B. Widlund
Keyword(s):  
Elliptic Problems ◽  
Three Dimensions ◽  
Iterative Substructuring

Three-Dimensional Massively Parallel Computing of Suspensions

1998 ◽  
Vol 09 (05) ◽  
pp. 759-775 ◽  
Author(s):  
B. Wachmann ◽  
S. Schwarzer
Keyword(s):  
Parallel Implementation ◽  
Brownian Particle ◽  
Particle Surface ◽  
Three Dimensional ◽  
Building Blocks ◽  
Liquid Mixtures ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Particle Volume ◽  
Slip Boundary

Numerical simulations of suspensions often suffer from the fact that the simulated systems are rather small compared to experimental setups. We present a numerical scheme for non-Brownian particle-liquid mixtures in three dimensions at particle Reynolds numbers between 0.01 and 20 and describe its parallel implementation. The fluid equations are solved by a time-explicit pressure-implicit Navier–Stokes algorithm and the particle motion is tracked by molecular-dynamics methods. The two are coupled by imposing no-slip boundary conditions between the particles and the fluid. We integrate the stress distribution on the particle surface numerically to obtain forces and torques. The building blocks of the algorithm are local and scalable and we have reached particle numbers up to 106 (1.41*108 fluid nodes) on a 512 node CRAY-T3E. We compare our simulation results to theoretical predictions and experimental data and find good agreement for particle volume fractions up to 0.30.

Numerical Simulation of Sand Ripple Evolution in Oscillatory Boundary Layers

2014 ◽  
Author(s):  
Justin R. Finn ◽  
Sourabh V. Apte ◽  
Ming Li
Keyword(s):  
Boundary Layers ◽  
Stokes Equations ◽  
Parallel Implementation ◽  
Three Dimensional ◽  
Mixture Theory ◽  
Fluid Phase ◽  
Variable Density ◽  
Three Dimensions ◽  
Sand Ripple ◽  
Oscillatory Boundary Layers

We perform simulations of sand ripple evolution in an oscillatory boundary layer flow typical of the ripple regime. The simulation framework is a parallel implementation of a three dimensional, variable density, incompressible flow solver, which solves the ensemble averaged Navier-Stokes equations on a fixed, structured grid. The sediment phase is evolved by computing hydrodynamic and inter-particle forces acting on each Lagrangian particle. Particle-particle collisions are treated with a soft sphere model incorporating both normal and tangential collision forces. Realistic and consistent coupling of the sediment to the Eulerian fluid phase is achieved through a typical inter-phase drag force term as well as the effects of volume displacement by the sediment. The Euler-Lagrange computational approach is developed in three-dimensions and its accuracy is verified using two test cases with analytic or empirically known solutions. It is then applied to simulate ripple evolution in oscillatory boundary layers and results are compared with Nielsens ripple predictor model as well as mixture-theory based Eulerian computations.

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