Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU

Gupta, Rohit; Gijzen, Martin B. van; Vuik, C.

doi:10.1007/978-3-642-38718-0_7

Cited by 4 publications

(4 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since the system matrix is very ill conditioned, the use of preconditioners is required to achieve convergence at acceptable computation times. In this work we implement the Preconditioned Conjugated Gradients (PCG) solver in GPU using two types of suitable preconditioners to parallelize: diagonal scaling (Jacobi's preconditioner) and a Truncated Neumann Series based preconditioner [23]. Designated respectively as D and T N, in each case the preconditioning matrix looks like:…”

Section: Flow Equationmentioning

confidence: 99%

GPU implementation of Explicit and Implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

et al. 2022

View full text Add to dashboard Cite

In this work we present an efficient implementation of Eulerian TVD methods. We apply parallelization strategies based entirely on GPU for the solution of the 2D transport equation in heterogeneous porous media. Additionally, a parallel strategy is proposed for the generation of exponentially correlated lognormally distributed permeability fields in GPU. The programs are developed using C++/CUDA. The implemented methods are used to solve advective dominant problems, in a context of Monte Carlo type simulations to numerically determine the longitudinal and transversal macrodispersion coefficients averaging over 100 simulations for permeability fields for a large range of variances. The following types of transport are considered for testing: pure advection, advection-diffusion and advection-dispersion. The performance in terms of the computation time of explicit and implicit methods are compared. We show that the implemented algorithms allow to efficiently solve problems in computational domains of up to 134.5 million cells in a single GPU.

show abstract

Section: Flow Equationmentioning

confidence: 99%

GPU implementation of Explicit and Implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

et al. 2022

View full text Add to dashboard Cite

show abstract

“…We have been investigating, [1], the idea of Two Level Preconditioned Conjugate Gradient method on GPUs starting with a simple problem and testing our preconditioning schemes and deflation on it. We have found that it is possible to efficiently map the deflation operation onto the GPU so that most of the fine-grain parallelism can be exploited on it.…”

Section: A Focus Of This Workmentioning

confidence: 99%

3D Bubbly Flow Simulation on the GPU - Iterative Solution of a Linear System Using Sub-domain and Level-Set Deflation

Gupta

Gijzen

Vuik

2013

2013 21st Euromicro International Conference on Parallel, Distributed, and Network-Based Processing

View full text Add to dashboard Cite

Abstract-Solving an ill-conditioned linear system with a two level preconditioned Conjugate Gradient method on the GPU presents many options. The viability of these options is studied for different bubbly flow problems. On the basis of experiments conducted, we propose strategies that make our approach computationally suitable. We use the Truncated Neumann series based preconditioning scheme in combination with Deflation for implementing the two-level preconditioned Conjugate Gradient method and test different configurations on a unit cube with varying number of bubbles. Our results exhibit up to an order of magnitude speedup on the GPU. Our preconditioning scheme combined with deflation proves competitive (in terms of computation time and convergence) when compared to deflation with Incomplete Cholesky preconditioning.

show abstract

“…We consider a variety of first‐level preconditioning techniques along with deflation for a two‐level preconditioned conjugate gradient (PCG) implementation.…”

Section: Introductionmentioning

confidence: 99%

“…However, in this approach, incomplete Cholesky preconditioning is a bottleneck in a GPU implementation of the DPCG method. An implementation of the DPCG method on the GPU with a preconditioner exhibiting fine‐grained parallelism was first reported in , and better variants of deflation vectors were studied in . Both these works implemented DPCG on the GPU.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the deflated preconditioned CG method to solve bubbly and porous media flow problems on GPU and CPU

Gupta

Lukarski

Gijzen

et al. 2015

Numerical Methods in Fluids

View full text Add to dashboard Cite

SUMMARYIn both bubbly and porous media flow, the jumps in coefficients may yield an ill-conditioned linear system. The solution of this system using an iterative technique like the conjugate gradient (CG) is delayed because of the presence of small eigenvalues in the spectrum of the coefficient matrix. To accelerate the convergence, we use two levels of preconditioning. For the first level, we choose between out-of-the-box incomplete LU decomposition, sparse approximate inverse, and truncated Neumann series-based preconditioner. For the second level, we use deflation. Through our experiments, we show that it is possible to achieve a computationally fast solver on a graphics processing unit. The preconditioners discussed in this work exhibit fine-grained parallelism. We show that the graphics processing unit version of the two-level preconditioned CG can be up to two times faster than a dual quad core CPU implementation.

show abstract

Efficient Two-Level Preconditioned Conjugate Gradient Method on the GPU

Cited by 4 publications

References 8 publications

GPU implementation of Explicit and Implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

GPU implementation of Explicit and Implicit Eulerian methods with TVD schemes for solving 2D solute transport in heterogeneous flows

3D Bubbly Flow Simulation on the GPU - Iterative Solution of a Linear System Using Sub-domain and Level-Set Deflation

Evaluation of the deflated preconditioned CG method to solve bubbly and porous media flow problems on GPU and CPU

Contact Info

Product

Resources

About